Desmos Marble Slides: Parabolas

Desmos just released their newest set of activities on Tuesday, aptly named "Marbleslides".  I decided to use the last day before Christmas vacation to let my algebra 2 students give the Parabola challenges a try.  I forced students to work as pairs instead of having them work independently.  I have found that my room is very quiet when students work on Desmos activities by themselves.  I wanted more collaboration and thinking out loud; I wanted more noise.

It appears Desmos hit a home run with their latest release.  More than once I had students arguing about whose turn it was to run the controls.  Many students left class with a new addiction.

Desmos Activity Builder Part 2

In case you missed my first post 5 short weeks ago about Desmos Activity Builder, please feel free to check it out.

It appears as though Santa came early because this was on my wish list.  Great new via Twitter today:

We are now able to copy someone else's activity and customize it to make it fit our specific needs.

For example, we used this activity on rotations by Andrew Stadel in geometry class a few weeks ago.  I now have the ability to duplicate the activity and make small tweaks to fit the needs of my specific students.  I don't have to try to re-create the magic that Andrew already created, yet I now have the ability to put my personal spin on these activities.

One final thought:
This open sharing of resources that is taking place is so powerful.  I love it that the people at Desmos and anyone who shares their wonderful creations through Desmos are not concerned about getting paid or someone else copying their ideas.  Sites like teacherspayteachers.com have some great resources, but it bothers me when teachers aren't willing to share resources with each other without getting something ($$$) in return.  The folks sharing via Desmos are willing to share resources for others to use and potentially for others to improve.  It's such a different mindset when compared to those teachers willing to share but only if they get something in return.

Happy customizing in activity builder!

Using Desmos to find the quadratic model of a real-world image

Desmos is at it again...

Since I started using Desmos more regularly this summer, I have found that it is gradually replacing a number of my other math software options.  The latest instance happened when my algebra 2 students were finding examples of things that take the form of a parabola.

In the past, I have had students find an example of a parabola in their everyday lives and snap a picture of it.  I've seen images of everything from the McDonald's logo to a water fountain to a mug shot of someone's jaw line.  Then I would have students upload their images into Geometer's Sketchpad and construct a number of points along the parabola.  Here is an example...

After that, I would have the students enter the ordered pairs into a TI-84+ or TI-Nspire graphing calculator, find the regression equation, and go back to Sketchpad and graph the function on top of the image.  Again, an example:

Some years I would have students explore around with vertex form a bit to try to fit a quadratic model before we found the regression equation.  But it was a painfully long process to bounce back and forth between Sketchpad and graphing calculator.

This year, I decided to direct students to Desmos to compute the regression equation.  After all, we had used Desmos to find linear regression equations earlier in the year and all students had access to Desmos w/ our 1:1 laptops.  (Not all students would have a TI-84 or Nspire to use in years past.)

It turns out the students had a great idea. Why use Sketchpad to plot the points and graph the regression function?  Why not just use Desmos?  I loved the idea and it really simplified the process.

Students simply inserted their images into Desmos, plotted points on the parabola, created a table with their ordered pairs, and found the quadratic regression equation (& graph) all in one place.

Follow this link for an example (image shown below).

Better yet, using the sliders in Desmos is a breeze.  Simply insert an image of anything parabolic and have students fit the model using vertex form.

Desmos Activity Builder

The team at Desmos has really hit the ball out of the park when it comes to user-friendly math technology.  If you haven't checked out the Desmos Activity Builder at teacher.desmos.com, you're missing out.

I've recently created some inquiry-based activities for my algebra 2 students.  The best part is that there are math educators much smarter than me working on creating activities as well.  Big names such as Michael Fenton and Andrew Stadel are sharing their ideas, and I'm able to use them!

My most recent activities for algebra 2:

Transformations of Functions

Absolute Value Graphs & Transformations

Quadratic Functions in Vertex Form

My most recent activities for geometry:

Equations of Lines - Part 1

Equations of Lines - Part 2

Again, it's great when giants like Andrew Stadel roll out activities (such as this one on rotations) right as we're working on transformations in geometry.

Keep up the great work, Desmos!

Un-structuring Word Problems

This year, I have the opportunity to teach two sections of advanced algebra 2.  My colleague, Todd, teaches the other five sections of advanced algebra 2.  Todd is an excellent educator and someone I have already learned a lot from.

We are both fans of Dan Meyer's TED talk and love the idea of un-structuring our math problems as much as possible.  In an attempt to force our students to think about what information is necessary to solve a problem, we've begun to modify a question or two each assignment in this way.


Here's a question found in a typical systems of equations lesson:

(c) Pearson Education 2015 Algebra 2

We give our students this problem instead:

*1.       You are considering renting a car from two different rental companies.  Write a function that shows the cost of renting from each company.  Which one should you choose?  Explain.

Our students are aware they do not have enough information to complete the task.  Not yet, anyway.
If we assigned this problem on a Monday, students would be expected to think about what information is important and necessary in order to correctly answer the problem.  On Tuesday, to start class, we give students 1 minute to ask anything they want about the problem.   The problem is then part of their homework for Tuesday night and is expected to finished by Wednesday.

It has been interesting to hear some of the questions students ask on problems like this one.  Often times, students ask for the necessary information very quickly and don't ask for anything unnecessary.  There have been times, however, that we get some interesting questions about things that have no effect on the problem.

Teaching Logic Using Games

It's Homecoming Week at Brookings HS this week.  As many of you know, Homecoming Week has an interesting way of making kids forget how to focus, especially on Friday afternoon.

For our geometry classes, we had students play a variety of logic puzzles and games.  Students could choose from three levels of sudoku, two levels of logic puzzles, the iPad app Chocolate Fix, and the board game Rush Hour.

Even though students thought they were given a day off, they were really developing their deductive reasoning skills and fully using conditional statements.

**Special thanks to Ryan Hofer, Horace Mann, and Donors Choose for providing funding to purchase the Rush Hour games.  The kids really gravitated to the hands-on board games!

Student Centered Advanced Algebra 2 Activities

I love it when students are active learners and are collaborating with one another.  I really love it when technology is involved.  The past two days of Advanced Algebra 2 have been a buffet of fun for me.

We have begun our unit on functions.  After a day of discussing topics such as mapping diagrams, function notation, domain and range, vertical line test, etc, we turned our attention to representing and modeling relationships with graphs.

On Wednesday, students analyzed distance - time graphs with a heavy thanks to this MARS MAP activity.  Students worked in groups of two to sort and match the graph, table, and story.

On Thursday, students completed the Desmos Water Line activity.  I have students reflect after doing Desmos activities, and here is what some of my students had to say today.

"It was a fun and simple way of looking at something that can be very complex."

"It made me think, and it was fun to create my own glass."

"It changed the way how I look at how water glasses fill up."



Responses like that are GLORY in its finest form.

I told students that I would take the most creative glasses and post pictures of them on Twitter.  We are hoping that @Desmos will retweet our post.  Time will tell if we were successful!

Here are some of the more creative glasses we had.

E.P. - 2nd Hour

O.D. - 2nd Hour

C.A. - 3rd Hour

Geometric Investigation and the Battle vs. Time

We recently finished up our first unit in geometry class, which includes an introduction to angles.  The last lesson we cover exposes students to the concepts of linear pair and vertical angles.

The Vertical Angles Theorem is one of the easiest for students to investigate using dynamic software.  There are a number of activities available for students to "discover" the theorem by exploring the relationships between the angles.  (Math Warehouse and GeoGebra to name a few.)

In our 1:1 setup, we prefer to use Geometer's Sketchpad to do our geometric investigations.  We have come to learn that it takes time to teach students how to navigate around the GSP5 software.  The dilemma we continually face is 'how much time to do we allocate to letting students struggle through the investigative discovery' vs. 'we can demonstrate this concept to the class in a matter of minutes'.

For example, it takes Jarrod or myself about 35 seconds to build a sketch that allows students to see the Vertical Angles Theorem (see diagram below).  Another two minutes of class discussion as we manipulate the points is really all the time needed for students to get a strong understanding of the theorem.

The Battle vs. Time is one that teachers continually struggle with.  It's hard to know when it's right to allow students the opportunity to struggle with the technology available to us.

Geometry Vocab Activity

In today's lesson, we borrowed an idea from Andrew Shauver and had our students complete an introductory vocabulary exploration.

Students had to come to class with introductory vocabulary words already defined (using their web resources and / or textbook).  Then they worked in groups to generate a "group definition".  They entered their "group definition" into a Google Form.  After all responses were gathered, we came up with a whole class definition and clarified any syntax and notations that went along with the terms.

Students work in table groups to complete the introductory vocabulary exploration.

In addition, we used all of the group's definitions to create a wordle for each term.  (It was very simple to do... go to the Google Form response sheet, copy all of the text for any term, and paste into wordle!)  We were pleased with what was created and decided to print some for our walls.

Learning on the Fly with Google Classroom

This past week, students walked through our doors again.  But this time, they each had a computer!

We (Jarrod and I) made the switch to Google Classroom as our classroom management system.  Students are using Google Drive for their storage and two work very nicely together... most of the time.

We have done plenty of troubleshooting this week, with most of our issues falling into one of three categories.

1.  Students are signing in / using their personal Google accounts instead of their K12 account.

2.  Google Drive becomes "disconnected", which then doesn't sync the files we send into the Drive folders.

3.  Students don't follow directions about how to access the files we send them.  We are asking students to "open" the documents in Google Classroom (which then creates a copy in their Google Drive folder, and we have access to it).  Then they are to work on their document via their desktop drive folder, save, and we're set.  Instead of doing that, some students download the document, save it somewhere except their Classroom Drive folder, and we can't see it.

Of the 138 total students in our classes, we've only had two that have had some serious issues getting their Google stuff setup.  Not too bad!

1:1 Laptop Roll-out & The New School Year

This past week at Brookings HS, we began to distribute laptops to the approximately 903 students set to enter the doors on the 25th.  Students are required to come to a "training" session in order to receive their laptops.  After three days of sessions, more than half of the students have their laptops.  For the most part, the roll-out process has gone very smoothly.

It was very helpful for Jarrod and I to pilot the laptop implementation in our classroom last year.  Many problems were alleviated.  The 1:1 laptop team and tech staff still had a number of items that needed to be ironed out throughout the planning process, but it has gone well.

Three final hurdles need to be cleared as the school year begins.
1.  The rest of the computers need to be distributed to the students.  There is a fear that a handful of students will flat out reject the computers and refuse to take one.  We're not exactly sure what to do if that's the case.

2.  The teaching staff needs to be trained on LAN School (our classroom management software).

3.  We need a day of school in which there is heavy internet usage to see how our network handles the increase in volume.


Speaking of the new school year, Jarrod and I are implementing a few changes to our team teaching model.  The first is that we will be using Google Classroom as our Learning Management System.  So long, Edmodo.  It's been a good ride.  But the ease of how Google Classroom distributes assignments and creates shared files with the students is too good to not use.

Secondly, we just saw our classroom numbers for our three sections of geometry.  Last year, our largest class when we brought both classroom together was 47 students.  This year, we're looking at 54.  I have a feeling that 54 is too many to comfortable fit into Jarrod's classroom at once.  We're going to test it out the first week and see how it goes.

Lastly, I am teaching two sections of Advanced Algebra 2 while Jarrod will be teaching two sections of Geometry Applied.  We still have mirrored schedules and will share our three geometry sections, but two hours a day we will be doing different things.

Let the fun begin!

One of the best rewards as a teacher

Being a teacher has many benefits and rewards - helping students reach the "A-HA" moment, summer break and holiday vacations, school lunch, etc.  But to me, one thing is more rewarding than anything else.

This evening I met up with two of my former students.  Both were strong math students; now both are going to be math teachers.

To me, nothing is more rewarding than knowing that I made a positive impact on a student and that he/she wants to be a math teacher as well.  I'm proud of these two gentlemen on a number of levels.  Best of luck to both of you!

Congrats to Mr. Peters!

This post is a quick shout out to Jared Peters, who recently landed his first teaching job.  Mr. Peters completed his student teaching requirement with us last spring and will be a great addition to our profession.  Best of luck, Jared!

Growth Mindset & the Smarter Balanced Assessment

I was first exposed to Carol Dweck's research on fixed and growth mindsets a few years ago when I was completing some of my graduate coursework.  For those of you who haven't heard about mindsets, you can find a lot of resources online (here and here to name a few).

Dweck's colleague, Jo Boaler, has completed some further research on mindsets and the implications in the classroom.   If you're really interested in learning about mindsets in a mathematics classroom, I would recommend taking Stanford's free online class (sign up here).

In Dweck's Self-Theories book, she discusses the reaction of students with a helpless mindset (fixed mindset) when they experience failure.  In short, when a student with a fixed mindset experiences failure they begin to fall into a helpless state of mind.  They quickly lose confidence in their abilities and lose perspective on the successes they had achieved in the past.  Moreover, many students who had fallen into the helpless mindset "abandoned or became incapable of deploying the effective strategies in their repertoire." (pg. 9)

After hearing that research, I grew concerned about students who have a fixed mindset and their ability to successfully complete the Smarter Balanced assessment.  The Smarter Balanced Assessment is a computer adaptive test.  Students are given grade-level questions for the first two-thirds of the test.  Then the computer software selects remaining one-third of the questions based on the student responses up to that point.  If a student is answering questions correctly, then the software can select questions from a higher grade level.  Conversely, if a student is answering questions incorrectly, then the software can select questions from a lower grade level.

Theoretically, this type of testing system makes sense.  It's designed to find the "boundary" of each students' achievement level.  My concern lies with the students with fixed mindsets.  For those students, the "boundary" is like an electric fence.  The test is designed for students to eventually touch the fence.  Once a student with a fixed mindset does touch it, the electrical current sends shocks throughout their body.  They lose ability to focus on the problems and are more focused on how much the fence shocked them.

Dweck summarizes her research by saying "...the helpless response is a reaction to failure that carries negative implications for the self and that impairs students' ability to use their minds effectively."  I fear the computer adaptive test could indirectly lead to major negative consequences for students with a fixed mindset.

What can we (teachers) do to help?

I think the best way to help combat this potential problem is to teach students about fixed and growth mindsets.  I am planning to introduce these ideas during the first week of school in all of my classes.  More to come as to what that will look like...



Dweck, Carol S. Self-theories: Their Role in Motivation, Personality, and Development. Philadelphia, PA: Psychology, 1999. Print.

It worked!

As you can see from my previous post, the email directly to blog post worked!  I’m very excited about this feature in blogger.

 

The way that Ramsey is implementing this in his classroom is he is having his students write blog posts (as reflections) at the end of each lesson / learning activity.  He has them write emails that post directly to their blogs.  Blog postings are typically part of their homework and students are expected to describe the learning activity and summarize what they’ve learned.  Students are also encouraged to ask questions about things they aren’t fully understanding.

 

I love this feature because it will allow students to use whatever they are comfortable emailing with to create their blog posts.

 

TIE Conference 2015

I am currently at the TIE Conference and learning some great new ideas.  One thing I just found out about was the ability to post to my blog by simply writing an email.  (Thanks to the Monday AM Keynote Ramsey Musallam!)

I believe I set this up correctly and am testing this newly discovered featured out.  I guess if you’re reading this, it worked!

How tall is the light pole?

In early March, Mother Nature was very cooperative with our lesson plans and we had a couple of 60 degree days.  We were in the middle of our similarity unit and wanted to get our geometry students outside for an activity.  My co-teacher and I had both done activities involving indirect measurement before in our previous schools, but we had both used clinometers and right triangle trigonometry as the vehicle.

This year, we decided to use mirrors and model our activity similar to the one shown here.

We modeled our lesson after Mr. Chuck Pack's lesson (from The Teaching Channel).  He does a much better job of explaining the activity on video than I could in writing.

The students loved getting outside and the day was a success.  Most importantly, students demonstrated strong understanding of the concept of indirect measurement and experienced it firsthand.

3.11.15 - Brookings HS

The indirect measurement activity using mirrors worked very well.

The one thing I really loved about Mr. Pack's activity that I had never thought of doing was collecting the data and tie in some data analysis / statistics into the day.  It's inevitable that at least one group make some major errors in their measurements or calculations.  Outliers and the effect an outlier has on the mean is begging to be discussed.  TI-Nspire does a very nice job of displaying the data from our three classes in the scatterplot. Great idea, Mr. Pack!

Next year, we're planning to improve our activity in two ways.  

1)  We used meter sticks and yard sticks to measure our distances along the ground.  Next year, we will hopefully have 100-ft tape measures.  It will be interesting to see if our data has less variation.

2) We are planning to use clinometers as well next year after our trigonometry unit.  We can then potentially use our mirror data and compare it to the clinometer data.  

If anyone has ideas of some statistical analysis type activities we can do to extend the lesson next year, please reply below.  I am especially interested in stats connections to the CCSS.

4-State Math Collaboration - Round 2

I recently returned from beautiful Phoenix, AZ and round 2 of the 4-state math leadership collaboration event.  It was again great to discuss and plan potential action strategies for helping implement the Common Core standards into 6-12 math classrooms across the region.

A couple of highlights from the meeting...
1.  Growth mindset vs. fixed mindset is something worth looking into if you haven't heard or seen the research yet.  (Keywords: Carol Dweck, Mindset)  This brain research can be applied to many areas of life.  The 4-state event facilitators had us analyze our mindset through the lens of a math leader.  I knew right away that I had a fixed mindset when it comes to me being a leader.  As a matter of fact, I blogged about it after the first leadership event in Rapid City this past fall.  I placed teachers into four categories and went on to say that I have no time for teachers that want to be left alone.  I had a very fixed mindset about being able to lead those particular teachers.

I want to expose my students to the concept of fixed vs. growth mindset in the fall.  I think it might be a great first week activity.

2.  The state of SD (and IA, ND, and MT) are closer to having a plan in place to help grade 6-12 math teachers have more support and resources as we implement the CCSS-M.  We have one more meeting in June that will finalize some of those plans.

3.  There are a wealth of resources available online that math teachers need to be made aware of.  I thought I knew about most of the Common Core resources and it turns out I was mistaken.  Once again, math teachers need one centralized location that provides details on the best resources available.

4.  The weather in Phoenix is beautiful in March.

I left the event feeling very empowered and ready to help initiate change.  Great professional development is very refreshing and motivating.  I'm excited for the final event in June.

Golden Ratio & Apple Cores

@BHSGeomety students recently studied the Golden Ratio and Golden Rectangles with a number of different activities.  For example, in one activity students found lengths on different measurements on their face and bodies and calculated to see if any of their ratios were "golden".

The activity I want to share about goes a little something like this...

1.  Give each student (or group of students) an apple.  Have the student cut the apple horizontally so that the cross section is a circle and it exposes the core.

2.  As you can see, the inside of the core has a pentagram shape.  This is one of many instances of the golden ratio found in the natural world.  We had students take a picture of their apple cores and import them into Geometer's Sketchpad.  Our document camera was extremely efficient at doing this.

3.  Using a regular pentagon custom tool in GSP, students constructed the pentagon around their apple core.

4.  Students then compared each other's apple core to see which had the most "golden" core.

This is a fun 10-minute activity that integrates technology and is very hands-on and student centered.  Students were interested to see what each other's cores looked like.  We actually used four different types of apples in our experiment.  No one type of apple seemed to be any more or less golden than the others.

Here are a few more examples:

Mr. Ott: Finding His Way

Mr. Ott (@iteach_kidsmath) was a student teacher in my classroom this past fall semester.  He was great with the students, very receptive to feedback, and open to new ideas.

Now that he has his own classroom, it's cool to see him continue to grow as an educator.  He has fully embraced the power of twitter as a tool for professional development and collaboration.  He has also begun to blog about his experiences in the classroom.

Keep up the great work, Mr. Ott.  We're glad you're going strong!

Student Created Videos

New year, new goals.

While doing some planning for our new semester, Mr. Huntimer found an activity on myOER that we decided to use to begin the second semester with our geometry classes.

Working in groups of two or three, students were given the task of finding real world objects that model a variety of 2-D and 3-D shapes.  Students were to either take a picture or a video clip of the object.  Then they were to create a video that fused all of the pictures or videos together.  As part of the video, students were required to define the object that they had found.

We allowed students to make a lot of decisions regarding their videos.  Students could define their objects using a number of different methods.  They could define objects as they recorded the video clips, they could record voice narration and align it to their pictures, or they could insert text into the video.  We had students use all three methods.

Students could create their videos around theme or concept.  We had one group use the theme of "shape hunters" and another use the theme of "mathletes".

We also allowed students to use whatever type of video editing software they'd like.  Our laptops have MovieMaker installed, so that served as our default video editor for those who had no preference.  Mr. Huntimer and I were rookies working with the software and found it very user friendly and easy to implement.  Some groups chose to use their iPhones and iMovie.  Another group used a third video editing software that we had never heard of before.  Our only stipulation was that students needed to submit their videos in mp4 or mov format so that we could view them from any computer (via Edmodo).

Overall, the task went very well.  We had some bumps in the road the first time through.  The biggest challenge was we had a number of groups submit their MovieMaker projects before they had converted them to mp4 format.  We simply had to ask those groups to convert and re-submit the videos.  A majority of the videos were similar in that they contained the minimum amount of effort / work needed to complete the task.  A few groups forgot to include all of the required information, thus costing them a few points.  Meanwhile, a few groups produced excellent videos that really caught our attention.

The content of the geometry in the task was really quite elementary, but the task did align to a CCSS ( G-MG.1).  The bigger skill that students practiced was collaboration and technology use.  We asked students to reflect on what they had learned in doing this project and many said they had never or rarely used software to create a video.  We were very happy with the technology application component.

I leave you with two links.  The first is a link to the task via myOER and Mr. Zachary Feldman (click here).

The second is a link to one of our best student videos.   The three gentlemen who created this video have agreed to share it.
Student Video

New Year's Resolutions

A couple of quick New Year's Resolutions for my classroom and @BHSGeometry...

1.  Focus on highlighting the standards of mathematical practice.  We use many of them every day in class.  Are the students aware of this?


2.  Less telling, more doing.  Force the students to do the heavy lifting in class.  This is always a goal of mine, and always a challenge to meet.


3.  More student self-reflection.  The more students reflect, the more that gets transferring into long-term memory.  Google forms, exit tickets, possibly student blogs... we'll see where 2015 takes us!

Google Earth in Geometry

We recently finished our unit on triangle centers in geometry.  Students were asked to do a lot of discovery / investigative learning with Geometer's Sketchpad (GSP).  

One activity we had students do was get into groups of three and using Google Earth and GSP, find the location that is equidistant to all three of their houses.

For most, this was a great way to have students collaborate and have direct meaning to the geometry involved in the lessons.  We saw some excellent sketches, such as the example below.

Google Earth is a very useful tool for this type of task.  We found it more user friendly than Google maps since Earth allows the user to pin more than two locations at a time.