Constructing Viable Arguments and NOT Critiquing The Reasoning of Others, Yet

I am still so catching the teachable moments. I am happy and annoyed that the CCSS chatter won't shut up in my head every minute of my teaching day. I know I can do better. I need to get the procedural stuff down too. I have to be patient.

I did get to have this moment with my Algebra 2 students:

We first did a Frayer Model for Linear Functions in our INB's. It looked like this:

Then I stopped and said, "prove to yourself, your neighbor, and me that xy =12 is not a linear function." (At the end of the day, I got looser and said, choose any one of the Non-Linears). OMG, it was so interesting! Granted this is only their 4th day of Alg 2 AND I thought they just had a year of Geometry with proofs and stuff. Proofs and Viable Arguments are clearly two completely different animals!

I loved that the students were engaged and active. I gave one person in the groups of four a whiteboard pen and spread them around the available whiteboard space (and two large whiteboards in the middle of the room). Guess what, NOT A SINGLE GROUP in one of my classes tried to show the function wasn't linear by graphing!


The word "formula" made me cringe, and they got it!

I thought their last argument went nicely with the one above.

These guys got stuck so I fed them a possible argument

I commended the students on what was good, I teased them (am I allowed to that?) about their lack of plotting points and looking at the graphs of the functions (when do the students understand the relationship between x, f(x) and a graph), I loved looking at their faces and "getting" what an argument means. I also loved KNOWING that the students were seeing that this was the math that connected to the rest of their academic life.

Happy Three Day Weekend Everyone!

Any thoughts, suggestions, concerns, next steps would be greatly appreciated.

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  1. "Proofs and Viable Arguments are clearly two completely different animals!" Well, that says it, doesn't it! Our kids don't get the point of proof when it's presented in this, "here's the right way," style. Nice lesson!

  2. Amy - I love this activity, and as you said, shows them how math is connected to thinking (not just calculating). I would love to try something like this, although I am not sure how it dovetails with my department's curriculum. Do you have a curriculum map/pacing calendar you could share? - Wendy Menard

    1. I haven't taught Advanced Algebra for awhile at this school, so I will hunt around and get back to you. What textbook do you use?