Making Connections

A couple of tweets in the last week resonated with me as we are wrapping up the year. Julie Reulbach shared

As we are preparing for final exams, I see a lot of this. Today, we were working on reviewing solving systems of linear equations and many of them had forgotten how to graph lines. And as I was walking around, helping students, it dawned on me why. You see, my students have just come off a section on solving quadratic equations. To be honest, it was a little rushed due to time constraints, but not as rushed as last year. Prior to solving quadratic equations by taking square roots, or completing the square, or the quadratic formula, we had spent quite a bit of time on graphing quadratic equations (here is a post on the start of the unit). While learning how to graph the quadratic equations, students used completing the square to rewrite an equation into vertex form. They also solved equations by either factoring or by taking square roots when finding the x-intercepts (depending on whether or not the equation was in standard form or vertex form). So when we got down to solving by these two methods, they had seen them used before and in a context. They did significantly better on these two learning targets than students had in the past, especially the completing the square learning target. When I finished grading their papers, I was pondering what had gone better this time around. Between that and today, it was pretty clear: the connection students had made while using these processes in graphing quadratic equations helped. In fact, the tweet Glenn Waddell responded to Julie with rang through my head today.

It is becoming clearer to me that I need to work on helping my students find connections between the doing of the mathematics and where it can be used and/or why it is used. Glenn has already begun to blog about how he does this in his classes and I am looking forward to reading more about it this summer. I think I have found yet another summer project for #summerlist2015.

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