I am giving this to my Pre-Calc class tomorrow. We’ve spent the last week graphing and playing with different conic sections. Students have gotten very confident with the standard form of each equation, and with some of the patterns in the ways that different transformations affect the graph.

(for context, this was what a student produced doing Des-Man last week)

Is this a good question? Why or why not?

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Here’s a hypothesis. This question is valuable because it is non-routine, but asks students to transfer general rules from their prior knowledge, and see which still apply in a new situation.

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Another hypothesis could be that this question is valuable because it came from student ideas. That sounds a bit far-fetched to me. Not sure.

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Perhaps I am being too literal (or a bit dense) but RE:

“Is this a good question? Why or why not?”

What

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I guess it isn’t a question, per se, but a prompt to consider a new type of graph. “How do graphs of this form behave” might be a better way to phrase it — I think a challenge this question will have is in the different ways that students interpret it.

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Without being in your classroom it is hard to judge how your students might respond to such an open prompt. I know it would frustrate some of my students without a little nudge toward the types of adjectives that they might use

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That’s pretty much what happened for a bunch of students. The goal here is for them to transfer what they know about conics to a new context and see what rules hold and what rules don’t. How could this be phrased to get at that idea without giving too much away for students? Or is this just too messy of a question?

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