There are several very cool blogs out there -- among them Math Mistakes and Bridging the Gap -- that highlight the value of thinking deeply about student responses, the mistakes they make, and the explanations they give for doing things the way they do.
One of the ideas behind Collaborative Mathematics has always been that participants could learn something from exploring other people's solutions, in addition to exploring the challenges. Some of the response videos in the archive contain mistakes, and I think that's fantastic. Rather than being an answer key of tidy solutions, they represent a library of arguments and ideas that require additional critical thinking.
One aspect of this is that I avoid posting my own answers to the challenges. I don't want my way of solving a problem to be interpreted as "the right way" just because I'm the one who posed the challenge in the first place. Over the next few posts, though, I would like to share my thoughts on a particular solution as a way to talk about my own mathematical curiosity, and what I've learned from a really creative approach to one of the video challenges.
But before I start going on and on about what I think, I want to give you a chance to explore for yourselves. Here's what I suggest:
Next time I'll share how I've come to think about the mathematics of Maile's approach.
One of the ideas behind Collaborative Mathematics has always been that participants could learn something from exploring other people's solutions, in addition to exploring the challenges. Some of the response videos in the archive contain mistakes, and I think that's fantastic. Rather than being an answer key of tidy solutions, they represent a library of arguments and ideas that require additional critical thinking.
One aspect of this is that I avoid posting my own answers to the challenges. I don't want my way of solving a problem to be interpreted as "the right way" just because I'm the one who posed the challenge in the first place. Over the next few posts, though, I would like to share my thoughts on a particular solution as a way to talk about my own mathematical curiosity, and what I've learned from a really creative approach to one of the video challenges.
But before I start going on and on about what I think, I want to give you a chance to explore for yourselves. Here's what I suggest:
- Take a few minutes to visit the archive page for Challenge 03: Finger Counting.
- Solve the challenge on your own, if you haven't already.
- Watch a few of the response videos.
- In particular, watch Maile's solution and see what makes you curious.
Next time I'll share how I've come to think about the mathematics of Maile's approach.
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