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SteveB's avatar

I also wonder about the premium that traditional math instruction places on efficiency, what's the most efficient path from problem to solution? Like we're all sitting at our desks solving equations all day, and the boss is going to write us up if we don't hit our quota. And if a student solves an equation through guess-n-check (or, heaven forbid, GRAPHING) do they understand less than the student who solves it algorithmically? If it's an application question, I'd think the student who graphs a rising function and finds where it crashes through the horizontal line might actually have a better understanding than the student who's correctly following procedure without know what makes it the correct procedure.

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SteveB's avatar

Yes, one thing I've always liked about the Desmos Classroom activities I've used (and that I try to do in the Desmos activities I write myself) is that you show consequences rather than green checkmarks and red x's. Here's a line, what's the equation? Student enters an equation, and it graphs the thing, so they can see for themselves whether their equation matches the line. If it doesn't it's not a BAD equation, it's just not the particular equation we're looking for at this moment. Set it aside, maybe we'll find a use for it later.

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