**[update 3/27/16: **I described how I use AngLegs to intrduce this lesson here**]**

I lied to my students today. Really, I fantasized, because I wish my lie was true.

I told them that I was going to choose some of their work and send it to Ohio for another math class to critique. Then I told them that I also got work from a class in Ohio (I have no idea why I picked Ohio, but they were into it!) . In reality I was using the materials that the Math Assessment Project includes in the triangle congruence lesson. They constructed their “proofs” first, convincing me that 2 triangles with 2 sides congruent in each triangle & 1 angle do not have to result in congruent triangles. They used mostly diagrams, very few had much of an explanation. They did put more effort into it, thinking that someone else, in Ohio, would be looking at it.

Then I gave them samples of student work.

*I teach at an alternative school. These students identify themselves as being “behind” the rest of the world. *

They all looked discouraged when I passed them “Jorge’s” work. It looks so nice – sentences, labels, proper notation. Then we read it. They realized that he had some false assumptions. One boy got so excited he asked if he could come to the board and he presented a beautiful argument comparing SAS to ASS and how one would result in congruent triangles but not the other. I immediately realized that I need to keep a charged battery in my camera at all times, just in case. Many of my students were so happy they could logically argue and prove an idea that someone in Ohio cannot!

Then we looked at “Kieran’s” work. Immediately a quiet student in the back yelled out “That’s how I did it!”. His body language changed, he sat up straight. he decided he was just as competent, maybe more, than students in Ohio!

Wouldn’t it be awesome if I didn’t have to lie…If we sometimes exchanged work with students in another state, maybe even share video clips of other students discussing one of my students real work. I don’t know how to start, but I have to find a way to make this happen.

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What a great post – thanks for sharing Lisa. Engaging learners who have low or no mathematical self esteem is crucial. Love how you’re finding a creative way to do so – even if it is “lying”. 🙂

Thanks. I completely agree. I am hoping to do this “for real” with something in the future.

Lisa, I’m from CA. I teach geometry to 8th graders at a private Christian school. I’m behind you in the curriculum so I don’t know how this would work, but I’d like to try to have our students analyze and critique each other’s work. Do you want to try it?

YES! I’m not sure either. I think a we should also make a short video of the students critiquing so that each group can put faces to the students. We should keep it simple to start, maybe just the same assignment. In the next month we will be working on polygon angles, then quadrilaterals, then transformations just before xmas. does any of that align semi close to anything you are doing? Im also planning to squeeze in mathalicious’s Domino effect & a project the week before thanksgiving (review linear equations) maybe that would work to collaborate with…let me know what you think!

Lisa, I can probably squeeze in the mathalicious dominoes lesson before thanksgiving in my algebra classes. I can’t spend anymore time on that in geometry. Would that work for you? Can we coordinate this through email?

[…] went well. Students struggled productively. I lied to them again, and it was surprisingly effective, […]

[…] Our unit began with the Shell Center task: Evaluating Conditions for Congruency, I don’t always follow these lessons exactly as described, but we focused on the Must the Two Triangles be Congruent? part of this lesson. I found that this activity is much smoother and more effective when using AngLegs instead of trying to draw each triangle (described here and here). […]

[…] From here the lesson continues as described in the SHELL center teacher guide linked above and described further in a blog post here. […]