tag:blogger.com,1999:blog-34680158821722461112024-02-29T02:13:14.137-06:00Kreie blog - Reflections of a HS Mathematics TeacherChallenging students and striving for continual improvementMark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.comBlogger90125tag:blogger.com,1999:blog-3468015882172246111.post-64866915484696485222024-02-10T15:29:00.365-06:002024-02-16T17:49:38.502-06:00NCTM Seattle Reflection<p><span style="font-family: inherit;">As</span> I sit here at the Seattle airport waiting to board my
flight back to MSP, I’m deep in thought about the past three days. I had the
privilege and honor of attending and speaking at the NCTM regional conference
here in Seattle.</p><p class="MsoNormal"><o:p></o:p></p>
<p class="MsoNormal">I am thinking about a buffet of items: the sense of relief
knowing that I no longer must prepare for my presentation, the validation and
motivation I feel sparked by the sessions I attended, and what my classroom is
going to look like tomorrow when I go back to school and prepare for class.<o:p></o:p></p>
<p class="MsoNormal">I also can’t help to think about the sense of déjà vu I’m
feeling right now. As I gathered my thoughts to compose this blog post, I
happened to read my <a href="https://markkreie.blogspot.com/2018/11/" target="_blank">post from November 2018</a> in which I reflected on the first time I spoke at an NCTM regional
conference.<span style="mso-spacerun: yes;"> </span>In that post, I was proud of
meeting a professional goal of presenting at an NCTM conference. The referenced
déjà vu occurred when I clicked over to <a href="https://sites.google.com/k12.sd.us/kreie/home" target="_blank">my website</a> and noticed that I had met
my goal of speaking again at an NCTM conference.<o:p></o:p></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjqu7vZ66Td5jD4sAPyf8XsCs5t9Zk8LxD9a-RbR6Y4n0uch33bgGcrqm8NKoZa-Z7cKoDbX28na3i1jYFaSR9frQVlw2VmnEYpn9BPs4Lqyx5AhGgLLm9at64_cm-BgL5cbNMd87ZlijYeMrPtxY4geRjglzIkjz3BPlsuwaFV5NJedMCAh3_W53vWjB0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="271" data-original-width="1065" height="162" src="https://blogger.googleusercontent.com/img/a/AVvXsEjqu7vZ66Td5jD4sAPyf8XsCs5t9Zk8LxD9a-RbR6Y4n0uch33bgGcrqm8NKoZa-Z7cKoDbX28na3i1jYFaSR9frQVlw2VmnEYpn9BPs4Lqyx5AhGgLLm9at64_cm-BgL5cbNMd87ZlijYeMrPtxY4geRjglzIkjz3BPlsuwaFV5NJedMCAh3_W53vWjB0=w640-h162" width="640" /></a></div><br /><span style="line-height: 107%;"><span style="font-family: inherit;">I
wish I could blog about all of the items swirling through my mind, but
unfortunately I don’t have time for that. The main purpose of this post is
reflect on one specific session I attended, titled “Leading from Within –
Improving the Instructional System While Remaining in the Classroom.”</span></span><p></p><p class="MsoNormal"><span style="line-height: 107%;"><span style="font-family: inherit;"></span></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg3TosP1GSsPl1snjlWlzZ1CcX4iHZhjZd200N0SxY4nLPaadRjnAu00BAQQ_yw5sA_vv5mJ45zpnAjB26z3ZXQUac0yJrPTCPuhYr8Tzmcw9oBXnR0cNMBxg7jyY4cLuk2TgjJR-XRGo4PubrNOnKXaSEIArXJJDP68L5Q6vIi68emxcgQi6Z2h5i8E_Y" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="450" data-original-width="554" height="261" src="https://blogger.googleusercontent.com/img/a/AVvXsEg3TosP1GSsPl1snjlWlzZ1CcX4iHZhjZd200N0SxY4nLPaadRjnAu00BAQQ_yw5sA_vv5mJ45zpnAjB26z3ZXQUac0yJrPTCPuhYr8Tzmcw9oBXnR0cNMBxg7jyY4cLuk2TgjJR-XRGo4PubrNOnKXaSEIArXJJDP68L5Q6vIi68emxcgQi6Z2h5i8E_Y=w320-h261" width="320" /></a></span></div><span style="font-family: inherit;"><br />The session began with Thomas and Brent asking us (session attendees) to think about which of our colleagues had the biggest impact on us professionally. They followed up with asking us to think about what roles those individuals were in when they impacted our lives. Their hope was for us to understand that we can positively impact those around us, as well as the greater system of education, without leaving the classroom.</span><p></p><p class="MsoNormal"><span style="line-height: 107%;"><span style="font-family: inherit;">Thomas spent a few minutes talking about a diagram that he found in the book called "Instructional Rounds in Education". The diagram summarizes "the instructional core" and focuses on the relationship between teachers, students, and the content. Thinking deeply about systems and changing the complex system of education took me back to the SDMath/Sci leadership trainings I attended. </span></span></p><p class="MsoNormal"><span style="line-height: 107%;"><span style="font-family: inherit;">Thomas and Brent then spoke at length about the "four act drama" for effective teacher leaders. It was sort of a checklist of things that really motivated me.</span></span></p><p class="MsoNormal"></p><ol style="text-align: left;"><li><span style="line-height: 107%;"><span style="font-family: inherit;">Fearlessly commit to best practice.</span></span></li><li>Operate with a leadership mindset.</li><li>Build collective teacher efficacy</li><li>Embrace courageous lifelong learning</li></ol><div>A bit more detail about each bullet:</div><div><br /></div><div><i><b>Fearlessly commit to best practice.</b></i></div><div>Thomas and Brent served up a beautiful reminder of what ambitious teaching requires: student-centered environment, problem based, collaborative, rigorous, 8 SMP, 5 Practices, high quality formative assessments, culturally responsive teaching, equitable instruction and grading practices, and social-emotional learning. They summarized this list by reminding us that these practices are "critical for some, but beneficial for all".</div><div><br /></div><div><b><i>Operate with a leadership mindset.</i></b></div><div>Thomas used a compass analogy very effectively. North: as teacher leaders, sometimes we push our administrators to help drive change. East/West: as teacher leaders, we need colleagues and other teacher leaders we can lean on for guidance. I think of the many professional colleagues nationwide I have via Desmos Fellowship, Twitter, NCTM committees, etc. South: as teacher leaders, we must be ready to help the new teachers and veteran teachers who are ready to be led.</div><div><br /></div><div>Thomas and Brent mentioned a few more things that hit home to me. First, we should always be monitoring our team's progress. Data should be driving our thinking. We should be using our MAP testing data and celebrating our successes while also analyzing our non-successes. Second, we must be strategic and know how to push the right buttons to drive change. Thomas mentioned that there are some colleagues in his department that don't care to hear any ideas for change from him. Therefore, he has to be strategic and enlist the help of others to pitch the ideas to those who don't care to change. Last, teacher leaders must remember that "We are always learning. We are always leading. Teaching causes learning."</div><div><br /></div><div><b><i>Build collective teacher efficacy.</i></b></div><div>We (as teacher leaders) believe that positive change to the system can happen. But does our team?</div><div><br /></div><div>Brent referenced Hattie's research and that teacher efficacy has and effect size of 1.57. </div><div>He also mentioned the idea that "wins lead to wins", in other words success breeds success. Our team should be trying to emulate the schools who are experiencing success right now.</div><div><br /></div><div>I can't help to think about the data showed to the school board at a recent school board meeting and how we are doing on the state exams relative to the other ESD schools. (Not well)</div><div>I am confident in saying that our teacher efficacy has not been good these past 3-5 years.</div><div><br /></div><div><b><i>Embrace courageous lifelong learning.</i></b></div><div>Thomas called on teacher leaders to stay up to date with the newest research, to attend <u>and speak</u> at conferences, and find peers who dare to do great work. He reminded us to continually spread the word because we never know who we will touch and we never know who is ready to learn.</div><div><br /></div><div>This was a motivating session because it reminded me that I have a plethora of leadership skill and knowledge and we (as teacher leaders) always need to be leading. I sometimes forget that because leading is hard work. </div><div><br /></div><div>One final thing that I was reminded about in this session was that in order to truly drive change in our own districts, everyone on the team needs to be working together... the school board, administrators, curriculum directors, TOSAs, teachers, TAs, etc. Our district has some work to do in order to achieve this goal. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6dOIOhEsy6_925P7x4w13uyn111PUVZK57kZOaqsvIp3l7A17vwsmUKMeUSYy-j5ZGdc6aiUmPWppIRZqbyW6kD7g9ia7CdUpPlHa35Ft7ExwCi8-IxZQyZ4UJFXLTFRLMIp0YITAJKEffym8QuBb9QWucmdb5FOcpNJSZeVgePXIPYkuTFQkAovsDEQ/s4032/Pic1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6dOIOhEsy6_925P7x4w13uyn111PUVZK57kZOaqsvIp3l7A17vwsmUKMeUSYy-j5ZGdc6aiUmPWppIRZqbyW6kD7g9ia7CdUpPlHa35Ft7ExwCi8-IxZQyZ4UJFXLTFRLMIp0YITAJKEffym8QuBb9QWucmdb5FOcpNJSZeVgePXIPYkuTFQkAovsDEQ/w640-h480/Pic1.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhheiUZ9OBZeWrfY6-6TKmOa0ammsKGu7EyZ43SjJiCpLl3rHdL7p1uY_zaURjjRy9DwJFbdJwd0Vyl8gt0PA_s4ckSEnkyhSGQEUaCjSgv8fj7eCoJ3aTOCEcRGYKiCaFauK9XavQfWvMoH7UFa7QBZMj3Wh1tSP8vv2IzU3T4hJtmp8EiQB9AupoeJ0w/s4032/Pic2.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhheiUZ9OBZeWrfY6-6TKmOa0ammsKGu7EyZ43SjJiCpLl3rHdL7p1uY_zaURjjRy9DwJFbdJwd0Vyl8gt0PA_s4ckSEnkyhSGQEUaCjSgv8fj7eCoJ3aTOCEcRGYKiCaFauK9XavQfWvMoH7UFa7QBZMj3Wh1tSP8vv2IzU3T4hJtmp8EiQB9AupoeJ0w/w640-h480/Pic2.jpg" width="640" /></a></div><div><br /></div><div><br /></div><div>Rapid fire reactions about other aspects of the conference:</div><div><ul style="text-align: left;"><li>Peter Liljedahl's "Building Thinking Classrooms" is quickly becoming a must-do in mathematics education. Not surprisingly, there are still many who are not yet aware of the research or who are not implementing the BTC strategies. I am happy with how we are implementing it in advanced algebra 2 this year. But I still need to become better at the fine details of implementation.</li><li>As I have seen with other past NCTM regional conferences, there were many time slots that had multiple sessions I wanted to attend and was forced to choose. If only I had Hermione's time turner, I could attend more than one concurrent session.</li><li>A number of sessions I attended had excellent presenters, whereas a few had presenters that were sub-par. Six years ago, <a href="https://robertkaplinsky.com/what-ive-learned-from-being-a-presenter/" target="_blank">Robert Kaplinsky blogged</a> about things he's learned from being a presenter. The post detailed some of the nitty-gritty details of creating a quality presentation. A lot of what he says holds up, but there almost needs to be an updated post about this due to improvements in technology.</li><li>This comes with no surprise, but there is also a high level of skill in creating and delivering a high quality presentation in conference settings like this. One of the best tips I can provide is to borrow presentation moves from other presenters who you view as high-quality. I was fortunate to listen to Graham Fletcher at the SD STEM ED conference just over a week ago, and he absolutely crushed both presentations I attended. I borrowed three or four presentation moves directly from him.</li><li>Speaking of my presentation, I was happy with how it went and that is mostly due to how happy I was with my preparation. My session was in a very large ballroom (capacity ~400). Honestly, I was fairly nervous heading into it, mainly because of the size of the room. I didn't know what to expect for attendance. The attendance turned out to be somewhere between 50 and 60 people, which wasn't so overwhelming. I received positive feedback from a few participants who stuck around after the presentation ask questions. </li></ul></div><div><br /></div><p></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_vrbptbXSyVqmKxL4N_YLLANs-oFtQJKYBJkO_FcM_0nluEU0OnMP2G9Ev8KqarWxpaSzNyVPTRqiI3yziA65KOVO0qNA9qQPObHtzXLgqK459pinofz6kHllPYrYw7yPEQklr9srntV-W19MHtLEjP9PEy0ZXhe8siFuUnIX3tVOxAmam_KwzNeW4xA/s3088/Pic3.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3088" data-original-width="2316" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_vrbptbXSyVqmKxL4N_YLLANs-oFtQJKYBJkO_FcM_0nluEU0OnMP2G9Ev8KqarWxpaSzNyVPTRqiI3yziA65KOVO0qNA9qQPObHtzXLgqK459pinofz6kHllPYrYw7yPEQklr9srntV-W19MHtLEjP9PEy0ZXhe8siFuUnIX3tVOxAmam_KwzNeW4xA/w480-h640/Pic3.jpg" width="480" /></a></div><div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglAPguOCRFAZ0WVwBDMMaA2Rr9ubx7fuWrcV3t_M3bP253-Zrq0aX2hm2cR6r4c2B8XCBqraXaCwsPuexWDyyXQMVUTX9tAMnw3jqAuXjYEf3U_MT6f8sE_XXIiJgSPSufKOasmiI_DV9-0S4x3lxTrH_Wm3iUnb6FVWw8spEf8Xju02zjYORFYLVR6S8/s3088/Pic4.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3088" data-original-width="2316" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglAPguOCRFAZ0WVwBDMMaA2Rr9ubx7fuWrcV3t_M3bP253-Zrq0aX2hm2cR6r4c2B8XCBqraXaCwsPuexWDyyXQMVUTX9tAMnw3jqAuXjYEf3U_MT6f8sE_XXIiJgSPSufKOasmiI_DV9-0S4x3lxTrH_Wm3iUnb6FVWw8spEf8Xju02zjYORFYLVR6S8/w480-h640/Pic4.jpg" width="480" /></a></div><br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-15487546783201103622023-02-23T16:42:00.003-06:002023-02-23T16:42:28.199-06:00Mathigon: A must-use resource<p>Okay math teachers... let's have a chat. <a href="https://mathigon.org/">Mathigon</a> is something you need to look into using <b>today</b>. </p><p>I have a confession... since COVID teaching, I've been much less energetic about looking into the "next cool math tech tool". But during this past winter break, I was able to spend a little time getting a bit more intimate with Mathigon, and I have fallen in love. (S/O to David Poras [@davidporas] for your help!)</p><p>Then, a few weeks ago at the SD STEM ED conference, I attended a presentation by Dr. Kevin Smith (@kevinsmithsd) and there was a lot of buzz from the attendees about the awesomeness of Mathigon.</p><p>I'd still call myself a Mathigon rookie, but I'd like to share a few things that I do like about Mathigon. I wrote about a few of the things for the <a href="http://www.sdctm.org/documents/newsletter/23jan.pdf">SDCTM winter newsletter</a>. </p><p>Recently in advanced algebra 2, we were working on extracting nth roots of variable expressions. While Mathigon didn't help with the variable parts of the expression, it was very useful when looking at the integer values.</p><p><br /></p><p>Example problem:</p><p><span style="font-family: "Times New Roman",serif; font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;">Rewrite each
expression by extracting all possible roots.</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhslWhU5ZOS5dbF7JZibly4bh-WwPCygsP7jP0OiPI7mamlZWz6Bnky5nTU3tpIHp5Ar2f2zBxzNNpzeFx9uTH65BZMD-KRozWUIp-TuB0o8PBeVrH9BbbRwTD9jgo1iIoTANU1WyVUr6IfDoZDHMsDZ6euZNt5KnIqdFvi2m8-mHDHi8xsN5IUlvN/s306/Ex.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="175" data-original-width="306" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhslWhU5ZOS5dbF7JZibly4bh-WwPCygsP7jP0OiPI7mamlZWz6Bnky5nTU3tpIHp5Ar2f2zBxzNNpzeFx9uTH65BZMD-KRozWUIp-TuB0o8PBeVrH9BbbRwTD9jgo1iIoTANU1WyVUr6IfDoZDHMsDZ6euZNt5KnIqdFvi2m8-mHDHi8xsN5IUlvN/s1600/Ex.png" width="306" /></a></p><p><br /></p><p>Mathigon provided a very useful visual with the prime factor circles.<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKPskehdrRBr9lrvW4FAlp2Ba6QNMxw97HFrF_Q_nxOtz2zHZ4zcIYiTiG1icig80SOzdy1D8CU9PEx7Est9BKcFZBUgdtKbOvjD1kkeAqh9P9s7nM3TULizpn-bSiV8RL6JrMkV59k6UcAnGsqCluJc7q-TQaMU_9rMY4iDOYKYdDuBI1suSYJP4P/s547/Ex1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="547" data-original-width="490" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKPskehdrRBr9lrvW4FAlp2Ba6QNMxw97HFrF_Q_nxOtz2zHZ4zcIYiTiG1icig80SOzdy1D8CU9PEx7Est9BKcFZBUgdtKbOvjD1kkeAqh9P9s7nM3TULizpn-bSiV8RL6JrMkV59k6UcAnGsqCluJc7q-TQaMU_9rMY4iDOYKYdDuBI1suSYJP4P/s320/Ex1.png" width="287" /></a></p><div><br /></div>If you've never worked with prime factor circles, I invite you to open a blank Polypad in Mathigon and play around for a few minutes. In less than 1 minute, I was able to show students how the prime factor circles work and had them thinking about why we could extract a factor of 16 (2^4). Something that has always been fairly abstract for students now has a very clear, neat visual model.<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKffrja9NwC5Cam23FZK47yODgQXwDnElEO6xMPEJonwIEIO5oC8ssFRhLlK3_PXnUT2SJdVXbVYDoL9PlAMIhV_WTzExjhqWgmOL2_ykGMh7cj9c_ThEMIXANdrLV9oME8XnI66n18JDgb6DDMmf6YxWXN9kNjmSLQOXimXjf_6RxYd36k_lB6T-0/s267/Ex2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="145" data-original-width="267" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKffrja9NwC5Cam23FZK47yODgQXwDnElEO6xMPEJonwIEIO5oC8ssFRhLlK3_PXnUT2SJdVXbVYDoL9PlAMIhV_WTzExjhqWgmOL2_ykGMh7cj9c_ThEMIXANdrLV9oME8XnI66n18JDgb6DDMmf6YxWXN9kNjmSLQOXimXjf_6RxYd36k_lB6T-0/s1600/Ex2.png" width="267" /></a><br /><br />I'm super excited to see where else I can use Mathigon. <div><br /></div><div>P.S. A recent update allows users to split algebra tiles. WHAT?!?!!</div><div><br /></div><div><br /></div><div>Go check out Mathigon today!<br /><div><br /><div><br /></div><div><br /><p><br /></p><p><br /><span style="font-family: "Times New Roman",serif; font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"><br /></span></p><p> </p></div></div></div>Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-25288172876061114812022-05-27T23:11:00.000-05:002022-05-27T23:11:20.494-05:002021 - 2022 End of Year Reflection<p><span style="-webkit-text-size-adjust: auto; font-family: Calibri, sans-serif; font-size: 11pt; white-space: pre-wrap;">Full disclaimer: I’m writing this blog post for very selfish reasons. I’ve already highlighted the <a href="https://markkreie.blogspot.com/2017/11/the-positive-effects-of-blogging.html">positive effects of blogging</a>. This post serves as somewhat of a scrapbook for me. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">As my 20</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">th</span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"> season of teaching wraps up, I finally found a moment to breathe and reflect. I’m a big believer in the mentality of “what you put into life is what you get out of it”. It’s been an extremely grueling, yet rewarding, year. I am thankful that we were face-to-face for the entire year (during peak-COVID mid-year I believe we were close to shutting down). I am also grateful that the COVID numbers dropped to a level that allowed our masks to be “strongly recommended”. It continues to amaze me how different students look when have their masks on/off. There were a number of times this year I saw a student who was in my class last year (face-to-face with masks) and they look completely different than what I expected them to look like with their mask down. I speculate they feel the same way about me!</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">This season was the first season since my rookie year that I didn’t teach a geometry class. Two recent retirements in our department created openings that needed to be filled. I taught three sections of advanced algebra 2, one section of algebra 1, and one section of AP Statistics. By our department absorbing those positions, our class sizes ballooned to volumes higher than ever before. At the start of the year, my algebra 1 section had 31 students, my AP Stats section had 24, and my advanced algebra 2 had 31, 33, and 33. I only had 30 desks in my room, so I had to borrow 3 desks from a colleague down the hall just so everyone could have a seat. Increasing class sizes from 24 to 30+ may not sound like much, but I can’t overstate how much more of a challenge it is to be an effective teacher. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">Even though I’ve taught advanced algebra 2 and algebra 1 in the past, our district adopted a new textbook series last summer. Traditionally, I’m not one who follows the textbook step by step; rather, I use the textbook as a resource to help develop the lessons, activities, and tasks that students experience. The series we adopted at the high school is the latest Carnegie Learning series. I’m in love with about 80% of the series, which is a huge upgrade over our previous textbook. The lessons are designed to develop conceptual understanding by being inquiry-based and student-centered. Did we still need to tweak and supplement some of the lessons? You bet. Did we still write our own assessments? Yes, we did. Do I still need to improve my delivery to put more learning in the hands of students? Absolutely. The neatest thing about the series is that I learned </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">a lot</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"> about the mathematics in those courses and some really mind-blowing connections between main topics. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">Using a new textbook series takes a lot of preparation time if done correctly. Analyzing the content of each lesson, planning the pacing, identifying where modifications should be made, creating / finding supplemental resources, building the Canvas modules, etc. all take time. Some of that work was done prior the school year starting, but many of those decisions include a reactive component that require me to know my students and their strengths, weaknesses, interests, and abilities. In other words, those decisions shouldn’t be made during the summer prior to even seeing my rosters. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">This was the first time I have ever taught AP Statistics. I felt like a first year teacher again. To help prepare, I attended (virtually) a week long course last July. It was very helpful and connected me with the right people to help me on my journey. Was it a challenge to teach something for the first time again? Absolutely. I’ve always believed that you don’t truly understand something until you can teach it to someone else. There were a number of nights that I was up late preparing (& learning) the lesson I was teaching the following day. Did I enjoy teaching the class? Immensely. I really enjoyed teaching seniors again (for the past 5-6 years, I have mostly worked with 9</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">th</span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"> & 10</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">th</span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"> graders). There were some 11</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">th</span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"> and 10</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">th</span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"> graders in the class as well. Overall, it was an excellent class of students who are far brighter than I ever was at their age.</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">I wouldn’t have survived without <a href="https://www.statsmedic.com/">Stats Medic</a> and the resources on their website. I love their philosophy of EFFL (Experience First, Formalize Later) and how open to sharing the AP Stats community is. I think it’s extremely helpful that all AP Stats teachers are teaching toward the same targets and that most of the major textbooks and resources are aligned on things like scope and sequence of the curriculum. Because a majority of AP Stats teachers are teaching the same units in the same general timeframe, there are relevant, rich conversations happening online. Each day I would skim the posts on the AP Stats Twitter and Facebook groups. I learned a lot and knew where I could go to ask questions if needed.</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">I enjoyed working with two student teachers this past fall. Mr. Venner and Mr. Pierzinski were awesome and will both be strong mathematics teachers. I love helping develop the next generation of mathematics teachers.</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">This year I also got back into coaching high school basketball. My oldest child was a freshmen and I was able to coach the freshmen boys basketball team this year. I hadn’t coached high school boys basketball since 2006 (I coached many years of girls since then). I loved being able to coach my son and be a bigger part of his high school experience. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">Being a high school coach takes a lot of time and commitment. Adding that to my plate meant that something else had to be removed. As a result, I scaled back in the realm of math leadership. I decided to pause my pursuit of National Board Certification for the school year. I was not able to attend the SDCTM conference in Huron this February. I attended only one (of four) regional math circles that I had intended to help facilitate. I have not written a blog post in nearly a year. The list of articles, journals, blog posts, etc. that I had planned to read continues to grow each day. I decided to “<a href="https://markkreie.blogspot.com/2019/01/the-inability-to-say-no.html">say no</a>” to a number of opportunities that I might have previously taken.</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">I did have the opportunity to present at the TIE conference this spring. It felt to great to share my knowledge of Desmos in a face-to-face conference again. I did complete the written test portion of National Board Certification last June and scored extremely well. I’m excited to resume pursuing that goal. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">As I write this post, I am actually on my way back from the NCTM HQ in Reston, VA. I have served on the NCTM Classroom Resources Committee for the past 2+ years. We have done all of our work virtually since I began serving prior to this weekend. It was great to finally meet in person and gain a clearer vision of the work ahead of us. [This was the first time I was on an airplane since COVID began.] These past few years of not having in-person professional development & networking opportunities has truly made me realize how much I rely on those events to put wind in my sails. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">To recap, this has been a grueling, yet rewarding year for me for a number of reasons. </span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">Looking ahead, I’m excited for a number of reasons. Next year, it looks as though I will be teaching the same classes as this year. I’m excited for year 2 of AP Stats and how much more confidence I will have in my content knowledge. As our district begins to transition to a Competency Based Educational model, we will be implementing a form of target-based grading once again. I’m excited to bring that back into my classroom with my advanced algebra 2 students next year.</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">If you’re still reading, thanks for sticking with me. I invite you to put pen to paper and reflect on your journey as well!</span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="-webkit-text-size-adjust: auto; line-height: 1.295; margin-bottom: 8pt; margin-top: 0pt;"><span style="font-family: Calibri, sans-serif; font-size: 11pt; font-variant-east-asian: normal; font-variant-ligatures: normal; font-variant-position: normal; vertical-align: baseline; white-space: pre-wrap;">P.S. You can still <a href="https://forms.gle/6inLomeeDe3Zz6pr5">vote on your favorite graph</a> from my advanced algebra 2 Desmos art project!</span></p><br style="-webkit-text-size-adjust: auto;" /><br style="-webkit-text-size-adjust: auto;" /><br style="-webkit-text-size-adjust: auto;" />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com1tag:blogger.com,1999:blog-3468015882172246111.post-67239776563101278582020-10-29T23:39:00.008-05:002020-10-31T12:02:51.419-05:00Water the Lawn Project<p> </p><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Each year, my colleague Jarrod and I tweak our geometry curriculum with the intent to improve and build on the previous year. Some years we make major changes, such as an overhauled <a href="https://markkreie.blogspot.com/2020/05/target-based-grading-v10-2019-2020.html" target="_blank">grading system</a>. Other years we <a href="https://markkreie.blogspot.com/2019/01/geometry-project-logo-design-flipgrid.html" target="_blank">integrate new technology</a>. (This year, another colleague [Adam] is teaching geometry as well.)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">One of the goals of our high school is to improve student engagement. We (the geometry teachers) are trying to implement more problem-based activities into our classrooms. We've had great success each spring semester with a <a href="https://markkreie.blogspot.com/2016/04/geometry-field-trip.html" target="_blank">Floor Plan project</a>. We wanted to create a project for the fall semester that met these checkpoints: low floor / high ceiling, open ended, (semi) real-world application, and connected a number of learning targets together. Additionally, we knew that we wanted to build something that we could expand on in future years, specifically to be able to connect community experts / partners with our students.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">In our HS geometry curriculum, we focus on writing the equation of a circle and finding areas of sectors. In years past, we would not cover those topics until the spring semester. However, last year we moved the target of writing the equation of a circle into the first semester. In our first unit, we revisit the Pythagorean Theorem, derive the distance formula, and then write the equation of circles on a coordinate plane. This year, we decided to also move the concepts of arc length and area of sector into the first unit. (We treat circumference and area of a circle as prerequisite skills that students have learned in middle school.)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We were intrigued by a Desmos activity called "Water the Lawn". In the activity, students are asked to place sprinklers at locations of their choice in order to cover a rectangular region that represents a lawn. (<a href="https://drive.google.com/file/d/1_UIwmojqILHvdZ8pJXjzoVtfnB5m1wO-/view?usp=sharing" target="_blank">Take a peek</a>.) The Desmos activity primarily focuses on finding the areas of circles. We needed to make the activity more challenging and aligned to our HS learning targets. Let's dive in...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Task:</b></div><div class="separator" style="clear: both; text-align: left;">Install a sprinkler system in the yard of the given diagram. (<a href="https://www.desmos.com/calculator/gp3i7v5hqi">Link to diagram</a>)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1nvKR42qJMnixs67CvhSyJ4_L2K4gyz5_BlSBNIxe97D2W2l9hIV5ogtPpiTuDrupmjgweyCvpqgSUZZN-Ro0AbB69lohToB1LaGKuvWxKHAhVc3Ttow2eJqCM3GS88ZMeSIbTsxD-5s/s567/Lawn.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="557" data-original-width="567" height="393" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1nvKR42qJMnixs67CvhSyJ4_L2K4gyz5_BlSBNIxe97D2W2l9hIV5ogtPpiTuDrupmjgweyCvpqgSUZZN-Ro0AbB69lohToB1LaGKuvWxKHAhVc3Ttow2eJqCM3GS88ZMeSIbTsxD-5s/w400-h393/Lawn.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><b>Rules:</b><br /><div class="separator" style="clear: both; text-align: left;">1.<span> You must water the entire yard.</span></div><div class="separator" style="clear: both; text-align: left;"><span>2.<span> You must stay within the boundary of the yard.</span></span></div><div class="separator" style="clear: both; text-align: left;"><span><span>3.<span> Overlapping areas are necessary. The amount of overlapping area must be less than 3000 sq ft.</span></span></span></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Requirements:</b></div><div class="separator" style="clear: both; text-align: left;">1.<span> Neatly sketch (using a compass, ruler, & protractor) your plan on the blueprint.</span></div><div class="separator" style="clear: both; text-align: left;">2.<span> For each sprinkler head, you must find the following information.</span></div><div class="separator" style="clear: both; text-align: left;"><span><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi43JZck_1uOLL_KHY3JmB7aM61mEuYkEawCgLdTPAGD9QaZYmR1ROaxbai3fPVyGpOmZjJ7zA7a8mJYXp6j2-OaFd8dXJHZfRolDwotT7Baj7nEmuYxTroHslZu7YglhT8XL7twuBo4I4/s397/info.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="388" data-original-width="397" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi43JZck_1uOLL_KHY3JmB7aM61mEuYkEawCgLdTPAGD9QaZYmR1ROaxbai3fPVyGpOmZjJ7zA7a8mJYXp6j2-OaFd8dXJHZfRolDwotT7Baj7nEmuYxTroHslZu7YglhT8XL7twuBo4I4/w320-h314/info.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">On the Lowe's website, we found three different types of sprinkler heads. (Note: the two bigger sprinkler heads had minimum degree restrictions. Also, none of the heads have a radius between 16 and 18 feet. This created a bit of a challenge for students.)</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGJVmYYKy6f2V3hOSOS90qDSSoQSNQOUNRBowF_xTxHRsr7UmCSHkzo4qDl3DlSbFFE7aRf3MY-BNGyMv_ut5SoW6gkdxrfkQtecCpNXT_hHieKIUv0aPTCaJ3skhkhrz3R9VcnLwrhmU/s1057/sprink.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="595" data-original-width="1057" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGJVmYYKy6f2V3hOSOS90qDSSoQSNQOUNRBowF_xTxHRsr7UmCSHkzo4qDl3DlSbFFE7aRf3MY-BNGyMv_ut5SoW6gkdxrfkQtecCpNXT_hHieKIUv0aPTCaJ3skhkhrz3R9VcnLwrhmU/w640-h360/sprink.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We showed students an example (albeit, a bad example because of too much overlapping area) to help get them started.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjHGpshxYuKo7vItcf983omXgFPmkNdrmB9JPeoiyPn2PcA836vuDtRNzBsNDz0lMxCje9RPC7ME_i4lNuLIuhVvMHrnCe_e3VxQIf2rQRv7RAvkyrc5XUxBz3Mk0Ni6h68IU6Z8u3Ps4/" style="margin-left: 1em; margin-right: 1em;"><img data-original-height="572" data-original-width="767" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjHGpshxYuKo7vItcf983omXgFPmkNdrmB9JPeoiyPn2PcA836vuDtRNzBsNDz0lMxCje9RPC7ME_i4lNuLIuhVvMHrnCe_e3VxQIf2rQRv7RAvkyrc5XUxBz3Mk0Ni6h68IU6Z8u3Ps4/w640-h478/image.png" width="640" /></a></div><br /><br /></div><div class="separator" style="clear: both; text-align: left;">And that is it! We gave students 1 full block day (90 minutes) to work on this project in class. It was then due one week later.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Results:</b></div><div class="separator" style="clear: both; text-align: left;">I was very pleased with the overall results of the project. Here are some examples of what students created.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUf9nGOOoTbDhe-BuLuadLjIXC6N9T_5-jZi4FhFmPPXgEPrtcy68Yq12qUpGIUTiHra8SPm47FPk4wAFaqdmIao-ojhhiEMMQBOtb4462qQLDynFakL_4eammY4CpRjhw-_Cz8zmdlu4/s2048/2020-10-27+09.14.41.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUf9nGOOoTbDhe-BuLuadLjIXC6N9T_5-jZi4FhFmPPXgEPrtcy68Yq12qUpGIUTiHra8SPm47FPk4wAFaqdmIao-ojhhiEMMQBOtb4462qQLDynFakL_4eammY4CpRjhw-_Cz8zmdlu4/w300-h400/2020-10-27+09.14.41.jpg" width="300" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYVBAVv0OyQKquREqxk-CaVKXUEbeNjNg3e4BXPf2jV8bX9fxV66mXh_j6xdkEqMhKxEAGIB118f-0hMxD8Dtpp9cm7rR_lbpJUiUn6VY05iV4zJFxwWu0H2jeykaSfZJ19Fq8PLxup_k/s2048/2020-10-27+09.14.51.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYVBAVv0OyQKquREqxk-CaVKXUEbeNjNg3e4BXPf2jV8bX9fxV66mXh_j6xdkEqMhKxEAGIB118f-0hMxD8Dtpp9cm7rR_lbpJUiUn6VY05iV4zJFxwWu0H2jeykaSfZJ19Fq8PLxup_k/w300-h400/2020-10-27+09.14.51.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxTqp0k2rm8qzGPO8BaJxCDZCk_Lc_iM2s_chuXWQGYgrSWhHHgsjait6PcViTdvzAmXpQQrUS_OjIvHOwYT37IB_4RIHOCmwIjSURnlFiueYLpDTbbk63sV1Aq9dFyRawXFPyNffSEwQ/s2048/2020-10-27+09.15.33.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxTqp0k2rm8qzGPO8BaJxCDZCk_Lc_iM2s_chuXWQGYgrSWhHHgsjait6PcViTdvzAmXpQQrUS_OjIvHOwYT37IB_4RIHOCmwIjSURnlFiueYLpDTbbk63sV1Aq9dFyRawXFPyNffSEwQ/w300-h400/2020-10-27+09.15.33.jpg" width="300" /><span> </span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqD048CFXkha8RHmr1THZ8L_PhnLV6utzXVocR7_Y9F-aTr8AWxQy3cGT7d2mIpLcuO1-1XpfQD1cEhXYjfTCiZu7DPyzRO2kGhHJfMfHFXxEy-Zv5Yp7d0m1QFI6tBfm7CqQM8RPTYDw/s2048/2020-10-27+09.15.54.jpg" style="margin-left: 1em; margin-right: 1em; text-align: left;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqD048CFXkha8RHmr1THZ8L_PhnLV6utzXVocR7_Y9F-aTr8AWxQy3cGT7d2mIpLcuO1-1XpfQD1cEhXYjfTCiZu7DPyzRO2kGhHJfMfHFXxEy-Zv5Yp7d0m1QFI6tBfm7CqQM8RPTYDw/w300-h400/2020-10-27+09.15.54.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjieHTwU0j7UKGjF1GSWZrSKjR-VukFocOHeBQA_orPhfpRLx2O8VHRmza56NMZsUnL_fw75FI88-nSqFy7d_PAVHvPGGkO7TUsL4SalBY8l9Mg5fgFuZ46SRQVnWWBc1VJojoUW9PkSPw/s2048/2020-10-27+09.16.21.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjieHTwU0j7UKGjF1GSWZrSKjR-VukFocOHeBQA_orPhfpRLx2O8VHRmza56NMZsUnL_fw75FI88-nSqFy7d_PAVHvPGGkO7TUsL4SalBY8l9Mg5fgFuZ46SRQVnWWBc1VJojoUW9PkSPw/w300-h400/2020-10-27+09.16.21.jpg" width="300" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEJxTPGMpuD3u4iNyHG2TdHppcGe2lF49T4D-j7LIbKUpNLFhRLQbzVbh07ZsZTBxdWfpvFdUecHejhstbiUGbU9vuLBrCxBfTLibX63MHOycMuMv2CPdt7zZLyrT0-VitVKvle8zvBeI/s2048/2020-10-27+09.16.29.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEJxTPGMpuD3u4iNyHG2TdHppcGe2lF49T4D-j7LIbKUpNLFhRLQbzVbh07ZsZTBxdWfpvFdUecHejhstbiUGbU9vuLBrCxBfTLibX63MHOycMuMv2CPdt7zZLyrT0-VitVKvle8zvBeI/w300-h400/2020-10-27+09.16.29.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGO3ujzf-NSPvFxOuoiSurX2FF_vjEFEqZWytlu51grEdiOEgcD6QXK30YuyYCy8AU89PkDEbeT-Th5C4E9tulRjUhjZKZHFAPgB0tmhMdx9j3OE8TluFBq8POUmAI8RboTec-6DWPKBI/s2048/2020-10-27+09.16.39.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGO3ujzf-NSPvFxOuoiSurX2FF_vjEFEqZWytlu51grEdiOEgcD6QXK30YuyYCy8AU89PkDEbeT-Th5C4E9tulRjUhjZKZHFAPgB0tmhMdx9j3OE8TluFBq8POUmAI8RboTec-6DWPKBI/w300-h400/2020-10-27+09.16.39.jpg" width="300" /><span> </span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWwN9rX9Zi_VFsj2NH_wdK1ZZha_A4oXTM0mbYOgX8vvZ2_S1ibTiN-Jb0kG-cvilp8OQA7IzzjJzQlcDPPJMRQrZHJcHv9QrLLMpWoRgS17_Te-0TvVfikKgAbZl_fQGGg8SiKJYIZ_k/s2048/2020-10-27+09.17.23.jpg" style="clear: left; display: inline; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWwN9rX9Zi_VFsj2NH_wdK1ZZha_A4oXTM0mbYOgX8vvZ2_S1ibTiN-Jb0kG-cvilp8OQA7IzzjJzQlcDPPJMRQrZHJcHv9QrLLMpWoRgS17_Te-0TvVfikKgAbZl_fQGGg8SiKJYIZ_k/w300-h400/2020-10-27+09.17.23.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIxpeQiLsgt8LpL-b3r95Xfrq4CZrqWHOExnGBo-f4lOOQKMNQGAEBO2NYTZNdjJx0WnQ539yFllWoPqqEMzbiW6DoEpYevmqILEtA_MfO4HnLZPdz8jtV3KlYg8_tc3nG1gMgtAQ7940/s2048/2020-10-27+09.17.35.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIxpeQiLsgt8LpL-b3r95Xfrq4CZrqWHOExnGBo-f4lOOQKMNQGAEBO2NYTZNdjJx0WnQ539yFllWoPqqEMzbiW6DoEpYevmqILEtA_MfO4HnLZPdz8jtV3KlYg8_tc3nG1gMgtAQ7940/w300-h400/2020-10-27+09.17.35.jpg" width="300" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgasuooWdh_2YV5vLUWMclwgYQAx4mxJJ1V5fvO6H40s6myCsm6keECtfzfgXoNBskOTqXJRzdqaWXYfbzMJrHMb7aQGQAEcZ4iMlXYxxvfEVyPETt9EbXpORQqmdgqui8D6K7J5opI2YY/s2048/2020-10-27+14.53.55.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgasuooWdh_2YV5vLUWMclwgYQAx4mxJJ1V5fvO6H40s6myCsm6keECtfzfgXoNBskOTqXJRzdqaWXYfbzMJrHMb7aQGQAEcZ4iMlXYxxvfEVyPETt9EbXpORQqmdgqui8D6K7J5opI2YY/w300-h400/2020-10-27+14.53.55.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Student Reflection:</b></div><div class="separator" style="clear: both; text-align: left;">At the conclusion of the project, we asked students to reflect on their experience. In an email to their parents / guardians & their geometry teacher, students had to answer the following questions.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">1. What are two things that you learned by completing the project?<br /><br /></div><div class="separator" style="clear: both; text-align: left;">2. What was the most challenging part of the project for you?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">3. What piece of advice about completing the project would you give to future geometry students?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">4. What do you think the geometry teachers could do to improve the project for future classes?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Here are a few quotes from the student emails:</div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span face="Arial, sans-serif" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-size: initial; color: #222222; font-size: 10.5pt;">"</span>If
I were to give advice to future geometry students about this project, I would
tell them not to overthink the goal and try ideas first. When I started this
project, I found myself thinking too hard and not trying the ideas I had come
up with because I feared the area of overlap would be too great. After
finishing the project, I was under the maximum requirement of overlap. I should
have carried through with my other ideas instead of trying to make it perfect."</li><li> "Two
things I learned from this were that building sprinkler systems are hard, and
even when you think you can’t solve the problem, you can."</li><li>"This project allowed me to learn quite a lot, and I enjoyed it. It made learning more exciting."</li><li><span face="Arial, sans-serif" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-size: initial; color: #222222; font-size: 10.5pt;">"</span>It is also fun to be
creative with this project. I found that it was useful to use other angles
besides 90, 180, 170, and 360-degree angles."</li></ul><div><br /></div><div>The students gave us some great ideas on how to improve the project for next year. One common suggestion is to have a budget on the cost of the sprinklers.</div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Future Years</b></div><div class="separator" style="clear: both; text-align: left;">We think it would be great if we could have a professional landscape specialist from the community be a part of this project in the future. The community expert could potentially help launch the project by providing greater details about how sprinkler systems are installed and bring some of the sprinkler heads for students to see (and maybe learn about how they restrict the degree of spray). Or, we could have students present their plans to the landscape specialist and they could provide feedback.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Final Thoughts</b></div><div class="separator" style="clear: both; text-align: left;">Overall, I'm happy with the first year of the project. Students applied areas of sectors and wrote equations of circles, which met our learning targets. They also improved their skills with a compass. I look forward to improving this project in years to come.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I do understand the project has its limitations. I mean, come on...who needs to design a sprinkler system that doesn't extend a little outside of the boundary of your yard? What if the wind is blowing hard one day? Isn't the water going to leave the yard a bit anyway? </div><div class="separator" style="clear: both; text-align: left;"><br /></div>How would improve this project? What sort of things are we forgetting that could make this better?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">If you're interested in any of the files we used, enjoy!</div><div class="separator" style="clear: both; text-align: left;"><a href="https://drive.google.com/file/d/1izhjMr6q5t3qxwa9fghk39p8Sct5A9Pg/view?usp=sharing" target="_blank">Launch Page</a></div><div class="separator" style="clear: both; text-align: left;"><a href="https://drive.google.com/file/d/1PxCAhYmS0kKpVW-Yle3cb-4RhvUz-LN7/view?usp=sharing" target="_blank">Blueprint</a></div><div class="separator" style="clear: both; text-align: left;"><a href="https://drive.google.com/file/d/1XKzdHDXEsfZS6ZBsz99FrOMd_9mph6Lk/view?usp=sharing" target="_blank">Student Work Page</a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><span><br /></span></div><br /><p><br /></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><p><br /></p><p><br /></p>Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-6594034008804005092020-05-18T15:05:00.000-05:002020-05-18T15:05:02.305-05:00Target Based Grading v1.0: 2019-2020In this blog post, I will detail why and how I implemented a target based grading system in geometry this past year. I will share my thoughts and reflections about what went well, what didn't, and what changes I'm contemplating for next year.<br />
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I've been meaning to write this blog post for many months. I gave a presentation at the SD STEM ED conference in February about this topic, and there was a high level of interest about it. Thanks to being stuck at home for the past seven weeks, I've found a bit of time to write this post.<br />
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I typically blog as a vehicle for self reflection. When I have a lot going on in my brain, I find the process of writing something semi-coherent helps me organize my thoughts and think more deeply about things.<br />
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That said, I am very interested in hearing feedback about my target-based grading system as I begin to prepare for next year and target based grading v2.0. Please do not hesitate to comment, question, or push back on this post. I welcome the discussion around the topic of grading.<br />
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(Note: S/O to my <a href="https://markkreie.blogspot.com/2014/10/the-unforeseen-benefits-of-team-teaching.html" target="_blank">colleague Jarrod</a> for joining me on this journey. We continue to work in tandem and mirror each other day by day and are both better for it. A majority of this process was "we" instead of "I".)<br />
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<b><span style="font-size: large;">Part I. WHY</span></b><br />
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My decision to implement a target based grading system was influenced by a number of factors.<br />
<ul>
<li>I've always been intrigued by standards based grading, dating back to somewhere around 2014. I implemented a standards based grading system as part of my <a href="https://drive.google.com/file/d/1ud42aLtZYm3stNiQTABVy4fN8FuHAoKX/view?usp=sharing" target="_blank">Master's action research</a> during the 2014-15 school year. I didn't love the grading system I used for the action research, so I stopped using it after one year. But I was still intrigued by standards based grading.</li>
<li>In my school district, the K-3 elementary buildings began using standards based report cards in about 2016-17. I enjoyed seeing my children's standards based report cards compared to a traditional report card and continued to be intrigued.</li>
<li>In 2017-18, my district began to implement what we are calling "mass customized learning (MCL)" in the K-3 buildings. In 2018-19, MCL began in the Intermediate (4-5) building. In 2019-20, MCL began in the Middle School (6th grade class). It is scheduled to arrive at my high school in 2022-23. MCL is centered on students demonstrating mastery of learning targets, which are written in student-friendly "I can..." statements. One of the components of MCL is assessing (and reporting) student growth on the learning targets. In other words, MCL and target based grading go hand in hand.</li>
<li>I read <a href="https://www.amazon.com/gp/product/0470894520/ref=dbs_a_def_rwt_bibl_vppi_i0" target="_blank">Jo Boaler's <i>Mathematical Mindsets</i></a> and was convinced that traditional grading and assessing has some negative consequences. Boaler talks about <b>assessment for learning</b> and gives some advice on grading. The target based grading system that I hoped to implement followed many of Boaler's guidelines.</li>
<ul>
<li>One recommendation that Boaler makes is to not include homework as part of a student's grade. She makes a convincing argument that grading homework is an inequitable practice.</li>
<li>In past years, I have graded homework a number of different ways. Some years, I would have students do a self-check and report their score. Other years, I would collect and grade the homework on completion and/or accuracy. Either way, homework has been graded and counted between 15-25% of the student's grade. Recently, I grew tired of students copying answers or being dishonest when they self-graded. It wasn't all students each year, but a growing percentage of students. I was ready to completely remove the homework component from a student's grade.</li>
</ul>
<li>In 2018-19, I participated in a leadership cohort (called SDMath/Sci) through the South Dakota DOE. It was some of the best professional development I have ever been a part of. We learned about a leadership theory by <a href="https://simonsinek.com/product/start-with-why/?ref=home" target="_blank">Simon Sinek</a> centered on "Finding Your WHY". Equity was a major component of the training. Echoing Boaler's claims about equity, the cohort opened my eyes to some of the systemic structures that are a part of our educational system. Traditional grading practices were something we discussed. I had <b>found my WHY</b>: a target based system would create a more equitable way of assessing the students in my classroom. </li>
</ul>
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<b><span style="font-size: large;">Part II. Setup</span></b><br />
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<b><u>Target Based Grading vs. Standards Based Grading</u></b><br />
I mentioned earlier that I didn't love the standards based grading system that I had implemented for my action research. At the time, South Dakota had adopted the Common Core State Standards. I felt that certain standards were too broad to accurately assess student understanding.<br />
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Take Standard F.IF.C.7.B for instance:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTnGBna4HQGTZDcl0njPcvHF4nUZkO87lEMgNMzkwNUDjjsTLEOKJHEJ3o37qFO4bdg-ZhoHv4lMZiLm5FrSt1QzTl2La4VY2JKWo0UtjjMS8KK6KOU3VhyphenhyphenX3GFSHi4Mzu8sb5f9-AjTo/s1600/standard.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="345" data-original-width="854" height="258" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTnGBna4HQGTZDcl0njPcvHF4nUZkO87lEMgNMzkwNUDjjsTLEOKJHEJ3o37qFO4bdg-ZhoHv4lMZiLm5FrSt1QzTl2La4VY2JKWo0UtjjMS8KK6KOU3VhyphenhyphenX3GFSHi4Mzu8sb5f9-AjTo/s640/standard.JPG" width="640" /></a></div>
Graphing square roots functions, cube root functions, and piece-wise defined functions (including absolute value functions) were all topics I covered in Algebra 2. I claim that there are potentially students who have full understanding of graphing square root and cube root functions, but who struggle to graph piecewise functions. And vice-versa. In a <i>standards based</i> grading system, what sort of grade should those students get? If I'm using a 4.0 scale, would that student earn a 2.0? A 2.5? Would those scores truly reflect what the student understands?<br />
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That ambiguity helped me decide that I wanted a <i>target based</i> grading system, where I assess students on each learning target. So last summer I created the complete list of learning targets that I wanted to assess for geometry. [<a href="https://docs.google.com/document/d/1aUDSrNeNr8KggIzzvPAXqXzoQNsyuO4GVNox_CMJrPc/edit?usp=sharing" target="_blank">Geometry Learning Targets</a>]<br />
Note: I am already in the process of tweaking this list for next year. I realized that I needed to combine some targets together, especially in the surface area / volume unit. I also plan to re-sequence a few of the targets.<br />
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<b><u>Learning Target Quizzes</u></b><br />
Each learning target was assessed on an in-class QUIZ. Each quiz had between two and five learning targets on it. The quizzes were designed to be completed within one 50-minute class period.<br />
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Example: This is <a href="https://drive.google.com/file/d/1c--mSl4rxS3WPe-Jqm_GcWjAh7mjgLph/view?usp=sharing" target="_blank">Quiz #5</a>, which assess learning targets 16-19.<br />
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A couple of things are worth noting as you glance through the quiz.<br />
<ul>
<li>Students are scored on a 0.0 to 3.0 scale. A score of 0.0 is given if a student does not complete the questions for that target or demonstrates absolutely no understanding of the target.</li>
<li>Students cannot earn a score of 0.5. I don't have any good reason why that score wasn't allowed other than I felt that if a student gave full effort and demonstrated some level of understanding, a minimum score of 1.0 was valid.</li>
<li>The difference between scores of 1.5 vs. 2.0 vs. 2.5 varied by learning target. Some learning targets had only one question to answer (see target 19 above), while others had up to five questions to answer. </li>
<li>A score of 3.0 demonstrated quiz mastery.</li>
</ul>
<div>
<br />
<b><u>Retake Policy & Process</u></b></div>
<div>
If a student earned less than a 3.0 on any target target, they were <i>expected </i>to retake the part of the quiz aligned to the target. </div>
<div>
<br /></div>
<div>
There was the process to completing a quiz retake.</div>
<div>
<ol>
<li>Error analysis & reflection: For each target needing re-assessing, students completed a Quiz Correction Form (see below).</li>
<li>Practice & study: Students were encouraged to review the practice problems and previous quiz before retaking.</li>
<li>Retake: Students could come into my classroom any time throughout the day to retake, even if I had other class in session.</li>
</ol>
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<div>
Students stapled their quiz to the quiz correction form(s) and turned them into me. I would check to make sure students had correctly completed the problems on the quiz correction form. If they did so, I would use a rubber stamp to "stamp" their correction form, indicating that they had earned the opportunity to retake that learning target assessment. "Stamped" forms were returned to students to be able to review and study from. If there were errors made on the quiz correction form, I would return the form back to the student for revision.</div>
</div>
<div>
<br /></div>
<div>
When a student completed a retake of any learning target, the new score replaced the old score. It rarely happened, but students could earn a lower score on their retake.</div>
<div>
<br /></div>
<div>
If a student did not yet earn a score of 3.0 after retaking the assessment once, then a second retake was available. Before the second retake, I would have a one-on-one help session with the student instead of repeating the quiz correction form process. The help sessions were typically fairly brief (between 3-10 minutes) and took place whenever there was enough free time to have one (before or after school, during my planning periods, or even between class periods). </div>
<div>
<br /></div>
<div>
Quizzes were graded and returned to students the next day. Students then typically had 10 calendar days to complete the quiz retake process. I know that some standard-based grading systems call for students to be able to retake / improve their scores for as long as needed (or at least until the end of the semester or grading period). I struggle to see the benefit of that theory <i>for mathematics classes</i>. So much of mathematics builds on prior knowledge in a logical & sequential manner. I need my students to gain understanding of the learning targets in a timely manner so that they will possess the prior knowledge needed for the next set of learning targets. Therefore, I set a retake deadline for each set of learning targets.<br />
<br />
<br />
<b><u>Enrichment Tasks</u></b><br />
After a student earned a 3.0 to demonstrate quiz mastery, they had an opportunity to earn a 4.0 and enrich their understanding. For each learning target, I created an enrichment task. Enrichment tasks were intended to deepen understanding and extend thinking. Enrichment tasks were released (via Google Classroom) to all students on the day of the quiz. Students could work on the enrichment tasks individually or with partners / in small groups; each student had to turn in their own copy of the task for credit. Enrichment tasks followed the same deadline as the quiz retake.<br />
<br />
Examples of the enrichment tasks for learning targets 16-19:<br />
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<br />
More things worth noting about the enrichment tasks:<br />
<ul>
<li>Students could earn scores of "Not Yet", 3.5, and 4.0. (Recall: in order to submit an enrichment task, students must have first earned a 3.0 on the quiz.)</li>
<li>Enrichment tasks were not a one-and-done deal. If a student submitted work that wasn't correct, I would give feedback and allow students to fix their mistakes. There were many occasions where a student earned a score of "Not Yet" or 3.5, I gave feedback, and they made revisions and ultimately earned a 4.0.</li>
<li>The content on the tasks varied in nature, depending on the learning target. Sometimes the enrichment task would include a problem or two that involved a little tougher algebra (see learning target 16 - solving a quadratic equation and considering extraneous solutions). Other times the task might be to research some deeper idea that we simply don't cover in our regular instruction (see learning target 17 - considering spherical geometry). </li>
</ul>
<br />
<b><u>Grade Conversion:</u></b><br />
In an ideal target based grading system, I wouldn't have to report traditional A-B-C-D-F grades. Unfortunately, my district requires me to because we need to report things like GPA and class rank. Boooooo!</div>
<div>
<br /></div>
<div>
I needed to create a way to convert the target based scores into traditional grades.<br />
<br />
Before I forget, here is the grading scale for my school.<br />
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As you can see, semester grades were calculated by a weighted average of the quarter grades (40% each) and the semester final tasks (20%).<br />
<br />
Quarter grades were calculated by a weighted average of the learning target assessments (80%) and miscellaneous tasks (20%).<br />
<br />
<b><u>Learning Target Assessments (80% of quarter grade):</u></b><br />
Each quarter, all of the learning target scores were averaged to create an "Average Target Score". The Average Target Score was then converted using this conversion chart.<br />
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Notice:</div>
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</div>
<ul>
<li>Students needed an average score of 2.0 or higher to earn a passing grade in the "Learning Target Assessments" category.</li>
<li>An average score of 3.0 earned a student a B+ in the "Learning Target Assessments" category. In order to earn an A in the category, some enrichment tasks needed to be completed.</li>
</ul>
<div>
<br /></div>
<div>
I used a Google Sheets <a href="https://docs.google.com/spreadsheets/d/1DASvtu_TZ0qGkxbNK44GHCZEkCYsHY148AE5Kw1z0XI/edit?usp=sharing" target="_blank">Gradebook</a> that automatically averaged and converted the score to a letter grade. I also had to record scores in Infinite Campus. I wasn't a fan of having to manage two separate gradebooks, but I survived.</div>
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<div>
<b><u>Miscellanous Tasks (20% of Quarter Grade):</u></b></div>
<div>
I did a lot of thinking about the types of assessments that I have used in past years and how they would fit into a target based grading system. I wasn't ready to completely remove the variety of assessments that have been a staple in my classroom, so I decided to create a separate category and maintain the ability to assess students in a variety of ways. The learning target average score counted as 80% of the quarter grade, while the "miscellaneous tasks" counted as 20% of the quarter grade.<br />
<br />
One of my biggest concerns about implementing target based grading was that the assessments would become "silos" - too focused on one particular target. I want students to see and understand the connections between the learning targets.<br />
<br />
Some examples of assessments that went into this category included:<br />
<br />
<ul>
<li>In class group tasks</li>
<ul>
<li>Every couple of weeks, I have students work in pairs during class to solve review problems. A majority of the problems relate to the geometric concepts and topics that we have learned about up to that point. Some of the problems review middle school and algebra 1 topics; others focus on probability and statistics. I pull a lot of questions from ACT reviews to expose students to those types of questions. I also include problems that connect multiple learning targets together and/or include different solution methods.</li>
</ul>
</ul>
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<ul>
<li>Choice Assignments</li>
<ul>
<li>To help try to increase student engagement in my high school, all teachers were asked to implement assignments where students had a choice of options.</li>
</ul>
<li>Desmos activities</li>
<ul>
<li>From time to time, I will assess a Desmos activity. Typically, these activities are completed in class as part of the lesson for the day. I will assess them when I want to ensure that students who were absent during class complete the activity.</li>
</ul>
<li>Projects</li>
<ul>
<li>Each quarter, students complete at least one project. Some projects are in groups, others are individual.</li>
</ul>
<li>Reflection tasks</li>
<ul>
<li>I had students reflect on their learning with the help of Flipgrid.</li>
</ul>
</ul>
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<ul><ul>
<li>I also had students write an email each week to reflect on their learning. The email went to their parents / guardians and to me. Students would have to answer a series of prompts that helped guide their reflection. See an example of my prompts <a href="https://docs.google.com/document/d/1-gOIqz55JLR7kV7szV4q-zg4IfAZ7ekQftpqBp6O0nY/edit?usp=sharing" target="_blank">here</a>.</li>
</ul>
</ul>
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One thing that I removed from class this year was "Parent Tests". In the past, I would send a multiple choice assessment home each unit for parents / guardians to complete. The questions would relate to the concepts we were learning about in class. There was a process that needed to be completed and students would earn extra credit if they completed the tasks and returned the paper.<br />
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I've learned that awarding extra credit - especially in way that involves a student's situation at home - is an inequitable practice. I have decided to not award any extra credit from this point forward. I am in the process of researching ways to include parents / guardians in the learning process again.<br />
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<div>
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<div>
<b><span style="font-size: large;">Part III. Implementation Details</span></b></div>
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I want to highlight and comment on a couple of things I learned during this first year of implementation.<br />
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I made three sets of each quiz. Each set was intended to be equally difficult. Students had the opportunity to take the quiz earlier that the designated quiz day. Students taking the quiz early were given Set #1. Set #2 was given to every student who took the quiz on the quiz day. Set #3 was given to students who wanted to retake. If a student needed a second retake, they would then take the quiz that they hadn't yet taken.<br />
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On the day following a quiz day, students would have "WIN" (what I need) time. Students would get their graded quizzes back and do the following:<br />
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<ol>
<li>Write their reflection email (see above).</li>
<li>Begin the quiz correction process if they scored less than a 3.0.</li>
<li>Work on enrichment tasks if all scores were 3.0.</li>
</ol>
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Some students would also use that time to work on quiz retakes from previous quizzes, assuming the retake deadline had not passed.<br />
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I would meet individually with each student to check in with how they were doing during this time.<br />
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Some students used the WIN time very effectively. Students were able to ask questions of each other. A lot of peer helping took place.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVF2fZ_ZB5K9ZDdik6rKx6hSKMwfqW06kSjoE33oO-Yb7S885LPNWva11yE8BknMj5EfoPYvoF0tqimk9mkbQV1G_bCfdIoQ1Ciez1MgLf9O5tJEthGlzHW7fJTzt2h68feogFO4lJ_1o/s1600/P1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVF2fZ_ZB5K9ZDdik6rKx6hSKMwfqW06kSjoE33oO-Yb7S885LPNWva11yE8BknMj5EfoPYvoF0tqimk9mkbQV1G_bCfdIoQ1Ciez1MgLf9O5tJEthGlzHW7fJTzt2h68feogFO4lJ_1o/s400/P1.jpg" width="300" /></a></div>
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As the year went along, more and more students started abusing their time during WIN days. I would see students working on assignments from other classes. Others would treat the time as a social hangout. I need to improve my classroom management a bit on those days moving forward.<br />
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Each class had its own tray on my desk for students to turning their work in. This helped manage the steady flow of papers that were turned in each day.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzHeeUZG6ZaNCuoeqHTnxlw1jn2XpW_y3v9KHomqCBml9_oHn8FX0hO_NEHoxAbnOW-uP-uTjKe-FICSaOiAG2JMIguMlJ4PgPgNNIsPbu53rA2txbcl_kY48GvimbvRBPNpMYQyd3MN0/s1600/P2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="394" data-original-width="792" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzHeeUZG6ZaNCuoeqHTnxlw1jn2XpW_y3v9KHomqCBml9_oHn8FX0hO_NEHoxAbnOW-uP-uTjKe-FICSaOiAG2JMIguMlJ4PgPgNNIsPbu53rA2txbcl_kY48GvimbvRBPNpMYQyd3MN0/s640/P2.jpg" width="640" /></a></div>
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Each student had their own hanging folder in a basket at the front of my room. I would put all papers (graded quizzes, quiz correction forms, notes from class they missed, etc) in their basket. It was their job to empty their basket as they entered the room each day. Being able to "hand back" papers at any time was a huge time saver.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpPJvfdXbtw20hQHDB5jS3s_Iq1WUs-NU0GJN3mXhnzSdKrqOfQrdsfVczzPCKD1TD_fsNHHUfXrermBXuEOWEmLf-7jG4eLQwTTMren84X8tp8Ts6mLi0XXJJIwkzL0ybrMd2IxaCA8I/s1600/P3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="459" data-original-width="773" height="380" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpPJvfdXbtw20hQHDB5jS3s_Iq1WUs-NU0GJN3mXhnzSdKrqOfQrdsfVczzPCKD1TD_fsNHHUfXrermBXuEOWEmLf-7jG4eLQwTTMren84X8tp8Ts6mLi0XXJJIwkzL0ybrMd2IxaCA8I/s640/P3.jpg" width="640" /></a></div>
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Speaking of grading papers... it was a daily job. Each day, there was always something turned into the trays. I felt the responsibility to grade papers and update grades every night. If it was a quiz day, students needed their quizzes returned the following day for WIN time. If it wasn't, students needed daily feedback on quiz correction forms and quiz retakes. The process of retaking depended on it.<br />
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That said, in past years I would find myself grading every night as well - often times homework. I felt much more motivated to grade quizzes, retakes, and quiz retake forms versus homework. At minimum, I knew that the quizzes and quiz retakes were authentic evidence of what the students had learned. I dreaded grading homework knowing that a certain percentage of students had copied their answers from someone else and learned nothing along the way.<br />
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One grading note:<br />
I did have a few students average between a 1.75 and 2.00 on their target based assessments, which converted to a 64% in the learning target assessment (80%) category of the gradebook. Their grade on the miscellaneous tasks (20%) was fairly good, so those students did pass the semester when the weighted grades were calculated.<br />
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Communication to parents / guardians about the grading system was important. There were some parents who asked for clarity on the grading system at the start of the year. I included a <a href="https://drive.google.com/file/d/1DDP5INt9ifrPWaRWxLgpjieuoETP2bq5/view?usp=sharing" target="_blank">detailed explanation in one of my newsletters</a>. <br />
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I started the year with a quiz over the prerequisite skills. The quiz didn't count towards the student's grade but I scored the quiz using the target based system. It served as a good example for students to see how they were going to be assessed.<br />
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<b><span style="font-size: large;">Part IV. Reflection / Next Steps</span></b><br />
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I felt the target based system was effective in helping develop growth mindsets in students. I liked that students didn't get their graded quizzes back and immediately saw a score / total points or a percentage. Instead, they saw scores for each target. In the case where a student didn't do very well on one or more targets on a quiz, it was still easy to shine positive light on the targets they did do well on.<br />
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I had to train myself to not be frustrated when students struggled on the first attempt on the quiz. I had to remember that this was their first attempt at each quiz and that they did have the opportunity to retake. I needed to focus on the final scores <i>after</i> the retake deadline had passed. After all, those were the final scores that students were earning.<br />
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Opponents of a target based grading system have a worthy argument centered around that previous paragraph. What's stopping a student from not studying / preparing at all for the first quiz when they know they always have an opportunity to retake? What type of bad habits and lack of work ethic / preparation does that develop?<br />
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My counter to that argument lies in my belief that if we teach students to be mindful of their <a href="https://drive.google.com/file/d/1xzHBNJJu5ALV1CqIeyHVdfoETl_xcD6L/view?usp=sharing" target="_blank">learner agency</a> and the <a href="https://www.teachthought.com/pedagogy/what-are-the-habits-of-mind/" target="_blank">16 Habits of Mind</a>, students will begin to make make the correct decision when it comes to preparation and work ethic. Yes, I believe that the mathematics I teach in geometry is important for students to have future success. But teaching students to be lifelong learners and to possess a growth mindset and self confidence is more important. <br />
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In the future, one long term change that I'm interested in looking into would be the idea of "mastery" learning. A student would need to demonstrate mastery on each standard before they would be allowed to move on. In other words, a student <b>must</b> earn a 3.0 on each learning target (or group of targets on a given quiz) before they move forward. A big change in the structure of our class schedule would need to take place in order for this type of change to be implemented. It is something our district is looking into pursuing and would help fight against students doing the bare minimum to pass.<br />
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<br />
I do welcome all feedback and discourse around this system in an effort to improve for future years. I hope to convince my colleagues that target based grading is something we should be doing throughout our entire department. Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-3696214758977572072020-02-15T11:51:00.002-06:002020-02-15T11:51:40.524-06:00Algebra 1 ProjectAs part of a first semester project for Algebra 1 this year, students completed a two-day activity called "All Knotted Up". I first found this activity in the September 2013 edition of NCTM's <i>Mathematics Teacher</i> publication. (Credit to Jamie-Marie L. Wilder and Molly H. Fischer for the great activity and supporting article.)<br />
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Materials needed: poster board, marker / colored pencils, meter sticks or tape measures, a variety of ropes or string.<br />
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Working in pairs (or groups of three if needed), groups chose one type of rope (or string) and cut a piece that was at least 100 cm long. (More about the length in a minute.)<br />
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Students measured the length of the rope and recorded the length. (It was helpful to have tape measures instead of meter sticks or rulers.) Then students tied one knot in the rope and re-measured the length. They repeated this process until 10 knots had been tied.<br />
I provided groups a table to organize their data.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinj3A3LXtW4uMQ7OXuH7dZKODHZaH2lmIlsKYFWDZVb7jbsn5tmT757qAdqjsBDQ791_C5REO1ivZ0i_r8H379YYbEOhA3DWPiXbSf_ZMa9fAtttp-IPZr510R-N8f_iLFr_AZfLxjy-g/s1600/table.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="260" data-original-width="290" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinj3A3LXtW4uMQ7OXuH7dZKODHZaH2lmIlsKYFWDZVb7jbsn5tmT757qAdqjsBDQ791_C5REO1ivZ0i_r8H379YYbEOhA3DWPiXbSf_ZMa9fAtttp-IPZr510R-N8f_iLFr_AZfLxjy-g/s200/table.JPG" width="200" /></a></div>
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Groups then made a scatterplot of their data on the poster board. I asked that groups be sure to include their data table on the poster.<br />
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To finish the first day, students reflected on the following questions:<br />
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<span style="font-family: "Times New Roman",serif; font-size: 11.0pt;">A) Looking at your graph and table of
values, what trends do you see?<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman",serif; font-size: 11.0pt;">B) Suppose you were to tie three more knots
in your string. How long do you think
the string would measure? Explain how
you arrived at your estimate. <o:p></o:p></span></div>
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To prepare for the second day, I chose three groups that used different rope and had started with different lengths of rope. I created a Desmos graph that included the data from three groups. I calculated the linear regression equation for each set of data. (<a href="https://www.desmos.com/calculator/it3v9a0efu">https://www.desmos.com/calculator/it3v9a0efu</a>). I also hung three posters on my board, along with the rope they used.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ_BbeFFjn7Nb3jG-26Q4vlWu5p0hEWIqYdkFd4g_YyzFaXwwzwFj5Z4uOyw1JbHp1dIuyXRZ28TKT58Owbh0wfHzJNyFZ5n0R53foTbqbNh2gL6SD9dBXxw1EoSvAvX7XBqmJsog4By0/s1600/Knot+Photo.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="775" data-original-width="1600" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJ_BbeFFjn7Nb3jG-26Q4vlWu5p0hEWIqYdkFd4g_YyzFaXwwzwFj5Z4uOyw1JbHp1dIuyXRZ28TKT58Owbh0wfHzJNyFZ5n0R53foTbqbNh2gL6SD9dBXxw1EoSvAvX7XBqmJsog4By0/s640/Knot+Photo.jpg" width="640" /></a></div>
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When students entered the room, they naturally started looking at the board and making observations. I asked students to individually write down "What do you notice? What do you wonder?" After two minutes of individual thinking, students engaged in a large group discussion. I let their observations and wonders drive the discussion.<br />
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Here is a partial list of things students noticed, discussed, and analyzed:<br />
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<ul>
<li>The y-intercepts of the graphs are the initial length of rope.</li>
<li>The slope for each line is different; the slope for the thickest rope is steeper than than the slope for the thinnest string.</li>
<li>The data is fairly linear, but not perfectly linear for any of the graphs. We discussed why that is the case.</li>
</ul>
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<div>
One tip with the initial length of the rope: The rope must be long enough to be able to tie 10 knots in it. If the rope is too short, the knots end up knotting together and the data becomes a lot more variable. I had a group that chose a very thick piece of rope and by the 7th knot, their rope was just one huge chunk of knot that was impossible to measure. That group had to restart with a longer piece of rope.</div>
Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-44066791632413254352019-08-23T02:45:00.001-05:002019-08-23T02:45:56.073-05:00Back to School 2019-20First official day of school starts today. Here is a quick glimpse around my classroom.<div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNFZEaK2M7q93eXNKW9Pgf6K_f-iAp9C4tCJEvvPfKVh6JrzIkJ2K0UBL1Fb2BNy2-4paxA35nJlF-Z8ypiLD3BViSBQYN-emuju3NsxVVdUlBZuVjUlorWgrJGbEnMMYLt7z8jAT1jbY/s1600/Edited.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1140" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNFZEaK2M7q93eXNKW9Pgf6K_f-iAp9C4tCJEvvPfKVh6JrzIkJ2K0UBL1Fb2BNy2-4paxA35nJlF-Z8ypiLD3BViSBQYN-emuju3NsxVVdUlBZuVjUlorWgrJGbEnMMYLt7z8jAT1jbY/s400/Edited.jpg" width="285" /></a></div>
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Computer + Smart Board + Document Camera</div>
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I don't think I could survive without any of these three things.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbPKceFlANDicX3g5k7_rWOA6iNQi8EGblSJlNv0oqJXOOowpdW1zp2Uutojrdom1VANIEef9P53p0zb0r4hc__-9SXtNTvlqS0wLGcScHLm6Mn580VHJCESIeJaGiZ7doccsv9W2OIZ0/s1600/2019-08-21+08.22.59.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbPKceFlANDicX3g5k7_rWOA6iNQi8EGblSJlNv0oqJXOOowpdW1zp2Uutojrdom1VANIEef9P53p0zb0r4hc__-9SXtNTvlqS0wLGcScHLm6Mn580VHJCESIeJaGiZ7doccsv9W2OIZ0/s400/2019-08-21+08.22.59.jpg" width="400" /></a></div>
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Excited about the new WODB posters!</div>
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I rotate a variety of things that I put on the back table for students to play with...</div>
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Pattern blocks, tiling turtles, 500 - 1000 piece puzzles to name a few.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjzTn7oQrjSvb0ysKmBa1bjBY-fwf1ckmlilg6Ai21R8zDzElaIn2_ReCdmmxc7fEPWJFCAARFUkCmXmyi5OzklAyKmTam7WFlVBOZW6pV_GD0uwooaeB-GUxwLKTL66mQSBs0LkjetUA/s1600/2019-08-21+08.23.17.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjzTn7oQrjSvb0ysKmBa1bjBY-fwf1ckmlilg6Ai21R8zDzElaIn2_ReCdmmxc7fEPWJFCAARFUkCmXmyi5OzklAyKmTam7WFlVBOZW6pV_GD0uwooaeB-GUxwLKTL66mQSBs0LkjetUA/s400/2019-08-21+08.23.17.jpg" width="300" /></a></div>
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I saw this idea on a site visit to Alexandria, MN last year. A Lego station!</div>
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I'm interested to see what students will build.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS25tqAR6tBuebuf8SvahN3BOq6BAxkTT1cDSP92LZ2-s-JNQYG0HDf8Mq9xnbC8QaT4IA7kjLrybPHDLeEl11FFJCBmiCmk9LitGZxOv6ovCvgeg-HRkWaH95X1PBFCpbe1ezZM8WOvI/s1600/2019-08-21+08.23.31.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS25tqAR6tBuebuf8SvahN3BOq6BAxkTT1cDSP92LZ2-s-JNQYG0HDf8Mq9xnbC8QaT4IA7kjLrybPHDLeEl11FFJCBmiCmk9LitGZxOv6ovCvgeg-HRkWaH95X1PBFCpbe1ezZM8WOvI/s400/2019-08-21+08.23.31.jpg" width="400" /></a></div>
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Excited to start the year with VNPS!</div>
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These 5 boards on wheels arrived last spring.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcB6XwU7eP9Sy8mIuxE1o47PwgYEaop0V8rcRQltbUuzZThQQ3Ogdl4eBAxhrsq-9xWhoz9MJhrxtGhIYTKMkh0322-jOXza_QGXPcxAjnQDS7ywhCntMqy_mM0Qt7iKGJz9ezUMO1wDA/s1600/2019-08-21+08.24.02.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcB6XwU7eP9Sy8mIuxE1o47PwgYEaop0V8rcRQltbUuzZThQQ3Ogdl4eBAxhrsq-9xWhoz9MJhrxtGhIYTKMkh0322-jOXza_QGXPcxAjnQDS7ywhCntMqy_mM0Qt7iKGJz9ezUMO1wDA/s400/2019-08-21+08.24.02.jpg" width="400" /></a></div>
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Notice the crates in the bottom left... this is how I hand back papers and where I put handouts when students are absent.</div>
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One crate per class...</div>
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One hanging folder per student...</div>
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Students check their folder when the enter the room each day.</div>
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This has saved me a lot of class time when I don't have to hand back papers.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-TDfNZubexzm81TAgt1KNHlnv9yIwPNT57NQZrYDTzBgDXO7XE73-ARPygjjdVhwFA1jFNIOpI_9YaHQdyFw7Vug_GA6xMlPao4NyNIF2pepom4Q1iCnnoNBGu8r5Zhyphenhyphen5G1l80Crj32U/s1600/2019-08-21+15.27.23.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-TDfNZubexzm81TAgt1KNHlnv9yIwPNT57NQZrYDTzBgDXO7XE73-ARPygjjdVhwFA1jFNIOpI_9YaHQdyFw7Vug_GA6xMlPao4NyNIF2pepom4Q1iCnnoNBGu8r5Zhyphenhyphen5G1l80Crj32U/s400/2019-08-21+15.27.23.jpg" width="400" /></a></div>
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My home base</div>
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Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-22260423396161054572019-07-15T22:42:00.000-05:002019-07-16T11:54:37.633-05:00Desmos Fellows Weekend v2.0<br />
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Two years ago, I was a member of cohort 2 of the Desmos
Fellowship.<span style="mso-spacerun: yes;"> </span>On my way home from
Fellowship weekend, I wrote a <a href="https://markkreie.blogspot.com/2017/07/desmos-fellowship-2017-reflection.html" target="_blank">blog post</a> about my experience.<o:p></o:p></div>
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This summer, I was invited to join the cohort 4 weekend as an alumni Desmos Fellow.<span style="mso-spacerun: yes;"> </span>It was an honor
to be asked back and it was again a wonderful experience.<span style="mso-spacerun: yes;"> </span>As I sit on my flight back to Brookings, I
want to highlight my top five takeaways from the weekend.<span style="mso-spacerun: yes;"> </span>In no particular order…<o:p></o:p></div>
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<o:p><br /></o:p></div>
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<o:p>1. </o:p><span style="text-indent: -0.25in;">I
was reminded that I have a lot to learn about equity, access, and social
justice.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">This past year has been an
eye-opener for me.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">The SDMath/Sci
Leadership cohort I was a part of helped me realize that I have a long way to grow.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">This weekend helped me grow in ways I couldn’t
have imagined.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">I appreciate that Desmos
is committed to helping find solutions to these topics.</span></div>
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<span style="text-indent: -0.25in;">2. Imposter
Syndrome is real.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">On Friday at 4pm,
Fellows weekend officially kicked off with an icebreaker activity.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">Standing in a large circle, each person had
20 seconds on the clock to introduce themselves and talk about something that
they were bringing with them this weekend.</span><span style="text-indent: -0.25in;">
</span><span style="text-indent: -0.25in;">Responses varied, but there were many in the room feeling “I’m very
nervous about being here … I don’t feel as though I’m good enough to belong
here … I can’t believe I’m here … I’m not worthy!”</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">(BTW – nice equity move by Team Desmos by
putting 20 seconds on the clock and forcing people to adhere to the time
constraint.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">The very subtle equity
piece: if someone was done talking before the 20 seconds had elapsed, we were
to stand in silence until the time was up.</span><span style="text-indent: -0.25in;">
</span><span style="text-indent: -0.25in;">Not only did the 20 second mandate restrict someone from talking way too
long, it also ensured that everyone have an equal voice.)</span></div>
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<span style="text-indent: -0.25in;">3. Desmos
growth.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">Not only are there now 40+ more
Desmos Fellows, the Desmos Teaching Team continues to grow as well.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">In the past 12 months, Desmos has hired a half
dozen or so former teachers to join their teaching team.</span></div>
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<span style="text-indent: -0.25in;">4. It
was great to connect with other teachers who are wrestling with the same – for
lack of a better word – issues that I am.</span><span style="text-indent: -0.25in;">
</span><span style="text-indent: -0.25in;">I had a couple of deep conversations with various Fellows focused on a
variety of topics. One such conversation was about standards based grading and
the role of homework.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">I’m planning on
implementing a target based grading system this year and still have a few
wrinkles to iron out before school begins in August. It’s encouraging to know
that I have some people in the Fellowship who I can reach out to who are also
implementing SBG. </span></div>
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<span style="text-indent: -0.25in;">5. </span><span style="text-indent: -0.25in;">I
am extremely excited about the changes happening in mathematics education.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">The CCSS have been around for nearly a
decade.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">There are pockets of teachers
slowly breaking away from traditional methods and embracing inquiry-based,
conceptual-based methods.</span><span style="text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">There are
research based best practices that support collaboration, equity, student
identity, and access available to all teachers.</span><span style="text-indent: -0.25in;">
</span><span style="text-indent: -0.25in;">Colleges and universities are starting to worry less about GPA and class
rank and more about recruiting students who have learned how to collaborate, to
communicate, and to think.</span><span style="text-indent: -0.25in;"> </span></div>
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My flight is about over and it is time for me to snap back
to reality.<span style="mso-spacerun: yes;"> </span>On the forefront of my mind
is how can my department at BHS help all students become better mathematicians,
and in turn, help raise the percentage of students who are “proficient” or
better on the Smarter Balanced test.<o:p></o:p></div>
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Mid-credit scene:<br />
Fellow alumni Lauren suggested to us that we write ourselves a letter to help solidify the memory. This is the letter to myself. With that, I'll post a few pictures.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3B308Sa7AqLofknqlOpJF8qBB7q39f2ieTuZ93hQFIiNpeh1hDZH-xlMUqdWx2GGJ5jXOdKxN5d9kdahKUAnJClhcy09veIoB6BUbl5txKDi0BbzQFOgQkm1AXm7Ws8nOKFyhcz2-02s/s1600/2019-07-11+16.41.46.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3B308Sa7AqLofknqlOpJF8qBB7q39f2ieTuZ93hQFIiNpeh1hDZH-xlMUqdWx2GGJ5jXOdKxN5d9kdahKUAnJClhcy09veIoB6BUbl5txKDi0BbzQFOgQkm1AXm7Ws8nOKFyhcz2-02s/s400/2019-07-11+16.41.46.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">San Francisco from "The Rock"</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisNyyqhDg5C8f4pAHTqYrB6ezj1zitrGg6Om_bexpQGM4-o1E72GRwXkomZIHKnqPnQbdUS1ZaA6MtfmsRKl50oS-DU3_Ej3rZSY-tAHAHkZQHCk2wUfqffQ9icudeWPVWoS77xs3CKFs/s1600/2019-07-12+15.40.09.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisNyyqhDg5C8f4pAHTqYrB6ezj1zitrGg6Om_bexpQGM4-o1E72GRwXkomZIHKnqPnQbdUS1ZaA6MtfmsRKl50oS-DU3_Ej3rZSY-tAHAHkZQHCk2wUfqffQ9icudeWPVWoS77xs3CKFs/s400/2019-07-12+15.40.09.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Welcome to HQ!<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0q6c4bhatyxR0DJLscYiblLp5-zS7cY1SxO1qnDXOEBvs3lEXvWwvQdjWzwQuMy-lo_RuwKrCyvt0hS4P1a8K7c_SJKRdfg453AhQcxkXAOOMbEGLYsvG2le2_W0zb8l8Rst6T8aXT-c/s1600/2019-07-12+20.08.04.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0q6c4bhatyxR0DJLscYiblLp5-zS7cY1SxO1qnDXOEBvs3lEXvWwvQdjWzwQuMy-lo_RuwKrCyvt0hS4P1a8K7c_SJKRdfg453AhQcxkXAOOMbEGLYsvG2le2_W0zb8l8Rst6T8aXT-c/s400/2019-07-12+20.08.04.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Our "home group": Matt, Sam, Tim, and I (among other home groups)<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjoSbQJZLX0M_6h8v-QTwoFRWhOT3fTc-Nxg2JuM_faSChxEEmJy3blv1Wo8P5XxeJNZZU_mXBtNTsExuid1UWczblvD4OY8xrY8Q1rq-aUNnS24-ewalVEhagqDH1qw2FrggfBKplF7s/s1600/2019-07-14+17.25.58-1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjoSbQJZLX0M_6h8v-QTwoFRWhOT3fTc-Nxg2JuM_faSChxEEmJy3blv1Wo8P5XxeJNZZU_mXBtNTsExuid1UWczblvD4OY8xrY8Q1rq-aUNnS24-ewalVEhagqDH1qw2FrggfBKplF7s/s400/2019-07-14+17.25.58-1.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">I found time to walk across the Golden Gate Bridge!</td></tr>
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Post-credit scene: I will never think of seals the same way. Thanks, Joce!</div>
Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-64672579776329434772019-05-11T23:27:00.002-05:002019-05-11T23:27:16.002-05:00Cell Phones in the Classroom: My New BeliefAs recently as 2017, I was a firm believer that it was fine for students to have cell phones in the classroom. Part of my philosophy centered around the idea that it was our job as educators to help teach students about appropriate use (i.e. when is it okay to use your phone vs. when it is time to put it away). I was also a strong believer in maximizing tech integration into classrooms, with the goal of climbing the SAMR model whenever possible. (See my Oct. 2014 post about the SAMR model <a href="https://markkreie.blogspot.com/2014/10/above-substitution-step.html" target="_blank">here</a>. Also, more info on the SAMR model <a href="https://www.schoology.com/blog/samr-model-practical-guide-edtech-integration" target="_blank">here</a>.) My thinking was pretty simple: integrating tech into classroom often times increased student engagement and made class more interesting and exciting.<br />
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Let's fast forward to May 2019. <br />
My belief on cell phones in the classroom has completed changed. <b>I now believe that cell phones should be banned from classrooms.</b><br />
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My five reasons, in no particular order.<br />
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1. I have failed to integrate meaningful, engaging activities that <u>require</u> cell phones.<br />
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Don't get me wrong. I still love integrating tech into my classroom. But each student in my school is issued a laptop, and that laptop can do everything I want students to be doing.<br />
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The reason I don't hunt for activities and lessons that integrate cell phones is equity for all students. While a large majority of students in my classroom have smart phones, not everyone does. I want no part of widening the equity gap between the "haves" and "have nots".<br />
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2. Smart phones make cheating waaaaaay too easy.<br />
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Many students are far too good taking a picture and snapping it to their group of friends. I understand that this form of cheating could still take place in a variety of ways, but no phones in the classroom would at least put a band-aid on the problem.<br />
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3. We need to help student develop their social skills.<br />
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It's not that kids don't communicate with each other anymore, but their main form of communication is digital. I've seen a table of seven students sit at lunch and blankly stare at their phones for 15 minutes straight. No talking, no emotion, minimal awareness of their surroundings. One time, I asked a group at lunch what they were up to on their phones, and some said that they were sending Snap Chat messages to others at the table.<br />
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In addition, students often don't understand <i>how</i> to appropriately talk to each other nor how to listen to one another. Little things like making eye contact, reading non-verbal cues, and being a good listener are skills that need to be developed.<br />
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I love to use strategies such as <a href="https://www.saravanderwerf.com/stand-talks-the-best-thing-i-ever-did-to-get-students-talking-to-one-another/" target="_blank">Sara Van Der Werf's "Stand and Talks</a>" and a modified version of <a href="https://wodb.ca/" target="_blank">"Which One Doesn't Belong?"</a> that asks students to listen to what their partner answered and share their answer. (Another variation of WODB is to find a reason that <u>each </u>one doesn't belong.)<br />
[I stole those variations from someone but couldn't locate the source. Sorry!] These strategies help students develop some of those communication person-to-person skills.<br />
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Desmos also has some very useful tools that can help create conversations in the classroom. (Check out the <a href="https://blog.desmos.com/articles/introducing-our-classroom-conversation-toolset/" target="_blank">Classroom Conversation Toolkit</a>.) Yes, I realize that Desmos activities can be implemented using smart phones, but once again, I will have my students on their computers if we're doing a Desmos activity.<br />
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4. Students need to learn that they can survive without their phones.<br />
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I'm going to summon Abraham Maslow for this one. Contrary to popular belief, cell phones are not basic human need (see table below... the basic needs are at the bottom). I see cell phones fitting snugly into the "social" level of this pyramid. Much of what students do on their phones (in and out of the classroom) caters to their social needs. Put me on record for saying that good teachers create a culture in their classrooms that can satisfy the social needs of students. Cell phones are not needed.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRU1A_dPbeEpoejfQTRnQbchO38WFyWigkrSGwcIyhW6ssA8zn14031GlAjmWQQaIViHe9mOHBCPgliu_z-mOIFg4i3k41mMhdFJ7oXnBo5Jy-1ExLYKCQiwxgrOYBPpq5B5qDLXko59U/s1600/needs.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="584" data-original-width="639" height="365" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRU1A_dPbeEpoejfQTRnQbchO38WFyWigkrSGwcIyhW6ssA8zn14031GlAjmWQQaIViHe9mOHBCPgliu_z-mOIFg4i3k41mMhdFJ7oXnBo5Jy-1ExLYKCQiwxgrOYBPpq5B5qDLXko59U/s400/needs.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.psychologytoday.com/us/blog/hide-and-seek/201205/our-hierarchy-needs">https://www.psychologytoday.com/us/blog/hide-and-seek/201205/our-hierarchy-needs</a></td></tr>
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Part of this "phone addiction" stems from parents. I invite you to watch different families the next time you go to a restaurant. I can't count the number of times I've seen parents solely focused on their screens while life moves on around them. (As a parent, I am guilty of this as well.)<br />
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I hate to say it, but part of our job as educators is to help students realize that they don't need to be attached to their cell phones.<br />
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(A corollary to this idea is for parents to learn that it is okay to not have direct access to their child 24/7. I understand that parents pay large sums of money in order for their child to have a cell phone accessible at all times... but, parents: you're not helping here. Countless times I have asked students to please put their phone away, only to hear the reply of "but I'm just texting my mom (or dad).")<br />
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And this brings me to my last point. <br />
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5. Phones are a distraction, even when students aren't touching them.<br />
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Take a look at this video. Please watch it. (2 minutes)<br />
<a href="https://www.edutopia.org/video/theres-cell-phone-your-students-head">https://www.edutopia.org/video/theres-cell-phone-your-students-head</a><br />
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I've had a gut feeling about this more and more these past two years, but have never acted on it until this week. This past week, I changed the policy in my classroom to "If I see your phone, I will take it." I put the phones <a href="https://blog.mrmeyer.com/2017/this-is-my-favorite-cell-phone-policy/" target="_blank">in a box</a> and students can have them back after class.<br />
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I'm happy that I work in a building where I can set my own cell phone policy and the administrators will support it. After watching the video, I might even tighten my policy for next year.<br />
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I'm curious to hear your thoughts on this "cell phones in the classroom" debate. <br />
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com1tag:blogger.com,1999:blog-3468015882172246111.post-68400625579340438862019-01-18T14:48:00.002-06:002019-01-18T14:48:40.606-06:00Geometry Project: Logo Design + FlipgridFor the past four years, I have had my geometry students complete a project as part of their semester 1 final exam. The task is for students to design a logo for a company of their choice. Students are graded using a rubric that calls for specific features to be embedded within their logo.<br />
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The minimum requirements:<br />
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<ul>
<li>There must be something that is reflected. The line of reflection must be identifiable. </li>
<li>There must be something that is rotated. The angle and center of rotation must be identified.</li>
<li>There must be two triangles that are congruent.</li>
<li>There must one set of parallel lines. Intersecting the lines is a transversal. At least two special angle pairs must be identified.</li>
</ul>
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Students are also scored on neatness, use of color, effort, and their sales pitch. </div>
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In past years, students would explain in writing where the required items were located and what type of company they would pitch their logo to. </div>
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This year, instead of writing their explanations, I had students create a video using Flipgrid. (<a href="https://markkreie.blogspot.com/2018/08/seesaw-flipgrid-great-tools-but.html" target="_blank">Read about our previous trials using Flipgrid and our attempt at climbing the SAMR model for technology integration.</a>) <b><u>Flipgrid was amazing for this task.</u></b> Students were asked to demonstrate on the video where each of the required items were found. Then they were asked to complete a brief sales pitch that would help sell the logo. I made sure that students were not able to view each other's submissions. That helped ease the pressure of performing in front of others.</div>
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When students wrote their explanations on paper (in past years), I would often find myself trying to make sense of what they were explaining. Occasionally I would have to ask a student for clarity. It was often a tedious process. <br />
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This year, the videos were very easy to assess. I didn't have to search through the logos, looking for things that were not clearly explained. The monotony of grading 75 projects was absent.<br />
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I wish I could post a video or two as an example, but I made it clear to all students that I would be the only person watching their videos. Instead, I will show a few examples of the logos themselves. See if you can spot the required elements in their designs.<br />
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-54916900618333962242019-01-17T00:17:00.000-06:002019-01-17T00:17:16.063-06:00The (In)Ability to Say "No"Confession #1:<br />
I love the National Basketball Association (NBA). Those who know me well know that I love just about anything related to basketball.<br />
<br />
Confession #2:<br />
I have a hard time saying "No" to things related to my job and career. Allow me to elaborate.<br />
<br />
As many of you know, teaching is much more than an 8:00 to 4:00 job. Planning, grading, emailing parents, etc. all require time. Moreover, keeping up to speed on the latest topics and innovations takes time. Most evenings [after my four kids are in bed, the dishes are clean, and the laundry is folded] I spend 1-2 hours skimming through blog posts, my Twitter feed, the Desmos Slack, etc., keeping my eyes open for ideas and resources that I can use in my classroom.<br />
<br />
Over the past five years, I've added a number of leadership roles at the district and state level to my plate. I'm humbled and honored to be viewed as a leader in the mathematics education field, and I love serving in leadership roles. Of course, each of these roles and commitments requires time and energy. Because time is a finite resource, the time committed to these roles equates to time sacrificed from other areas of life. For me, that often meant sacrificing time with my family.<br />
<br />
<br />
Back to the NBA for a minute...<br />
<br />
Last week while chauffeuring my kids around, I was listening to an NBA podcast hosted by Zach Lowe. Zach works for ESPN and is widely known as one of the best NBA writers / analysts in the world. His guest was his good friend and former boss, Bill Simmons. As Zach and Bill were wrapping up the podcast, this conversation took place:<br />
<br />
BS: How old is your daughter now?<br />
ZL: Almost four.<br />
BS: This is right when your job performance is going to get affected.<br />
ZL: Really?<br />
BS: It's gonna be great. I can't wait to watch.<br />
ZL: Why?<br />
BS: When they [children] hit four, now all of the sudden you've got recitals. They hit six and they start playing sports a little bit more and now on the weekends you're at a soccer game instead of watching Orlando / Philly. [FYI - Bill has a 14-year old and an 11-year old.]<br />
ZL: You know what? At a certain point you have to make an internal resolution where like, "That's good. That's okay. If your job performance slips a little bit because you have actual human being things to do, and they involve little children that you helped produce into the world, that's what it should be. That should happen."<br />
BS: You're preaching to the choir, my friend.<br />
<br />
<br />
Zach's analysis really struck home with me. This past year, I've learned to say "No" every now and then. In the past, I would felt as though I was not doing my best or I was letting people down. I've now made the internal resolution that Zach was referring to. <br />
<br />
Fear not -- my plate is still plenty full. Between serving on the SDCTM board, presenting at conferences, mentoring a student teacher, applying for the PAEMST award, getting ready to begin the NBCT process, serving as a virtual mathematics coach, and participating in a state leadership cohort, I've got plenty to do.<br />
<br />
<br />
So this blog post goes to all of educators out there who have filled their plates full. It's okay to say "No" once in a while. Don't lose sight of the most important things in life.<br />
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com5tag:blogger.com,1999:blog-3468015882172246111.post-19670762322788708062018-12-21T03:40:00.000-06:002019-01-03T22:39:17.274-06:00Giving Students Extra Information<br />
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{NOTE: This post will appear in the Winter 2018 edition of <i>Wahpe Woyaka, </i><a href="http://sdctm.org/publications.htm" target="_blank">SDCTM's quarterly newsletter</a>.}</div>
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<span style="text-indent: 0.5in;">In
Dan Meyer’s 2010 Ted Talk “</span><span class="MsoHyperlink" style="text-indent: 0.5in;"><a href="https://www.ted.com/talks/dan_meyer_math_curriculum_makeover/transcript">Math
Class Needs a Makeover</a></span><span style="text-indent: 0.5in;">”, Dan suggests that the types of problems
typically found in textbooks don’t require students to think critically due to
the amount of information given to students in the context of the problem.</span><span style="text-indent: 0.5in;"> </span><span style="text-indent: 0.5in;">Far too often students are given exactly the
information needed to solve a problem.</span><span style="text-indent: 0.5in;"> </span><span style="text-indent: 0.5in;">Consequently,
students come to believe that all pieces of given information must be used as
part of the solution-finding process.</span></div>
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<span style="font-style: normal;">The
following example was part of a set of practice problems for a lesson on
isosceles triangles found in a certain textbook.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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</w:wrap></v:imagedata></v:shape><span style="font-style: normal;">Students were asked to “find the
value of x”.<o:p></o:p></span></div>
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<span style="font-style: normal;"><o:p><br /></o:p></span></div>
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<span style="font-style: normal;">For
those of you who remember the converse of the base angles theorem for isosceles
triangles, you can see the problem gives students exactly enough information to
solve.<span style="mso-spacerun: yes;"> </span>{Set the two expressions equal to
one another and solve the resulting two step linear equation.}<span style="mso-spacerun: yes;"> </span>One might claim that a student could
correctly solve this problem by simply guessing the two expressions are equal
to each other without actually understanding the theorem.<o:p></o:p></span></div>
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<span style="font-style: normal;">I’m
not here to say that we should overload students with oodles of useless
information in a given problem.<span style="mso-spacerun: yes;"> </span>However,
by adding one or two additional pieces of information to this same problem, we
can deepen the level of thought that needs to be applied by students to solve
the problem.<o:p></o:p></span></div>
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<v:shape id="Picture_x0020_1" o:spid="_x0000_s1026" style="height: 135.1pt; left: 0; margin-left: 129.55pt; margin-top: 17.7pt; mso-height-percent: 0; mso-height-percent: 0; mso-height-relative: page; mso-position-horizontal-relative: text; mso-position-horizontal: absolute; mso-position-vertical-relative: text; mso-position-vertical: absolute; mso-width-percent: 0; mso-width-percent: 0; mso-width-relative: page; mso-wrap-distance-bottom: 0; mso-wrap-distance-left: 9pt; mso-wrap-distance-right: 9pt; mso-wrap-distance-top: 0; mso-wrap-style: square; position: absolute; text-align: left; visibility: visible; width: 190.1pt; z-index: -251656192;" type="#_x0000_t75">
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</v:imagedata></v:shape><span style="font-style: normal;">Here is the same problem as above,
only I added one piece of given information.<span style="mso-spacerun: yes;">
</span><o:p></o:p></span></div>
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<span style="font-style: normal;">I
invite you to think about the different misconceptions that this new problem
could identify versus the previous problem.<span style="mso-spacerun: yes;">
</span>{To be clear, the problem is still solved by setting 3x + 13 = 5x +2.}<span style="mso-spacerun: yes;"> </span>Two mistakes that my students made because of
the change:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "symbol"; font-style: normal;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";"> </span></span></span><!--[endif]--><span style="font-style: normal;">Set the wrong two expressions equal to each
other.<span style="mso-spacerun: yes;"> </span>{Ex: 3x + 13 = 2x + 35}<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "symbol"; font-style: normal;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";"> </span></span></span><!--[endif]--><span style="font-style: normal;">Set the sum of the three expressions equal to
180.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto;">
<span style="font-style: normal;">{3x + 13 + 5x + 2 + 4x + 16 = 180}<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-style: normal;"><span style="mso-tab-count: 1;"> </span>Additionally, I had a number of students solve the problem
correctly but ask “what are we supposed to do with the 4x + 16”.<o:p></o:p></span></div>
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<span style="font-style: normal;"><span style="mso-tab-count: 1;"> </span>By giving students information that is irrelevant to the
problem, we can raise the level of thinking done by students.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span style="font-style: normal;"><span style="mso-tab-count: 1;"> </span>[Side note: Dan offers a strategy to help students become
better at deciding what information is and is not important for a given
problem.<span style="mso-spacerun: yes;"> </span>I invite you to dig into his <span class="MsoHyperlink"><a href="http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/">3-ACT
tasks</a></span> for more information. <a href="http://www.watsonmath.com/2012/04/24/spreadsheet-of-dan-meyers-tasks-in-three-acts/" target="_blank">Here </a>and <a href="https://www.livebinders.com/play/play_or_edit?id=330579" target="_blank">here </a>as well.]<o:p></o:p></span></div>
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<span style="font-style: normal;"><span style="mso-tab-count: 1;"> </span><o:p></o:p></span><br />
<span style="font-style: normal;"><span style="mso-tab-count: 1;"><br /></span></span>
<span style="font-style: normal;"><span style="mso-tab-count: 1;"><br /></span></span>
<span style="font-style: normal;"><span style="mso-tab-count: 1;">UPDATE: In my original post, it was brought to my attention that my triangle was not accurate. I have attempted to fix the error and appreciate the feedback. Thanks @Teachmathtorr for helping me be a better teacher!</span></span></div>
<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-25481476761176433582018-11-03T01:02:00.001-05:002018-11-06T12:35:40.182-06:00NCTM - Kansas City Reflection<br />
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<span style="font-style: normal;">I thrilled to say that today
I achieved a professional goal that I had set for myself back in the summer of
2015.<span style="mso-spacerun: yes;"> </span>Today I presented at the NCTM regional
conference in Kansas City.<o:p></o:p></span></div>
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<span style="font-style: normal;">As I sit here tonight, I
wanted to take a moment to reflect and record my thoughts much like <a href="https://8ismyluckynumber.blogspot.com/2018/10/reflecting-on-my-1st-nctm-presentation.html?showComment=1538881484286#c2571133015644898905" target="_blank">Jennifer Fairbanks</a> did a few weeks ago.<span style="mso-spacerun: yes;"> </span>I found
Jennifer’s reflection and tips very helpful when preparing for this conference,
so thank you Jennifer.<span style="mso-spacerun: yes;"> </span>People helping
people…<o:p></o:p></span></div>
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<span style="font-style: normal;">The realization that I might
actually be a quality presenter at an NCTM conference came to last October when
I attended the <a href="https://markkreie.blogspot.com/2017/10/nctm-conference-orlando-reflection.html" target="_blank">NCTM regional in Orlando</a>.<span style="mso-spacerun: yes;">
</span>It was there where I gained the confidence and motivation to take action
toward being a presenter.<span style="mso-spacerun: yes;"> </span>I attended a
couple of sessions put on by Desmos Fellows and saw how powerful their
presentations were.<span style="mso-spacerun: yes;"> </span>I knew I could
present something on Desmos and it would be helpful to whoever attended.<span style="mso-spacerun: yes;"> </span>I noticed that Kansas City was hosting a
regional conference this year.<span style="mso-spacerun: yes;"> </span>Kansas
City is a short 6 hour drive from Brookings; I knew I wouldn’t find an NCTM regional conference
much closer anytime soon.<o:p></o:p></span></div>
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<span style="font-style: normal;">When the session proposal
window opened, there was a lot of buzz in the Desmos Slack about people planning
to attend the three regional conferences this fall.<span style="mso-spacerun: yes;"> </span>Fellow Jessica Breur (@BreurBreur) and I agreed to present
together and we decided to submit two proposals, with our fingers crossed at
least one would be accepted.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span style="font-style: normal;">One proposal, “<a href="http://bit.ly/NCTMKCDesmos" target="_blank">Facilitating Productive Classroom Conversations with Desmos Activities</a>,” was approved.<span style="mso-spacerun: yes;"> </span>I shared the news with Jessica and we were
excited.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span style="font-style: normal;">Jessica and I have both
presented a number of times and various conferences on this topic.<span style="mso-spacerun: yes;"> </span>We both had same idea of how the session
should run.<span style="mso-spacerun: yes;"> </span>I need to give Jessica a lot
of credit for taking the lead on the planning and preparation.<span style="mso-spacerun: yes;"> </span>We used an older presentation of hers as our
starting point and made appropriate adjustments to fit our needs.<span style="mso-spacerun: yes;"> </span>On the eve of our presentation, we met after
dinner to practice and made final tweaks. <o:p></o:p></span></div>
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<span style="font-style: normal;">Our presentation was
scheduled for 9:45 am this morning.<span style="mso-spacerun: yes;"> </span>I
arrived at the room plenty early.<span style="mso-spacerun: yes;"> </span>Jessica
arrived a few minutes later.<span style="mso-spacerun: yes;"> </span>Once the
session before ours ended, we headed into the room and set up.<span style="mso-spacerun: yes;"> </span>Jessica connected her computer to my phone’s
hotspot to ensure we had strong WiFi for our presentation. <o:p></o:p></span></div>
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<span style="font-style: normal;">Jessica and I had planned to
float around the room to introduce ourselves as people started to settle
in.<span style="mso-spacerun: yes;"> </span>Our goal was to get a feel for the
Desmos knowledge and experience in the room in case there was a need to adjust
our presentation at all.<span style="mso-spacerun: yes;"> </span>We correctly
assumed there would be a wide variety of users in attendance.<span style="mso-spacerun: yes;"> </span>As the room started to fill, we began to fail
at our goal of introducing ourselves to everyone.<span style="mso-spacerun: yes;"> </span>Soon every seat in the room was taken and
people were being turned away at the door.<span style="mso-spacerun: yes;">
</span><o:p></o:p></span></div>
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<span style="font-style: normal;">We began our presentation
with brief introductions and then jumped right into Marbleslides.<span style="mso-spacerun: yes;"> </span>We asked participants to team up with a neighbor
and to complete the activity.<span style="mso-spacerun: yes;"> </span>We soon
found out that the WiFi was going to struggle to support the 90+ users in the room.<span style="mso-spacerun: yes;"> </span>Some people started using their phones for
hotspots, while others simply tried the activity on their phones.<o:p></o:p></span></div>
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<span style="font-style: normal;">After about two minutes of
floating around the room and seeing a lot of people struggling to get into the
activity, we decided to go off script.<span style="mso-spacerun: yes;">
</span>Our original plan was for participants to take on the role of a student and
complete the activity in pairs.<span style="mso-spacerun: yes;"> </span>Instead,
I went into the activity as a student and talked them through what the students
would be doing in the activity.<span style="mso-spacerun: yes;"> </span>I also
modeled what a teacher would be seeing on the dashboard and showed off some of
the conversations tools.<span style="mso-spacerun: yes;"> </span>We were able to
answer a few questions from the audience before moving on.<o:p></o:p></span></div>
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<span style="font-style: normal;">Jessica then led the next piece
focused on the Pool Border Problem.<span style="mso-spacerun: yes;"> </span>It
is such a great activity to use to generate a variety of responses.<span style="mso-spacerun: yes;"> </span>Jessica did a superb job of demonstrating how
to use Snapshots and modeled so many great teacher moves.<o:p></o:p></span></div>
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<span style="font-style: normal;">We then had participants
play Polygraph: Quadratics for a few minutes.<span style="mso-spacerun: yes;">
</span>While walking around the room, I could sense the enjoyment from the participants.<span style="mso-spacerun: yes;"> </span>Polygraph is a pretty simple activity to
understand and when have a room full of math teachers and ask them to play with
math, the results tend to be pretty solid.<o:p></o:p></span></div>
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<span style="font-style: normal;">Jessica and I had a Card
Sort ready to unleash if time allowed for it.<span style="mso-spacerun: yes;">
</span>Unfortunately, largely in part thanks to the WiFi issues, we were behind
schedule already and decided to bypass the Card Sort activity.<o:p></o:p></span></div>
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<span style="font-style: normal;">Next on our agenda was to
give an overview of the teacher.desmos.com site.<span style="mso-spacerun: yes;"> </span>Jessica handled the discussion of how to
search for an activity and how to navigate around the teacher site.<span style="mso-spacerun: yes;"> </span>I spoke on what it looks like when you go to the
activity screen and how to preview an activity and generate a classroom
code.<span style="mso-spacerun: yes;"> </span>There was a lot of information presented
in a short amount of time; I wish we had a bit more time to talk in more detail
about those features.<o:p></o:p></span></div>
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<span style="font-style: normal;">Lastly, we gave participants
about 10 minutes to create a Desmos account if they didn’t already have one,
browse around the teacher site, and search for an activity they could take back
into their classroom.<span style="mso-spacerun: yes;"> </span>Some participants
headed out the door to their next session (there were some overlapping times
for sessions).<span style="mso-spacerun: yes;"> </span>We were able to answer a
lot of questions on an individual basis.<span style="mso-spacerun: yes;">
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<span style="font-style: normal;">Overall, I thought the
presentation went very well.<span style="mso-spacerun: yes;"> </span>I hope the
people who attended were able to take something away from it.<span style="mso-spacerun: yes;"> </span>I really hope those who had not heard about
the Desmos activities will take a chance and use one in their classroom.<span style="mso-spacerun: yes;"> </span>Their students will thank them if they do.<o:p></o:p></span></div>
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<span style="font-style: normal;">A couple of quick shout outs.<span style="mso-spacerun: yes;"> </span>First, thanks to Joel (@</span>joelbezaire), Hedge (@approx_normal), and Annie (@mrsforest) for
attending our session and for the positive vibes on Twitter. Second, shout out to Jessica for being a
superb co-presenter. It was great
working with you. Third, thank you to the administration at Brookings School District for supporting the professional growth of your staff and allowing me professional leave to attend these conferences. I learn a lot while at these conferences and always bring back something new for my students.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4pxu1x8xX3crLdEiFaijn0ddETWP7KzV9PV9_mZe0uNF3r7-TJ3EMAzs25a5AKZDGoColSMc7EPPgkdRi0TNvxzyS9PhewsCdIphl8tB2ex2lYKQTgLAVXSqS2vTwdxy1LdKCjocDuqc/s1600/hedge.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="845" data-original-width="725" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4pxu1x8xX3crLdEiFaijn0ddETWP7KzV9PV9_mZe0uNF3r7-TJ3EMAzs25a5AKZDGoColSMc7EPPgkdRi0TNvxzyS9PhewsCdIphl8tB2ex2lYKQTgLAVXSqS2vTwdxy1LdKCjocDuqc/s400/hedge.PNG" width="342" /></a></div>
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<span style="font-style: normal;">Finally, a shout out to my
wife Stephanie and my kids for allowing me to chase my dreams.<span style="mso-spacerun: yes;"> </span>I’m no SuperDad, but I know it’s not easy
when I leave town for a few days.<span style="mso-spacerun: yes;"> </span>I love
you all!<o:p></o:p></span></div>
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com1tag:blogger.com,1999:blog-3468015882172246111.post-87282875059146883152018-10-06T20:08:00.001-05:002018-10-06T20:08:45.014-05:00District PD Day: Thoughts and Lingering QuestionsEach year, on the first Friday in October, my school district has an all-staff professional development day. Two years ago, David LaRose led our staff into the realm of PLCs. After that day, all staff members were assigned to a PLC team. Each PLC team meets once a month for 75 minutes.<div>
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[Last October, Lee Jenkins presented on continuous improvement and something called <a href="http://markkreie.blogspot.com/2018/01/something-new-for-2018-from-l-to-j.html" target="_blank">"L to J"</a>.]</div>
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This year, my district brought in Jack Baldermann to help provide more clarity and direction for our PLC teams. Each PLC team has a designated "leader", and the PLC leaders met with Jack on Thursday afternoon to help set the stage for Friday's all-staff training. I was part of the "leadership" team who met the Jack on Thursday. </div>
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The two days were quite good and there is a lot stewing around in my head right now. My takeaways:</div>
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<li>PLC teams need to have NORMS, and not friendly norms that help meetings run efficiently. Rather, norms that are serious about increasing student achievement. Norms that call for data analysis and actions taken based on that data.</li>
<li>Standards needs need to be unpacked and essential understandings need to be identified. Essential learning targets need to be written in student-friendly "I can..." language. [Good news - we have already done that work with L to J.]</li>
<li>Assessments need to be aligned to learning targets and we should be tracking achievement data for each student, according to each learning target.</li>
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Mr. Baldermann shared an example of what the math department in his school had done that led to large achievement gains. The math teachers switched to a standards-based grading system. Hold on a second... they switched to a <strike>standards-based</strike> learning target based grading system.</div>
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I had a bit of an epiphany. Back in 2013-14, I did my master's degree action research on standards-based grading (SBG). I implemented a SBG for my algebra 2 classes. I really liked the idea and concept of SBG, but struggled with two things. A) I had aligned my curriculum to the Common Core Standards for Mathematics, and some standards were much more vast than others. Certain standards were ones that were covered over multiple years and classes; I never felt great about assigning a grade for those standards, knowing that there was more to the standard than what I was assessing. B) As a high school teacher, I was still required to report an A/B/C/D/F letter grade and percentage for high school graduation and GPA purposes. I developed a grade conversion system that took each student's standards-based scores and converted them into a percentage grade. To be expected, the system had its flaws but I knew no other way at the time.</div>
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The epiphany was this: I shouldn't use a STANDARDS-based grading system, but rather a LEARNING TARGET-based system. All of my concerns about (A) above would be removed!</div>
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The work ahead will be challenging and time-consuming. But I am excited to dip my toe back into the "learning target-based" grading system. I really wish our professional development day was in August, before the start of the school year. It's challenging to try to implement radical changes on the fly once the school year is underway. This may take me a while to develop and prepare anyway. At minimum, we will have a new system in place for next year.</div>
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I still need to write a post about the changes we made in our geometry curriculum this year. Look for that soon! </div>
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Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-8862403685313695692018-08-28T01:15:00.001-05:002018-08-28T01:20:23.581-05:00Seesaw & Flipgrid: Great tools, BUT...My 17th year of teaching kicked off last week with a few "Back to School" days and our first full day with students on Friday.<br />
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With a district-wide push to increase student engagement and student choice, my geometry co-teacher Jarrod and I made some changes in the delivery and assessment of our curriculum. [Expect a blog post soon highlighting some of the deeper details...]<br />
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We also have plans to integrate innovative tech tools with the goal of climbing the <a href="https://en.wikiversity.org/wiki/Instructional_design/SAMR_Model/What_is_the_SAMR_Model%3F">SAMR model</a> in order to enhance student learning. Two of the tech tools we plan to use this year are Seesaw and Flipgrid.<br />
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To give students an introduction to these tools, we decided to use the tools to have students introduce themselves. In the past, as a way to get to know students, we would have students fill out the following paper:<br />
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Instead of that, this year we had students complete the following prompts in Seesaw and Flipgrid.</div>
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In Seesaw:</div>
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In Flipgrid:</div>
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We spent today getting students logged into Seesaw and Flipgrid and had them work on completing the two tasks shown above. Our thoughts: tech integration = high; student engagement = high; student choice = low, but students will have the choice to use these tools throughout the year and need to know how to use them in case they so choose to do so.</div>
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While some students completely loved the tasks, Jarrod and I were both quite surprised at how many students were hesitant to complete these two tasks. We had some students take their selfie of just their eyes and up while others used their descriptive words and text to cover their faces. Some students asked if they could wait to complete the tasks at home; they wanted to think more about what they were going to say and requested a quieter setting while recording.</div>
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In hindsight, we shouldn't have been so surprised at the hesitation from so many students. After all, we have a large number of freshmen in our classes. This was just their second day of high school, which can be an overwhelming place. Yes, we witness many of our students taking selfies and sending them out on Snapchat and posting to Instagram. A major difference is that when doing that, students are sending only to those who they choose to send to, versus an entire class.</div>
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Next year, we may make a minor change to the tasks. In Seesaw, we have it set so that a student submission does not get posted to the class journal unless we (as teachers) approve the submission. We can simply tell students that their submissions will not be posted for all to see, only Jarrod and myself will be able to see them. I'm not sure if there is a similar option in Flipgrid, but it is something we'll think more about next year.</div>
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-2195080180057260852018-05-23T15:16:00.000-05:002018-05-24T08:25:21.284-05:00L to J -- Year 1 ReflectionI just wrapped up my first semester of implementing a strategy called "L to J". (Read more about how and why I implemented it <a href="http://markkreie.blogspot.com/2018/01/something-new-for-2018-from-l-to-j.html">here</a>.) It's now time to reflect back on how well or not-so-well it went.<br />
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<b><u>Feedback from Students:</u></b><br />
As part of the "Mr. Kreie Report Card" I ask students to complete (S/O to <a href="http://www.classroomchef.com/dessert/">The Classroom Chef</a>), students were asked the following question and were able to answer anonymously.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLCCkdfbfxMXH1ptHbQhaIdbDSzc2OPk6G6fMxPAtPln_PmzsO77ktEB6stP67Fe2RggCMWJBGOH2_nUjlVhRubcjPUeouPMvPO3RJK0rpmaahGnQzYXDSRl34JmAFZRZar-pJ9V8rndk/s1600/L+to+J+Q.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="160" data-original-width="721" height="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLCCkdfbfxMXH1ptHbQhaIdbDSzc2OPk6G6fMxPAtPln_PmzsO77ktEB6stP67Fe2RggCMWJBGOH2_nUjlVhRubcjPUeouPMvPO3RJK0rpmaahGnQzYXDSRl34JmAFZRZar-pJ9V8rndk/s640/L+to+J+Q.PNG" width="640" /></a></div>
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Their responses:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDhdzXQE798Bz20cQY7N_zEbTy56MB6jp3Hon6IcQgT3t15NRPdU2vgvgdt4Xy0iKQekUjlYvODqndGQQfvad1ImsR8IauamlNNUdMD7Dsbr3SRs4-X4GzpuaqG5419Z0iDatHdVkuSME/s1600/L+to+J.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="331" data-original-width="720" height="294" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDhdzXQE798Bz20cQY7N_zEbTy56MB6jp3Hon6IcQgT3t15NRPdU2vgvgdt4Xy0iKQekUjlYvODqndGQQfvad1ImsR8IauamlNNUdMD7Dsbr3SRs4-X4GzpuaqG5419Z0iDatHdVkuSME/s640/L+to+J.PNG" width="640" /></a></div>
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Further, I asked students for more open ended feedback.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgrF6-n5NHh4B0eXNq7bnpyANpFWxpkbGIymqZ1WZX9gbpwiC0YMZiX_wJxtjS3HXZk6Vc3OsJ3emfb_gNy-YICDWa3fE2esXcSaXG6xAtWrFLXNN9APGmGAHWr5l7bihpiPKHc5gSQYs/s1600/L+to+J+Open.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="129" data-original-width="744" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgrF6-n5NHh4B0eXNq7bnpyANpFWxpkbGIymqZ1WZX9gbpwiC0YMZiX_wJxtjS3HXZk6Vc3OsJ3emfb_gNy-YICDWa3fE2esXcSaXG6xAtWrFLXNN9APGmGAHWr5l7bihpiPKHc5gSQYs/s640/L+to+J+Open.PNG" width="640" /></a></div>
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Some positive quotes from students:</div>
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<ul>
<li>"It helped me remember stuff from early in the year and how to do things from first semester."</li>
<li>"I think it was good. The fact that we kept reviewing the same problems and slowly learning the math later in the year really helped me. Plus, once we got to our all time best that was really fun."</li>
<li>"I think it helped to review the learning targets throughout the year and that it should be used again next year."</li>
<li>"I loved it. It was a great improvement in class."</li>
<li>"I think that L to J was kinda fun. I found it a little frustrating when we didn't know the answer, but that was kinda the point. I think we should do it next year."</li>
</ul>
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Some not-so-positive quotes from students:<br />
<ul>
<li>"I did not really like L to J. It got really boring."</li>
<li>"It was the biggest waste of time. Get rid of it."</li>
</ul>
<br />
And some helpful feedback from students:<br />
<br />
<ul>
<li>"i liked it but i wish it only applied to the semester we were currently in"</li>
<li>"It sometimes made me feel stupid because there were somethings that i didnt know that i probable should have. it was good but not my favorite"</li>
<li>"L to J was fun but a lot of people cheat and say they get 8's, 9's, and 10's when they really get 2's, 3's and 4's. Peer pressure is a problem."</li>
<li>"You should do it again next year but find a new way of choosing questions so we don't repeat the same ones over and over. Maybe you should do it once a month instead of once a week also."</li>
</ul>
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<br />
A quick note about the cheating comment:<br />
There were times that students would see the question and be whispering to each other. I was not very strict during these quizzes because I knew that they are not graded. I can do better by not allowing students to converse during the quiz. However, I feel that sometimes valuable learning can take place within those conversations.<br />
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<b><u>Student Achievement:</u></b><br />
Many students showed growth as the semester moved along. Here are a few examples of two student's progress throughout the semester:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhG0OlER3iFBWD6XDrCySd9reDwxET9Ekq2C-jBJAMfkRjHal24yVrOPVSRZEQAMnRT8rdq2Np_bBnytTOypemkQBcIYHwDZdcVCEtbSVDyOANIz94YVYeTWzzmGf16CK1nQj5iWh4SiMY/s1600/IMG_2888.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1270" data-original-width="1600" height="317" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhG0OlER3iFBWD6XDrCySd9reDwxET9Ekq2C-jBJAMfkRjHal24yVrOPVSRZEQAMnRT8rdq2Np_bBnytTOypemkQBcIYHwDZdcVCEtbSVDyOANIz94YVYeTWzzmGf16CK1nQj5iWh4SiMY/s400/IMG_2888.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Student A</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG9wwBmIwW48FBjgx6pT50xVNytTz87eXM9DLeJZUZNSGPSsUH2OFUkeD-XBtTK4ONrgi3Z_w4mHtpOfKEPHNYOr1EG2TjH5FH_rI3UAxxauykoltCCB0tmVWR-L0_0gdD_0QJBJP3xvM/s1600/IMG_2889.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1355" data-original-width="1600" height="338" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG9wwBmIwW48FBjgx6pT50xVNytTz87eXM9DLeJZUZNSGPSsUH2OFUkeD-XBtTK4ONrgi3Z_w4mHtpOfKEPHNYOr1EG2TjH5FH_rI3UAxxauykoltCCB0tmVWR-L0_0gdD_0QJBJP3xvM/s400/IMG_2889.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Student B</td></tr>
</tbody></table>
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As you can see, student B scored a 10 the very first week. It just so happened that in this particular student's class, all ten of the first week's questions were from the first semester. The second week, however, a number of questions were from the second semester. This student's scored dropped from a 10 to a 6, largely due to the randomness of the questions.<br />
<br />
<br />
<b><u>Class Achievement:</u></b><br />
Each of my classes achieved at least one all-time best after setting the baseline during the first week. The class shown below set only one all time best. Two factors really influenced the goal of attaining an all-time best each week:<br />
1) How many students are absent the day of the quiz, and<br />
2) What questions are selected.<br />
<br />
Having only one student absent really hurts the chances of achieving an all-time best. There were some days that I was missing four or five students in a given section (such as week 9 for this class).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_FZXWbx6Wjh6CRwyB0avuMDhQGWTAi3ivK5WuzhrtJWeQioWAlVzv2FfNKUH4eWy7IZd6X-Q8asOICFrcRnevWgHxBinYUojIrEoG182O6hZ_ecrJA67qSEwOre62yH96i4zEiJ4iQHY/s1600/Class+Run.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_FZXWbx6Wjh6CRwyB0avuMDhQGWTAi3ivK5WuzhrtJWeQioWAlVzv2FfNKUH4eWy7IZd6X-Q8asOICFrcRnevWgHxBinYUojIrEoG182O6hZ_ecrJA67qSEwOre62yH96i4zEiJ4iQHY/s640/Class+Run.JPG" width="480" /></a></div>
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Students did show a very strong interest in the overall achievement of the class each week and showed genuine excitement when an all-time best was attained.<br />
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The celebrations for all-time bests were a bit challenging for students to think of and agree on. Students often tried negotiating for <i>rewards </i>-- extra credit, food in class, skipping homework assignments, etc. I need to do a better job next year of selling the excitement of a celebration.<br />
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This reward that one class chose did draw some attention around school for a day...<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs0GSXMmx7dzhQ1gMxm7V11TU2x2vo5yw7wcO_8cJehKB-9Xis42UAuMEFCDn7UO2U56Kw_W499hUbW6ndX1xBDiX2z1Jct_1t9aoIowKgbjuUgCEgCnm_bu5kmlmIKLhUum9zaYZ4Mb4/s1600/2018-03-20+08.08.35.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1569" data-original-width="1600" height="391" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs0GSXMmx7dzhQ1gMxm7V11TU2x2vo5yw7wcO_8cJehKB-9Xis42UAuMEFCDn7UO2U56Kw_W499hUbW6ndX1xBDiX2z1Jct_1t9aoIowKgbjuUgCEgCnm_bu5kmlmIKLhUum9zaYZ4Mb4/s400/2018-03-20+08.08.35.jpg" width="400" /></a></div>
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<b><u>Final Thoughts:</u></b><br />
I did enjoy doing L to J as something new this semester and I plan to do it for the full year next year. It took about 25 minutes do complete each week, which led to us not covering as many lessons as we have in the past. {Some weeks we simply didn't have time to fit the quiz in, as evident in the missing weeks on the graphs above. A few of those missing weeks were due to snow days and shortened weeks for spring break.}<br />
<br />
I believe the benefit of the spiral review and "No Permission to Forget" outweigh the cost of skipping a few lessons along the way. And most importantly, more than 80% of students said they liked doing L to J this year. I think that's a pretty high success rate.<br />
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-53326385768168321002018-04-28T22:50:00.000-05:002018-04-28T22:50:40.655-05:003 ACT TasksAs I am browsing through my previous blog posts, it appears as though I have never blogged about 3-ACT tasks. I've been using these types of activities for the past five or six years. I first found out about them in <a href="http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/">Dan Meyer's blog</a> back in 2011. <br />
<br />
A large majority of the 3 ACT tasks I use come from <a href="https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0">Dan</a> or <a href="https://docs.google.com/spreadsheets/d/19sms4MpuAOO71o4qFPJyVKK-OGLnNegMgSL6WAwIdb8/edit">Andrew Stadel</a> (follow the links for a list of their activities). There are quite a few really good ones to use this time of year in geometry, including Andrew's <a href="http://www.101qs.com/518">File Cabinet</a> activity that I used in Applied Geometry class on Friday.<br />
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I don't have time to get into the fine details, but let's just say that the activity was a hit for my class of student who usually don't get too excited about doing math each day. I wasn't fully prepared to record a video, but as we started watching Act 3, I could sense the excitement building. <a href="https://drive.google.com/file/d/1I8EA5cJ5ubXP0N1T1JPlhQcBrzYJgk-L/view?usp=sharing">Here is what I was able to record</a>.<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwRRGf80ftJRFyYfTKkHZv0R1WLQo_W2Ipvq1-9b9anrWrWzcoTzs3lETpAzR4rMZ-j89XhRKOnWrlMYSAqFA' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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Needless to say, it was a fun day in class. Thanks, Mr. Stadel, for the awesome activity!<br />
<br />
(Last summer, I imported this 3 ACT activity into Desmos. If you'd like the Desmos activity, here you go: <a href="https://teacher.desmos.com/activitybuilder/custom/5981dbdb67136c40b3e03053">3-ACT File Cabinet Desmos</a>.)<br />
<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-69909778078085586092018-04-10T23:26:00.002-05:002018-04-10T23:26:48.332-05:00When Conceptual Understanding Fails... My Dilemma with Special Right TrianglesI started writing this blog post over a week ago and have realized that I can't give it enough attention until this summer. So, I am going to post what I have thus far and resume this summer after a little more thought and with a little more time.<br />
<br />
**WRITTEN OVER A WEEK AGO**<br />
I want my students to leave geometry with a strong understanding of the two special right triangles (45-45-90 & 30-60-90). I know that the two triangles are foundational when it comes to the unit circle and trigonometric functions & their graphs. I also strive to connect as many concepts together in my lessons as I can; I believe those connections are critical and lead to true conceptual understanding.<br />
<br />
This past year, here is how I approached teaching the section on special right triangles.<br />
For the record, my learning target for these lessons are:<br />
<ul>
<li>I can derive and apply the properties of special right
triangles.</li>
</ul>
<br />
<br />
On day 1, students worked in pairs with their elbow partner to complete this task, which was handed out on paper:<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijxoo2fZQ9Twwg-PqWblI9Br19mOzXGcIyUyYZ1lt4UM1ROE22zi3Tk-B4b7reo_SkMDpvSR4rNeQmmqce2YspfUsymactw9d0uvv77itmP1uzjqvMRw8BFi1wAjd63bdH-ynzB2MWLL0/s1600/45-45.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="564" data-original-width="639" height="282" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijxoo2fZQ9Twwg-PqWblI9Br19mOzXGcIyUyYZ1lt4UM1ROE22zi3Tk-B4b7reo_SkMDpvSR4rNeQmmqce2YspfUsymactw9d0uvv77itmP1uzjqvMRw8BFi1wAjd63bdH-ynzB2MWLL0/s320/45-45.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Task: Find the length of the diagonal. <br />
Express answer as a decimal rounded to the nearest hundredth and a radical in simplest form.</td></tr>
</tbody></table>
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Each group had a different side length on their square. Groups had sides ranging from 1 to 12. No two groups had the same square.<br />
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At the same time, I handed each student the following table on a full sheet of paper:<br />
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Students have no problems identifying the shape as a square. Groups had very little problem finding the diagonal length. We had reviewed how to simplify basic radical expressions the previous week, so very few groups struggled with that. As I roamed around the room, I made sure each group had the correct answer and had found correct place to fill their answer into the table. After I confirmed their answer was correct, I invited one person from the pair to go to the Smart Board and fill in their row of the table.<br />
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As students filled in the table on the Smart Board, I asked that each student fill in the table on their paper. After about three rows were filled in, I could hear rumblings around the room about a pattern students were seeing. When all pairs had shared their answer, the table looked something like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSzzR2yYKtz-1_sxZrql4OHJfAsaDcZtayMKCfCvkL3fz3mSnZh7nffqsuqw-MkIV_jIJrfDKkfPX5FGavWqtE7PlqhsGIKN44k5T5h8rqr1j0Vej_s-rJNHcD7NZ75egDhPHzEuoH54M/s1600/45+Table+Complete.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="483" data-original-width="393" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSzzR2yYKtz-1_sxZrql4OHJfAsaDcZtayMKCfCvkL3fz3mSnZh7nffqsuqw-MkIV_jIJrfDKkfPX5FGavWqtE7PlqhsGIKN44k5T5h8rqr1j0Vej_s-rJNHcD7NZ75egDhPHzEuoH54M/s320/45+Table+Complete.png" width="260" /></a></div>
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None of my classes had more than 22 students this day, so the last row was blank each hour. At this point, I lead a little discussion about what we're trying to derive.<br />
<br />
I start by having students share with their partner what they think should go in the last row our table. Again, this patterns is not hard to see, so I hear a lot of "twelve root 2" being whispered. I call on a volunteer to share and ask to explain their thinking.<br />
<br />
I then go to the wipe board that hangs adjacent to my Smart Board and talk briefly about what it is exactly that we're doing today. I will draw a right isosceles triangle on the board and ask students to tell me what they know about the angles. I then introduce the term "45-45-90 triangle". I remind them that because each group's triangle was a 45-45-90 triangle, all of the triangles we are working with are similar via Angle-Angle. I will put a random, much larger side length on the leg and again ask them to share with their partner what they think the length of the hypotenuse is.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRMmTLnWzpT4QNNSzg4ywvnAgUZWc01h8lfQ_O7uveiKGJlPgV7SgAOIFRiqkZISuKf0JVBWEXfVffd8G-o_3R44t_p47FOEfwCcE1ped31QtRjN-z8Qzor7_p_i7TMVBO0YXh_CPHE_0/s1600/45+Extension.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="518" data-original-width="523" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRMmTLnWzpT4QNNSzg4ywvnAgUZWc01h8lfQ_O7uveiKGJlPgV7SgAOIFRiqkZISuKf0JVBWEXfVffd8G-o_3R44t_p47FOEfwCcE1ped31QtRjN-z8Qzor7_p_i7TMVBO0YXh_CPHE_0/s200/45+Extension.png" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Tell your partner what you think the value of x is.</td></tr>
</tbody></table>
Again, I hear a lot of "eighty root two" whispered between partners.<br />
<br />
At this point, I ask for someone to summarize the relationship between the lengths of the leg and the hypotenuse. The response I hear is "the hypotenuse is the leg times the square root of two". I write the relationship on the board and ask students to write it on the sheet with their tables.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic3cz3ZFZ352g-HO0bECGI7w9rAohU_LJgtRHPHV-uVf_J2MMJl9RY-_GmARaNRzDyLP7Mft46dMSTZDvZS-eSmebmHjSkJZ0zUSyoFSWPe1IqmbySDj9W0lItATjiyivlBb_m-SiVaN4/s1600/45+Rule.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="52" data-original-width="380" height="43" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic3cz3ZFZ352g-HO0bECGI7w9rAohU_LJgtRHPHV-uVf_J2MMJl9RY-_GmARaNRzDyLP7Mft46dMSTZDvZS-eSmebmHjSkJZ0zUSyoFSWPe1IqmbySDj9W0lItATjiyivlBb_m-SiVaN4/s320/45+Rule.png" width="320" /></a></div>
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I will ask the group that had the leg of length 1 to share what they found for the decimal value of the hypotenuse. They respond with "1.41". I will mention that the rule we derived is saying that the hypotenuse is always about 1.41 times as long as the leg (on a 45-45-90 triangle). I remind students that each group used the Pythagorean Theorem to find the value of the hypotenuse, and that they can always fall back on that process if they would happen to forget the rule we just derived.<br />
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That whole process takes about 15 minutes, which leaves about 30 minutes remaining for the next part of the lesson.<br />
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I ask groups to turn the paper with their square over and draw an isosceles right triangle on the back. Then they are to take the value that was their square side and label the hypotenuse of their triangle the same value. (So the group that had the square with side length of 4 from above would now have this triangle.)<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9t6WnU9NtiQ2xoKCcGY6v3um0UQY9ZWrn8-sLNw2Sn5kJkmQkVx0vXo6ix2KgDO7DKhddI06zzMxcpjMisxHuGhZmyDmw14mi0wGjG0zNDKIgMdNdX-YldunMVqBeYDHD2u2IfVN5MFI/s1600/45+Hyp.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="522" data-original-width="525" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9t6WnU9NtiQ2xoKCcGY6v3um0UQY9ZWrn8-sLNw2Sn5kJkmQkVx0vXo6ix2KgDO7DKhddI06zzMxcpjMisxHuGhZmyDmw14mi0wGjG0zNDKIgMdNdX-YldunMVqBeYDHD2u2IfVN5MFI/s320/45+Hyp.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Find the value of x.<br />
Express your answer as a radical in simplest form.</td></tr>
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I also have this table included on the back of the paper that has the previous table:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnHqka1Qp8Z8bzSHu-9wn1ezku4mB6pm7SrISBESjGquGfgrJ1yvCWtx5oPtZr_ZXty5YwRGS7TMmfSjvCqZqktZlb7swrInBrRZyOMPSB8NP4ZbgQ2GU8g4EmjLK6Hmqo7NrDix9-Kjg/s1600/Table.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="520" data-original-width="395" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnHqka1Qp8Z8bzSHu-9wn1ezku4mB6pm7SrISBESjGquGfgrJ1yvCWtx5oPtZr_ZXty5YwRGS7TMmfSjvCqZqktZlb7swrInBrRZyOMPSB8NP4ZbgQ2GU8g4EmjLK6Hmqo7NrDix9-Kjg/s320/Table.png" width="243" /></a></div>
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At this point, student thinking typically takes one of two paths. Some groups will use the rule that we had previously derived and come up with this answer:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjelJkSdeyuZFc7CsGBRuJponp9Fcys1Qv3615mQCWZ5P7M1WwaSTC1mQuxDJnAfIRYCMRX7XoAb6tc9GggThzXUtT3pXVkFVWLbWoB05adqFl1435r6RMXaTBxQ9VDPXzeS_OCCQcoPK8/s1600/45+divide.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="120" data-original-width="159" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjelJkSdeyuZFc7CsGBRuJponp9Fcys1Qv3615mQCWZ5P7M1WwaSTC1mQuxDJnAfIRYCMRX7XoAb6tc9GggThzXUtT3pXVkFVWLbWoB05adqFl1435r6RMXaTBxQ9VDPXzeS_OCCQcoPK8/s1600/45+divide.png" /></a></div>
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Or, they will use the Pythagorean Theorem and get something along these lines (with sometimes a little guidance):</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMu8gAStpNSK2pQxydz5nZU0avA43baFA5MA1Fpl0rrBEuYbO1QoegNPg2-SHkXKLHNTLv7R_yUmeMsrD1pqZzxRrDTLnbNuAVYRBEz4JZq0RD5tHSnZjb1Gykh_bKsYu3_YZCRSjW-DU/s1600/45+PT.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="196" data-original-width="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMu8gAStpNSK2pQxydz5nZU0avA43baFA5MA1Fpl0rrBEuYbO1QoegNPg2-SHkXKLHNTLv7R_yUmeMsrD1pqZzxRrDTLnbNuAVYRBEz4JZq0RD5tHSnZjb1Gykh_bKsYu3_YZCRSjW-DU/s1600/45+PT.png" /></a></div>
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Once again, I floated around to make sure groups are getting one of the two answers above and are filling in their table correctly. After I confirmed their answer was correct, I invite one person from the pair to go to the Smart Board and fill in their row of the table.</div>
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Each hour, I saw a mixture of solution methods and our class table looked something like this:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtMjnzN4CHaEOE7VQ_TYP0A5oNX5kHI_awVfaXRPPyRWjEAjsbek3FD7jf81obhA7qulei5lU1OxVHYjyS98hlBE65J_e9xugmcMipxBy8LzGDacNSZFMZ0zqDqwH7snm-gskq_9gD3OE/s1600/45+PT+table.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="479" data-original-width="389" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtMjnzN4CHaEOE7VQ_TYP0A5oNX5kHI_awVfaXRPPyRWjEAjsbek3FD7jf81obhA7qulei5lU1OxVHYjyS98hlBE65J_e9xugmcMipxBy8LzGDacNSZFMZ0zqDqwH7snm-gskq_9gD3OE/s320/45+PT+table.png" width="259" /></a></div>
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Prior to this lesson, we hadn't reviewed how to rationalize the denominator. I know students see the process briefly in algebra 1, but rarely does anyone remember it. I took the next five minutes and led a discussion about why "simplest form" doesn't include a radical in the denominator and how we can manipulate these radical expressions and rationalize the denominator. (There is a good explanation on <a href="http://www.coolmath.com/prealgebra/14-intro-to-radicals/06-radicals-rationalizing-the-denominator-01-83">coolmath.com</a> if you're curious.) </div>
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At the conclusion of the discussion, each hour had a table that now looked like this:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9lUkuTIYii5qDoZLx-Hva-_FJuBkp_iElsGPK77bfW6wVaP9xrWmKQrg579EK4pechyphenhyphenxW-b04o3fxzUzdZcY2YeK3uof24KuLoQcCQDhVto5AFbzNvmo8WbbR20dRqJSdA61jGQ7KThg/s1600/45+Complete.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="530" data-original-width="397" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9lUkuTIYii5qDoZLx-Hva-_FJuBkp_iElsGPK77bfW6wVaP9xrWmKQrg579EK4pechyphenhyphenxW-b04o3fxzUzdZcY2YeK3uof24KuLoQcCQDhVto5AFbzNvmo8WbbR20dRqJSdA61jGQ7KThg/s320/45+Complete.png" width="239" /></a></div>
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With the expressions in this form, students now had no problem detecting the pattern to our expressions. I then ask students to generalize the patterns they see, and we arrive at the following two equations:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIb_viQVADBXhoaGQyrhvIdGkk33BIuIicFKWSFweuvdmQgyiAGAQKnRinOlwLxuo5mCziIos4-c4c3r-fEnKiWO2XMgvtkhZLVf4OFDdnTQF8j7wBN3l2DlaE2aPD35W0Py6H2n2c4qc/s1600/Leg+rule.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="254" data-original-width="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIb_viQVADBXhoaGQyrhvIdGkk33BIuIicFKWSFweuvdmQgyiAGAQKnRinOlwLxuo5mCziIos4-c4c3r-fEnKiWO2XMgvtkhZLVf4OFDdnTQF8j7wBN3l2DlaE2aPD35W0Py6H2n2c4qc/s1600/Leg+rule.png" /></a></div>
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(Side mini-rant: When will mathematicians decide that it's okay to leave a radical in the denominator? I vote now. Each year I have students look at me funny when I try to sell them the idea that three root two divided by two is simpler than three divided by root 2. The simplification rules are extremely outdated... we have calculators now if we should happen to want to find a decimal approximation of these expressions.)</div>
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This concludes the lesson. Students have a homework assignment that I post online that isn't due for a few days later since the assignment also includes 30-60-90 triangles.</div>
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**END OF MY ORIGINAL POST**</div>
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The next day, we do a similar exercise to derive the rules for a 30-60-90 triangle. Students get some practice working with these rules when they complete the homework, and we assess with a quiz a few days later.</div>
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Here is my dilemma and questions for the audience:</div>
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One of the quiz questions is to find the missing variables in the diagram below. Many students did well on this question, but I had a handful of students who claimed y = 8 and x = 4 root 3. The error the students made was they applied the wrong rule. But what I struggle with is the idea that these same students would have done just fine with this question prior to us having our lessons on special right triangles. We had previously learned about isosceles triangles and the Base Angle Theorem Converse. If they were to analyze the triangle and notice that the two acute angle were congruent, they would have concluded that the legs were also congruent. Then, with two legs known, the Pythagorean Theorem would have led them home.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6Xb6yQFf-UQ4C2TZCHojjz090Sh5DhMl34c942EO40tGM_RqE1JEEVkczYjTGzsG9eT0_edbcniAGHaNanWdTS_T5mayZNfJmsfw23Rur3gRMJjCg5g0XNPBtGXhNw8VGkkKxq6ibmRk/s1600/45.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="186" data-original-width="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6Xb6yQFf-UQ4C2TZCHojjz090Sh5DhMl34c942EO40tGM_RqE1JEEVkczYjTGzsG9eT0_edbcniAGHaNanWdTS_T5mayZNfJmsfw23Rur3gRMJjCg5g0XNPBtGXhNw8VGkkKxq6ibmRk/s1600/45.png" /></a></div>
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It's also like the lesson clouded their thinking. </div>
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My questions for those still reading...</div>
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1. How would you improve the first day of this lesson? What could I change to do better?</div>
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2. Are there any other resources you'd recommend to use with this lesson?</div>
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3. What other insights do you have about my dilemma?</div>
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Thanks for reading!</div>
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<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com1tag:blogger.com,1999:blog-3468015882172246111.post-16132229557866896402018-03-02T01:49:00.001-06:002018-03-02T01:49:18.627-06:00Guest BloggerI just wrapped up my second <a href="https://mathtechsdsu.blogspot.com/2018/03/how-twitter-became-my-pln.html" target="_blank">guest blogger post</a> for SDSU's Math 371: Technology for Mathematics Educators. I wrote about how Twitter has become my Personal Learning Network.<br />
<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com1tag:blogger.com,1999:blog-3468015882172246111.post-64694227830394524252018-01-21T23:32:00.003-06:002018-01-21T23:32:27.432-06:00Something new for 2018: "From L to J"Last October, our district hired Lee Jenkins to come and train our grades 4-12 staff on a school improvement strategy he calls "From <a href="http://ltojconsulting.com/" target="_blank">L to J</a>". I had never heard of Lee Jenkins before, but I left that day knowing that I wanted to integrate "From L to J" into my classroom.<br />
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In case you're not aware of what "From L to J" is, here is a very brief overview:<br />
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<li>Teachers write learning targets for the entire year before the year begins; the learning targets for the year are given to students on the first day of school.</li>
<li>Teachers write an assessment question aligned to each learning target. Questions are typically entered into a PowerPoint / Slides presentation. This is done at the start of year.</li>
<li>Each week, students are given an "L to J" quiz. Quiz questions are randomly selected each week. The number of questions is a function of the number of learning targets.</li>
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A few more details:</div>
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<li>Each quiz, students track their own progress by plotting the number of questions answered correctly into a histogram.</li>
<li>Early on, students may get very few questions correct. This is to be expected if the learning targets are things that students haven't previously learned.</li>
<li>Yes, quiz questions may be over concepts and topics that haven't yet been covered in class. Because of this, "From L to J" quizzes do not effect a student's grade. </li>
<li>As the year progresses, [theoretically] students will begin to get more and more questions correct.</li>
<li>After each quiz, a class total of number of correct answers is calculated and plotted. Each time the class total reaches an all-time best, there is a "celebration".</li>
<li>[If you're wondering where the term "From L to J" originates, it comes from creating a class histogram after each quiz. On the x-axis is the number of questions answered correctly and on the y-axis is the number of students. Each student is a data point in the histogram. Early on, many students should get 0, 1, or 2 questions correct, creating an "L" shape distribution. Over time, the histogram begins to take a bell-curve shape. And by the end of the year, the histogram is hopefully shaped like a "J", meaning a lot of students got most or all of the questions correct. Take a look at some <a href="http://www.ltojconsulting.com/Graphs/SampleHistograms.pdf" target="_blank">examples here</a>.]</li>
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Jane, Jarrod, and I are the three geometry teachers in our high school. We spent a day writing our learning targets and creating quiz questions. We have <a href="https://docs.google.com/document/d/1ePw7DcWIdFyyaSKBqtEbyTwmEfuMEcufci6aKVh0HzM/edit?usp=sharing" target="_blank">72 learning targets</a> and decided to create three different questions for each target. [As of right now, we have one question for each target and are working on completing the other questions.]</div>
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Because we are implementing this at the beginning of the second semester, our histograms shouldn't necessarily ever be shaped like an "L". Next year, when we implement this starting at the beginning of the year, I expect a much truer "L to J" transition.</div>
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What was I drawn to with this strategy?</div>
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<li>In his presentation, Mr. Jenkins talked a lot about how this idea holds students accountable to remember what they have learned. Too often students believe that once they take the test over a topic or concept, they can forget about it. Or maybe it's that we [as teachers] allow them to forget about it. The "From L to J" quizzes provide a systematic spiral review for students. There is randomness in which learning targets are reviewed, but my feeling was that this review of previous topics is better than no review.</li>
<li>Students are aware of exactly what they are expected to learn (and retain) throughout the year. We have already been using learning targets with the students since the start of the year; this strategy provides a bit more formality to the learning target goals.</li>
<li>Mr. Jenkins also talked a lot about how this strategy helps students who have a tendency to struggle. Even if a student is getting a D or F for a grade, I can point out to these students that they are still learning <i>something.</i> [Future potential: Standards-based grading!?!]</li>
<li>Mr. Jenkins talked about how this strategy scored high on <a href="http://ltojconsulting.com/research/" target="_blank">John Hattie's</a> effect size research.</li>
<li>There is a little bit of statistics that gets worked into our classes.</li>
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What were my hesitations about implementing this strategy?</div>
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<li>Time. We're assuming that the quiz each week will take about 15 minutes. That's 15 minutes a week that I won't have to do other class activities.</li>
<li>Quiz questions need to be DOK level 1 & 2. The questions need to be able to be answered fairly quickly (< 90 seconds per question) and have one concrete answer. I can't ask questions where students are asked to explain their thinking because it would be too hard to score. My hands are tied with recall / skill level questions.</li>
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Last week, we took our first "From L to J" quiz. It seemed to go pretty well with the students. I found the randomness of the questions fun; my first class of students drew a lot of review questions and I had a lot of high score because of it. My second and third classes had at least two questions that were over topics that we haven't yet covered. Needless to say, they didn't score as well. </div>
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We will have another one on Tuesday of this week. I may post an update midway through the semester and tweet highlights and no-so highlights along the way. I'm excited to try this out and I'm looking forward to doing it for the full year next year.</div>
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Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-45223815074631976982017-11-25T23:49:00.003-06:002019-07-18T19:07:16.346-05:00The Positive Effects of BloggingI received an email notification yesterday morning about a <a href="https://crazymathteacherlady.wordpress.com/2017/11/24/two-kinds-of-simplicity/" target="_blank">new post</a> on <a href="https://crazymathteacherlady.wordpress.com/" target="_blank">Lisa Bejarano's blog</a>. It's an excellent post that talks about Lisa's internal thought process when deciding how to lead a lesson on simplifying complex fractions.<br />
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A couple of hours later, I see Dan Meyer tweet <a href="http://blog.mrmeyer.com/2017/watch-an-expert-math-teacher-put-three-kinds-of-knowledge-to-work-in-the-same-class/" target="_blank">he commented on Lisa's post on his blog</a>. I enjoyed Dan's analysis for a couple of reasons. He offers the thought that it is impossible to practice the process that Lisa takes with her lesson plan. I tend to agree with that opinion. Then, I what I really enjoyed was the nugget he left behind in his "BTW" section.<br />
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He links an article called <a href="https://theeffortfuleducator.com/2016/12/13/the-positive-effects-of-blogging-on-teachers/" target="_blank">"The Positive Effects of Blogging on Teachers"</a>. I hadn't seen this article before and it really hit home with me. Many of the items discussed relate directly to me and my professional growth and journey.<br />
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Thank you Lisa and Dan for helping me along my way!Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-42324275467296674782017-11-15T02:45:00.001-06:002018-11-25T11:09:59.527-06:00Desmos Transformation Golf + What My Assessment Looked LikeMy geometry classes just recently completed our unit on transformations. I was super excited to be teaching transformations this year because a few weeks ago Desmos released one of their coolest activities to date: <a href="https://teacher.desmos.com/activitybuilder/custom/59b01d08f4d48d0a0ee7526e" target="_blank">Transformation Golf: Rigid Motion</a>. If you haven't checked out this activity, stop reading this post and go take a peek.<br />
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I wrestled with figuring out the best time to do this activity with students. Should I launch the unit with it? Do I do the activity after the unit as a performance task? When does this best fit?<br />
<br />
I decided to do the activity as a review for the test. My intent was to help students solidify their understanding as well as to allow students to see that there is more than one composition of transformations that will yield the same result.<br />
<br />
So I had students complete the activity in class. I used quite a bit of <a href="http://learn.desmos.com/classroomconversation/" target="_blank">teacher pacing and paused</a> students often to discuss some of their thinking during the activity. It's such a fun day to lead. Students found a lot of pleasure finding their own ways to complete the tasks. Take a look at the various ways students did challenge #8.<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisgqRz4kPMersdwou00234UJ4KWnTSnKZYCsQkbtE6fJVszDMLwqA6w-Wtx1aEBJZvhpBSvPpDjZ8VF29dNIWN1yFhrI5elODL-Z94Xwe1sgPTga21MBiUU1cRwmQrBZGEYnUoHCygRz0/s1600/Desmos+Golf.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="532" data-original-width="1173" height="289" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisgqRz4kPMersdwou00234UJ4KWnTSnKZYCsQkbtE6fJVszDMLwqA6w-Wtx1aEBJZvhpBSvPpDjZ8VF29dNIWN1yFhrI5elODL-Z94Xwe1sgPTga21MBiUU1cRwmQrBZGEYnUoHCygRz0/s640/Desmos+Golf.png" width="640" /></a></div>
<br />
To wrap up the lesson, I had students complete an exit ticket to summarize their thoughts about the activity. Here are a few quotes from students:<br />
"It was fun and I liked how we got to make different things different ways."<br />
"It made me think in different ways than I normally would."<br />
"I like how it made me think outside of the box and creatively."<br />
"I liked that it was a little bit of a challenge."<br />
<br />
As part of the unit test, I wanted to give students some problems that were similar to the Transformation Golf activity. I wanted students to have the opportunity to be creative and get the correct solution in more than one way. At the same time, I wanted the problems to be a bit challenging and I wanted to assess the students' understanding of transformations on the coordinate plane.<br />
<br />
So I created six different problems that consisted of a pre-image figure and its image on a coordinate plane. (A link to the test problems is <a href="https://drive.google.com/file/d/1Wl3qtf3pH26NAyXwD-bpCyIa9z5iCFdP/view?usp=sharing" target="_blank">here</a>.) Students were required to provide the list of steps needed to map the pre-image onto the image. The level of precision expected was this: for translations, I needed the translation rule. For reflections, I needed the equation of the line of reflection. For rotations, I needed the center and degree of rotation. Counterclockwise rotations were the default; students could rotate clockwise if they desired, as long as they noted the direction.<br />
<br />
I was really stressing out about grading these problems because I knew there were many correct answers. I wouldn't be able to have one answer as a key; I would need to check each problem with a fine-toothed comb. With over 80 geometry students, I was worried about how long this task would take me.<br />
<br />
Here is a sample of some the student responses. All of these solutions are for the same problem.<br />
<br />
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<br />
<br />
As it turns out, I found great joy in grading these problems. Yes, it took a bit of time...more time than it would have had I given my students a multiple choice assessment. But to see the creativity, thinking, and effort that students demonstrated was well worth my time.<br />
<br />
I won't lie and say that all students did awesome work on this assessment. A common error was not being specific about the location of the center of rotation. [Often times the students intended the center to be the origin, but didn't specify. These errors led to a good conversation about precision.] <br />
<br />
A few students who struggled mentioned that this assessment was tougher than the Desmos activity for two reasons. First, checking their work on the assessment was a bit tougher than checking on Desmos. The Desmos activity provides immediate feedback when a student performs a transformation. Second, the transformations on Desmos did not require use of coordinates, equations of lines, etc. I have a handful of students who still struggle with writing the equation of a line. They are able to draw / sketch the line of reflection when given a pre-image & image, but they are not able to write the equation of that line very well. These students were able to complete the Desmos activity without too much problem but struggled to complete this assessment correctly.<br />
<br />
So, team at Desmos, here is my request. I LOVE the Transformation Golf activity. It made teaching transformations incredible enjoyable this year. I would love to see a "Transformation Golf: Round 2" activity that includes the x- and y-axes on the grid and that requires students to provide translation rules, equations of lines of reflections, and coordinates of centers of rotation in order to perform the transformations. My thought would be to have students start with the existing activity in order to learn some of the general transformation tools, and then send to the "Round 2" activity that ramps up the precision. Thanks in advance! ;-)<br />
<br />Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-17044395178877899522017-11-11T00:58:00.000-06:002017-11-20T12:23:55.089-06:00"When Will I Ever Use This?"In Geometry class last week, I shared a TED ED video with students titled "<a href="https://ed.ted.com/lessons/pixar-the-math-behind-the-movies-tony-derose" target="_blank">Pixar: The Math Behind the Movies</a>". In the video, Pixar Research Lead Tony DeRose talks to a room full of students about some of the mathematics happening behind the scenes at Pixar.<br />
<br />
One piece of the mathematics Tony talks about is something Pixar created in 1997 called "subdivision". Without giving away too much of the video, under the surface "subdividing" uses a bit of coordinate geometry and the concept of midpoints. On the surface, "subdividing" helps Pixar smooth the edges of their digital characters and makes the characters look a lot more life-like.<br />
<br />
What I found interesting that is that this concept of "subdividing" was invented until 1997. I graduated HS in 1998, which means my high school geometry instruction dates back to somewhere between 1995-97. If I would have asked my high school math teacher at the time "When will I ever need to find the midpoint of a line segment?", he would not have been able to mention the concept of subdivision as an application for finding midpoints.<br />
<br />
Likewise, it's safe to say that in five years, by the time my students are halfway done their undergraduate degrees, there will be math being used in the world that hasn't yet been invented. Whether it be an advanced statistical metric used to inform sports teams, some fancy new device that makes a iPhone X seem like an antique, or a parallel to Pixar's "subdivision", new math is being discovered and applied each year.<br />
<br />
As math teachers, it's not a bad idea to have a list of occupations and examples that highlight some of the usefulness and application of mathematics. However, math teachers should also help students realize that we don't fully know how certain mathematical topics will be used in the future.<br />
<br />
The video is under 8 minutes long; I invite you to watch it. It's really quite good.Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-53685105157104340852017-10-24T17:59:00.005-05:002017-11-19T22:49:10.614-06:00Desmos Marbleslides Challenge SetThis year, I'm trying something new with my students. The idea came from a Desmos Fellow name <a href="http://sweeneymath.blogspot.com/2017/08/a-full-year-set-of-36-weekly.html" target="_blank">Sean Sweeney. His blog post</a> does a great job explaining how this works; I invite you to read about his experiences with what he calls his <a href="https://teacher.desmos.com/activitybuilder/custom/5984b0d9723ca40cd48051d6" target="_blank">Marbleslides Challenge Set</a>.<br />
<br />
Two weeks ago, my geometry classes had just finished our unit on parallel and perpendicular lines. As part of that unit, I had students do the Desmos <a href="https://teacher.desmos.com/marbleslides-lines" target="_blank">Marbleslides: Lines</a> activity. Students loved the activity and asked for more Marbleslides. In response, I unleashed the challenge set to my students. [At least the first three challenges.]<br />
<br />
Each week I am unlocking one more challenge inside the activity. This past week was an especially cool challenge, with the screen almost like a Plinko board. I've had a number students find solutions and experiences the "Success!" found at the end of the Desmos rainbow. And as a teacher, you know you're winning when students are <i>begging</i> for the next challenge to be unlocked.<br />
<br />
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<br />
I challenge you to read Sean's post and try the Desmos Marbleslides challenge out in your school. Happy 'Slidin'!Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0tag:blogger.com,1999:blog-3468015882172246111.post-412867628738176252017-10-23T18:33:00.001-05:002017-11-19T22:49:58.927-06:00NCTM Conference @ Orlando Reflection<div class="MsoNormal" style="text-indent: .5in;">
I’m
on my way back home from the NCTM Regional Conference in Orlando. I had an awesome four days in Florida. My brain feels somewhere between the
consistency of oatmeal and Jello. I need
to get my thoughts recorded before I return home to four children and the
responsibilities of real life. [Update:
I didn’t get the full post written before I returned home; the movies on the
airplane stole my attention.]<br />
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<div class="MsoNormal" style="text-indent: .5in;">
I
had initially planned on doing a running diary-like blog post of my experiences at the
conference, but soon realized that there is too much info to consume to be
continually writing and reflecting.
Instead, I give you my five biggest takeaways from my conference
experience.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b>1. Desmos is still a mystery to too many classroom teachers.<o:p></o:p></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Okay, not all of Desmos.
But the teacher activities found at teacher.desmos.com. In the first session I attended on Thursday,
Matt Vaudrey (The Classroom Chef) had participants pair up with a partner and
play Polygraph. I rotated around to four
different people and asked each of them if they had heard of Desmos
before. Three of out four responded
along the lines of “Yeah, my students and I use the calculator quite
often.” When I asked them about every
using Polygraph before, all three responded “No” and had never been to the
Desmos teacher site. The fourth person
had never used Desmos at all before.<o:p></o:p></div>
<div class="MsoNormal">
Overall, I counted seven sessions (out of about 260) that
included Desmos in the title or the description. Other session may have absolutely used Desmos
as part of their presentations and simply didn’t include “Desmos” in the
description. Not all of the seven
sessions necessarily used the Desmos teacher site. I’m by no means advocating for Desmos to take
over the conference. However, I continue
to be floored at how many teachers have no idea that the Desmos teacher site
exists.<o:p></o:p></div>
<div class="MsoNormal">
When talking to some of my Desmos Fellow / MTBoS
colleagues, I mentioned my surprise at the lack of knowledge about the teacher
site. One conjecture we made is that if
you visit desmos.com there is a link to the teacher site, but the link doesn’t
really “stick out”. We felt as though flashing neon lights might help. Another
conjecture is that until textbook companies direct teachers to go to the
teacher site, it will never reach all who really need to see it. I’m curious about something… textbook
companies like Pearson and CPM are now starting to embed Desmos activities into
their curriculum. I’m wondering if
teachers using those resources are prompted to “Go to teacher.desmos.com,
create a class code, etc” or if they simply are able to run the activity via a
link found in their curriculum’s resources.<br />
<o:p></o:p></div>
<div class="MsoNormal">
Teachers need to be told about the Desmos teacher site
and need to be guided through setting up their account, searching for &
bookmarking activities, creating a class code, and using the teacher
dashboard. There is also a strong need
for a session where the Activity Builder is demonstrated, and the Activity
Builder Code is investigated. Which
brings me to…<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b>2. I feel really motivated to share with other teachers by
speaking at conferences.</b><o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
One NCTM regional conference next fall is in Kansas City,
which is less than 6 hours away from Brookings via car. The deadline for proposals to speak is
December 2<sup>nd</sup>. I’m going to
apply to speak and I’m leaning toward my proposal being about the Desmos
teacher site.<o:p></o:p></div>
<div class="MsoNormal">
This week, I prepared a number of proposals for sessions
at the SDCTM conference in February. My
colleague & fellow Desmos Fellow Jarrod and I are also going to submit a
proposal for an in-depth session at the TIE conference in April. I’m also happy to be presenting a full day
session on Desmos at the SDCTM Summer Symposium in July.<o:p></o:p></div>
<div class="MsoNormal">
Also this week, I gained a lot of confidence in my
ability to speak on ideas and things happening in my classroom that are not
connected to Desmos. Resources such as
<a href="http://wodb.ca/" target="_blank">Which One Doesn’t Belong?</a>, <a href="http://www.estimation180.com/" target="_blank">Estimation 180</a>, <a href="https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit" target="_blank">3 ACT tasks</a>, <a href="https://www.teachingchannel.org/videos/class-warm-up-routine" target="_blank">My Favorite No</a>, and <a href="http://padlet.com/" target="_blank">Padlet</a>
had their fingerprints in many sessions.
Manipulatives such as Algebra Tiles, Patty Paper, and GeoBoards were
demonstrated as tools that help student develop conceptual understanding. I regularly use all of these things in my
classroom. One of the session proposals
I prepared for the SDCTM conference demonstrates a few of these resources.<o:p></o:p></div>
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<b>3. I have fresh ideas about how to improve what I’m doing in my
classroom.</b><o:p></o:p></div>
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Continual improvement is something I like to think I
strive for. I gained a lot of new ideas
this week on things I can do to improve my craft. A couple of ideas I’m hoping to implement
soon are warm-up routines, tweaking my WODB a bit to make students think about
a reason each one doesn’t belong, and using <a href="https://teacher.desmos.com/activitybuilder/custom/59e9f981ef499b05b6f36524" target="_blank">GIFs embedded into Desmos</a> to help
students visualize the intended mathematics (thanks, Jedidiah!).
Also, I was reminded that I need to take a long look at Mathalicious and
Quizlet Live; both resources seem to have some pretty strong supplementary
resources.<o:p></o:p></div>
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<b>4. TI and I are <a href="https://www.youtube.com/watch?v=oEn9YvJ3Gfg" target="_blank">on a break</a>.</b><o:p></o:p></div>
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This takeaway needs its own blog post. Coming soon…<o:p></o:p></div>
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<b>5. The <a href="http://mathtwitterblogosphere.weebly.com/" target="_blank">online math community</a> is powerful.</b><o:p></o:p></div>
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I’m going to have to say that networking &
collaborating was one of the highlights of my week. It began before the conference even started
while I was walking to the Wednesday keynote session. I bumped into Sam Shah on my walk to the
conference center. He and I met this
summer in San Francisco at the Desmos Fellows weekend. He introduced me to two of his colleagues who
were walking with him.<o:p></o:p></div>
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Then in the keynote session, I happen to sit next to
Tracy Johnston Zager. Her and I have a
number of short conversations as part of the interactive session. Directly in front of us are Desmos Fellows Heather
Kohn and Lisa Bejarano. Heather had
asked Lisa and I to present on the Global Math Department’s webinar back on
September 19<sup>th</sup>. (Our session
was titled <a href="https://www.bigmarker.com/GlobalMathDept/What-s-new-at-Desmos" target="_blank">“What’s New at Desmos?”</a> and yes, Dan Meyer presented with us. Due to Dan’s loyal followers, there were over
500 people trying to view the webinar.
We crashed the host server & were unable to effectively show what
was new at Desmos.) Heather and Lisa
introduced me to #MTBoS faithful Hedge and Joel Bezaire. Michael Fenton was one of the keynote speakers
and I spoke with him briefly after his presentation. <o:p></o:p></div>
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The next two days, I run into Desmos Fellows Carl Oliver
and Jedidiah Butler. I chatted with
Christopher Danielson about this “Math on a Stick” at the Minnesota State Fair.
I sat next to Kyle Pearce in a couple of
different sessions. I met Justin Aion and
David Wees. I caught up with David
Barnes and Patrick Vannebush, both of who I met at NCTM Minneapolis back in
2015. The list goes on…<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoU94N__0tCOL58JxWpwjoWtaDca6p37phQ3XaWVn4d_zAHxCi8Pw9AWYoJ0SxSEmi6wJ-0nxj7DwwbgTCrEYKAs29-hswYoAf0bTnpSGkgKdFMo7dFQQS7i7aTF_TCekpfM586h_p9UE/s1600/2017-10-20+13.38.53.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1280" data-original-width="960" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoU94N__0tCOL58JxWpwjoWtaDca6p37phQ3XaWVn4d_zAHxCi8Pw9AWYoJ0SxSEmi6wJ-0nxj7DwwbgTCrEYKAs29-hswYoAf0bTnpSGkgKdFMo7dFQQS7i7aTF_TCekpfM586h_p9UE/s400/2017-10-20+13.38.53.jpg" width="300" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Holding down the fort at the #MTBoS booth.</td></tr>
</tbody></table>
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I’d strongly recommend attending an NCTM if you have the resources to do so. SO. MUCH. COLLABORATION. I feel extremely fortunate to be able to attend. I want to say “Thank You” once again to Daktronics for supporting <a href="http://www.sdctm.org/" target="_blank">SDCTM </a>and the <a href="http://www.sdctm.org/history.htm#omt" target="_blank">SD Math Teacher of the YearAward</a>. I'm keeping my fingers crossed that I'll be presenting <a href="http://www.nctm.org/Conferences-and-Professional-Development/Regional-Conferences-and-Expositions/Past-and-Future-Regional-Conferences/" target="_blank">next fall in Kansas City</a>. Time to get working on the<a href="http://www.nctm.org/Conferences-and-Professional-Development/Be-a-Speaker/" target="_blank"> speaker proposal</a>!<br />
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Mark Kreiehttp://www.blogger.com/profile/02405044207752416661noreply@blogger.com0