Dueling Banjos: Desmos-Style

Working out of the District Office can be a very lonely job because unlike being surrounded by math teachers at my old school who meet regularly and collaborated monthly with all the middle school math teachers in the district, my department is now tiny and it’s hard to find the same sense of community within the district office as one does at a school site.

I was honored to be chosen as a Desmos Fellow this year and it has been one of several places where I have worked to foster connections between myself and others who are looking at instructional technology through the lens of math and equity pedagogy. Although the fellows often collaborate as a group, there have been several fellows with whom I have worked with individually on projects.  Jenn Vadnais, a former math coach and newly minted TSA for Instructional Technology in Redlands Unified School District is one of them.

Today, Jenn blogged about teaching a 4th grade Geometry lesson using a Desmos Polygraph Activity she had written.  Her post is here and involves a group of extremely curious students and a tech-curious teacher, both of which are an exciting audience when you’re leading a model lesson.

Two weeks ago, I too aught a 4th Grade Geometry lesson, on similar standards using a Desmos Activity based off the Which One Doesn’t Belong ideas from Christopher Danielson’s book and Mary Bourassa’s web site, both with this same name.  Though we live in opposite ends of a very large state, I couldn’t help but smile at our Dueling Banjo mathematical work.  **SIDENOTE: As a banjo player, I can assure you that there is a fabulous Dueling Banjo Pandora station where musicians take turns improvising from  the riff played by the other, always returning to the same original riff before the next banjo player takes a turn. This style of music shares a name, but nothing thematic with the film of the same name.  I promise.**

When writing this activity, in additional to mathematical content goals, I was encouraged by a math coach in my district to have specific language goals.  Together, we wrote sentence frames, increasing in complexity, using conjunctions that student wouldn’t necessarily think to use in a math activity.  The Desmos Activity Which One Doesn’t Belong: 4th Grade Geometry is here and the half-sheet of sentence frames that students used is here.

My intention was to have them do this activity three times within the hour, each with a different lens.  The big idea behind a Which One Doesn’t Belong (WODB) activity is that any of the 4 images can be the one which doesn’t belong, depending on your reasoning.

ROUND 1: Give it your best shot.  I first wanted students to work through the math, not focusing on language.  So after doing slides #1-3 together at the rug, discussing that there was no one right answer, that their reasoning mattered, a lot, the students returned to their seats to complete the activity.  My intention for this first part of the lesson was for them to complete all of the slides, with minimal support or reframing from me.  The class was at the end of their geometry unit, and I had written this activity as a review of the major concepts.  After about 3/4 of the class was near the end, taking their time drawing lines of symmetry on the final slides, I called the class back to the rug.

ROUND 2: Mathematical Reasoning.  Did you use 2 of the words from the vocabulary bank on each slide?  Did you hastily choose the image that you believed didn’t belong or did you spend time thinking or discussing the different options?

changing-answersI used the histogram feature for multiple choice questions to show screens where zero or just 1 student had chosen a certain answer. Students turned and talk to explain which figure they thought didn’t belong and why, focusing on including at least 2 vocabulary words.  When a pair finished, I challenged them to choose a figure which hardly anyone had chosen and determine why it could be the one which doesn’t belong.  We did this for two sets of figures, and then students returned to their seats to read over the responses to each slide, check that they had used at least 2 vocabulary words, and improve their answers, mathematically, as much as possible.  Again, I encouraged those who finished quickly or said that they didn’t need to improve any to choose a figure which few others had chosen and develop a response for it.  The histograms for each slide changed dramatically which was fun for students (and I ) to watch.

ROUND 3: Use more sophisticated academic language.  After improving their work mathematically, students returned to the rug and I passed out these sentence frames.

screen-shot-2017-02-28-at-9-01-37-pmTogether we looked at student responses from this slide:


Specifically, the student responses for the letter A:


I had one student choose his favorite ‘mathy’ response that he thought we could improve.  He chose, “The A is different because it is not a parallel”  As a class, we used the sentence frames to come up with three versions of that response to make it sound more, “like what a mathematician would say.”

Here is what they came up with as a class:


Students then worked with a partner at the rug, chose one of the sentence frames, and improved a second response from those displayed on the board.  With the final 10 minutes of class, they returned to their seats and used these sentence frames to improve as many of their own responses as they could.

Quite sadly, I don’t have a screen-shot of this same set of Red-A responses after they improved them.  When I run Desmos Activities in someone else’s classroom, I always do it logged into the classroom teacher’s account so that the student work stays with them.  The downside of this is that if I forget to take a screenshot before leaving the class, poof, the work is gone for me once I leave.  From walking around the room, and showcasing a few responses on the big screen before recess, I saw an incredible amount of focus on academic language.  Separating the language lens from the mathematical lens seemed to especially encourage struggling students to take the time to truly consider both.

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