Why does this student answer for the first question, and for the second questions?
Why does this student express more confidence on the first question than the second question?
This is from yesterday’s survey, which was discussed over at this post. What do you make of the responses, particularly the differences between (2a+6) in the first response, and (2x+49) in the second?
The idea that kids walk into our classes with these intuitions is, I think, counter to the way that most math teachers talk and think about these mistakes. I think that realizing that these mistakes are the result of deep intuitions about how math should be is important. I also think thinking about where these intuitions come from is important, because maybe we can avoid setting them in earlier years.
I hope that some of you will give this survey to your students who haven’t yet received instruction on how to multiply polynomials. The original survey can be found here.
You’ll disagree with me in the comments, right? I’m counting on you all…
There’s a lot going on here. What about this work do you find the most interesting? How would you help this student?
Thanks to Heather for the submission!