Monday, July 20, 2015

Week 27 - Using Investigations to Teach Quadratic Functions

Part of using a flipped class model means identifying lessons that will not be best taught by mass instruction (i.e. video) but will be better served by something like an investigation. A big part of my current philosophy of math education is that most (if not basically all) students memorize algorithms and never really have a strong grasp of the material, so I seek to change this trend and try to push students to make connections between ideas and really understand why it works. "If you understand the basics, you can use them to figure out the hard stuff" is what I am often heard saying. I think I came to this realization when I was in my B.Ed year and/or my first year of teaching when my friends (a year ahead of me in school, so already teaching) were commenting that they couldn't believe how much they realized they did not understand in high school. In fact they did not understand it in university and were only getting it now because they had to teach it!

As part of these ideas I wanted to find a more effective way to teach quadratic functions that would (hopefully) lead to less memorizing. I set out to find/modify/create some investigative tasks for students to work on. This usually involved them doing the intro portion for homework the night before and then working through the rest of it in class in their groups. The first two investigations explored and linked step property (the pattern created by the changing slope - the idea being that students start to make a connection between linear and quadratic relations), first differences, and congruence (as well as symmetry). In the third investigation they were given some challenging problems that they would hopefully be able to solve using the ideas they had discovered.

These classes were then supported afterward with short video lessons to hopefully help students consolidate and to make sure everyone took away the key ideas I was hoping for. One of my biggest challenges has been creating that authentic, risk-taking environment where students are not afraid to be wrong while working through tasks like this. Many of them have never really worked through such challenging tasks or ideas and they seem to fear the unknown, to fear trying new things. I sometimes feel like a broken record, but I really do wonder if this might have been different if these tasks had come later in the semester.

What I am hoping to do in the future is to work toward creating this elusive learning environment is to focus more on talk strategies in class to help students enhance the communication among themselves (so they do not always have to have a conversation with me to feel like they have gotten anywhere). I think that this, in combination with a higher confidence with linear relations before embarking on this unit, will lead to better results (i.e. less memorization!).

I would love to hear from others who are trying anything similar. What worked in your class? What didn't? Why?

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