I just wrapped up my second guest blogger post for SDSU's Math 371: Technology for Mathematics Educators. I wrote about how Twitter has become my Personal Learning Network.

# Kreie blog - Reflections of a HS Mathematics Teacher

Challenging students and striving for continual improvement

## Friday, March 2, 2018

## Sunday, January 21, 2018

### Something 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 L to J". 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.

In case you're not aware of what "From L to J" is, here is a very brief overview:

In case you're not aware of what "From L to J" is, here is a very brief overview:

- 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.
- 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.
- 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.

A few more details:

- Each quiz, students track their own progress by plotting the number of questions answered correctly into a histogram.
- 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.
- 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.
- As the year progresses, [theoretically] students will begin to get more and more questions correct.
- 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".
- [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 examples here.]

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 72 learning targets 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.]

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.

What was I drawn to with this strategy?

- 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.
- 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.
- 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
*something.*[Future potential: Standards-based grading!?!] - Mr. Jenkins talked about how this strategy scored high on John Hattie's effect size research.
- There is a little bit of statistics that gets worked into our classes.

What were my hesitations about implementing this strategy?

- 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.
- 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.

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.

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.

## Saturday, November 25, 2017

### The Positive Effects of Blogging

I received an email notification yesterday morning about a new post on Lisa Bejarano's blog. It's an excellent post that talks about Lisa's internal thought process when deciding how to lead a lesson on simplifying complex fractions.

A couple of hours later, I see Dan Meyer tweet he commented on Lisa's post on his blog. 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.

He links an article called "The Positive Effects of Blogging on Teachers". 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.

Thank you Lisa and Dan for helping me along my way!

A couple of hours later, I see Dan Meyer tweet he commented on Lisa's post on his blog. 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.

He links an article called "The Positive Effects of Blogging on Teachers". 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.

Thank you Lisa and Dan for helping me along my way!

## Wednesday, November 15, 2017

### Desmos Transformation Golf + What My Assessment Looked Like

My 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: Transformation Golf: Rigid Motion. If you haven't checked out this activity, stop reading this post and go take a peek.

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?

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.

So I had students complete the activity in class. I used quite a bit of teacher pacing and paused 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.

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:

"It was fun and I liked how we got to make different things different ways."

"It made me think in different ways than I normally would."

"I like how it made me think outside of the box and creatively."

"I liked that it was a little bit of a challenge."

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.

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 here.) 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.

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.

Here is a sample of some the student responses. All of these solutions are for the same problem.

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.

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.]

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.

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 advanced! ;-)

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?

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.

So I had students complete the activity in class. I used quite a bit of teacher pacing and paused 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.

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:

"It was fun and I liked how we got to make different things different ways."

"It made me think in different ways than I normally would."

"I like how it made me think outside of the box and creatively."

"I liked that it was a little bit of a challenge."

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.

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 here.) 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.

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.

Here is a sample of some the student responses. All of these solutions are for the same problem.

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.

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.]

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.

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 advanced! ;-)

## Saturday, November 11, 2017

### "When Will I Ever Use This?"

In Geometry class last week, I shared a TED ED video with students titled "Pixar: The Math Behind the Movies". 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.

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.

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.

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.

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.

The video is under 8 minutes long; I invite you to watch it. It's really quite good.

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.

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.

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.

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.

The video is under 8 minutes long; I invite you to watch it. It's really quite good.

## Tuesday, October 24, 2017

### Desmos Marbleslides Challenge Set

This year, I'm trying something new with my students. The idea came from a Desmos Fellow name Sean Sweeney. His blog post does a great job explaining how this works; I invite you to read about his experiences with what he calls his Marbleslides Challenge Set.

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 Marbleslides: Lines 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.]

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 challenge you to read Sean's post and try the Desmos Marbleslides challenge out in your school. Happy 'Slidin'!

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 Marbleslides: Lines 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.]

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

*begging*for the next challenge to be unlocked.I challenge you to read Sean's post and try the Desmos Marbleslides challenge out in your school. Happy 'Slidin'!

## Monday, October 23, 2017

### NCTM Conference @ Orlando Reflection

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.]

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.

**1. Desmos is still a mystery to too many classroom teachers.**

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.

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.

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.

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…

**2. I feel really motivated to share with other teachers by speaking at conferences.**

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

^{nd}. I’m going to apply to speak and I’m leaning toward my proposal being about the Desmos teacher site.
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.

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
Which One Doesn’t Belong?, Estimation 180, 3 ACT tasks, My Favorite No, and Padlet
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.

**3. I have fresh ideas about how to improve what I’m doing in my classroom.**

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 GIFs embedded into Desmos 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.

**4. TI and I are on a break.**

This takeaway needs its own blog post. Coming soon…

**5. The online math community is powerful.**

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.

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

^{th}. (Our session was titled “What’s New at Desmos?” 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.
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…

Holding down the fort at the #MTBoS booth. |

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 SDCTM and the SD Math Teacher of the YearAward. I'm keeping my fingers crossed that I'll be presenting next fall in Kansas City. Time to get working on the speaker proposal!

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