Wednesday, December 4, 2013

Find Someone Who... Understands Transformations on Exponential Functions

We're slogging through exponential functions in Algebra.  I really think there's some merit to reordering the units and teaching quadratics before exponentials because the symmetry can be useful in graphing, although the algebraic methods associated with quadratics are heavier, so perhaps I'm wrong to consider moving that unit first. That's something to hash out later.

Anyway, my students have worked through arithmetic and geometric sequences and we've made the connection that graphing geometric sequences given a positive common ratio yields exponential functions.  We've graphed a slew of these functions and analyzed how transformations occur.  We've looked at combined transformations, dissected them, and matched these to graphs.  And it's hard for the kids.  They're really doing OK for how much has been introduced in the past few days, but they're feeling like it's hard.  So at the end of one class period yesterday, I gave out index cards and asked the kids to write down a question they had or a happy statement if they were doing fine, not really knowing entirely what I was going to do with the responses I got.

I got about half of each kind of response back and I wanted to figure out how to address the kids' questions without lecturing on some things they'd already spent days exploring on their own.  It came down to eight questions after I took out the duplicates.  The questions covered the whole gamut of exponential transformations.  At first, I thought about offering them as journal prompts for a left side assignment, but I quickly discarded that because either 1) if given a choice kids would pick the easiest question for them to answer and still wouldn't understand the question they posed or 2) if required to answer them all, kids wouldn't know what to say.  A group discussion wasn't accountable enough.  I came up with something that sort of combined the above. 

I typed the questions up verbatim, only fixing obvious mistakes (like "ship" for "shift") and put them into a worksheet.  As they finished another assignment, I had the students pick up the neon green worksheet and "interview" classmates to get the answers to the questions.  They could ask one question of each partner.  The partner would give a verbal answer.  The paper's owner would write down the response, once it made sense, and the partner would initial the response.  I reminded students that once they got going, they could share an answer they got from a partner if needed because that was now something they knew in addition to whatever knowledge they started with.  Kids who collect the answers early can continue to be an interviewee to help out classmates who are finishing more slowly and they'll all get the benefit of repeating the answers to each other as a way to reinforce the concept.  It ended up being remarkably helpful to have copied this sheet on neon paper; since the students were all starting at different times, they knew they could scan the room for someone with a green paper to interview. 

Anyway, this activity needs a name, but I think it's really like that icebreaker game called, "Find Someone Who..."

Mathematically yours,
Miss B

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