When students are able to make connections for themselves I find it truly exciting. I think moments when students turn the corner and begin to reason, become more human and less like a robot a celebration should occur. This past Friday a group of students made the connection between the area model and factoring and simplifying expressions. It’s a connection the task they worked on earlier last was promoting but I’ll tell you not every student did so.

Someone once told me, that kids don’t naturally make conclusions or summarized math concepts without teachers making it plain for them.

Picture above is the sequence of thoughts these students had in regards to factoring and simplifying expressions. The thought begins on the right and travels left. I was the scribe and facilitator through the process but NONE of the thoughts on the board are mind. The most beautiful part was right at the end when students were given the expression 5x + 20 and asked “what would you do with this?” Several of the students jumped describe the how they would create a large rectangle, split it and label the areas 5x and 20. They went on to reason that 5 had to be the width of the entire rectangle because the first area of 5x and if x were the width, the other area would contain an x. With enthusiasm they explain why the length was x and 4. From that, they wrote the factored expression. When given a factored expression, with even more excitement they explained their strategy of using a rectangle to help simplify.

I had not thought them this strategy, they made that connection from engaging in task from the GA math frameworks. More on that later…

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You’ve proven to your students that they can think for themselves. Well done. More hurdles are coming, but my guess is they’ll be easier to clear now that your students have begun to reason for themselves.

Looking forward to more of your students’ successes!

So do I. Its interesting to see how the different classes vary in their reasoning at this point in the year. My 2nd academic feed of each others’ knowledge. I even overheard them arguing about how to simplify an expression. One student said to the other, “I know how to do it, it was my strategy!”

My next step is getting my 3 other classes to follow suit :-/.

Love this Jenise!

You could videotape your 2nd period class when engaged in reasoning and have the other students watch and critique it. Maybe have them score the overall engagement of the 2nd class based off the rubric you created earlier this year. I used this while idea when implementing Number Talks at my school. No rubric but had 1 class watch a video tape of another class to get them moving in the right direction.

So instead of YOU modeling, you have one class modeling for the other 3. I’ll step out on a limb here and suggest that your other periods will want to be videotaped and critiqued as well….not a bad thing at all:-)

This is amazing! Would love to see something like this in my class!