Presented without comment, and with thanks to Andrew.

- Post author By mpershan
- Post date August 28, 2013
- 2 Comments on Cross addition isn’t a thing

- Post author By mpershan
- Post date August 27, 2013
- 8 Comments on Fractions and Solving Equations

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- Post author By mpershan
- Post date May 22, 2013
- 3 Comments on Inconsistent Polynomial Multiplication

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?

This post is part of a series analyzing a bunch of survey results. For previous posts, go here and here.

Noteworthy:

- The kids have a
*ton*of confidence, even in the stuff that they haven’t formally studied in class yet. (For this survey, Questions 1-3 had been covered formally, and Questions 4-5 had not.) To my mind, this continues to reaffirm that the most annoying mistakes aren’t the distortion of instruction; they’re the*failure*of instruction to override preconceptions. - Kids like to say that , and teachers like to say that this is due to overuse of the Distributive Property. That might be true, but those teachers also have to recognize that kids said that with almost the same verve and frequency. It’s hard to blame exponents or notation for
*that*mistake, right? So where does this intuition come from? - A couple of kids included a term in Q4 and a term in Q5. I find this interesting, but I’m not exactly sure what its significance is. Is the temptation to add and when the binomials are in the same visual position that they are for addition problems?

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…

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- Post author By mpershan
- Post date May 13, 2013
- 10 Comments on Cross-multiplying or Cross-cancelling?

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- Post author By mpershan
- Post date April 3, 2013
- 4 Comments on (-2)^5 + (2)^0 = 0

@mpershan Can’t tell you how many times I saw this mistake this quiz. Yikes! twitter.com/mr_stadel/stat…

— Andrew Stadel (@mr_stadel) March 17, 2013

What’s the fastest way to help this kid?

Incidentally:

@mpershan Yes, please post. Visually, if most of them graphed the line would identify +slope. Abstractly, they either rush or forget it’s +.

— Andrew Stadel (@mr_stadel) March 18, 2013

@mpershan I need to encourage them more to make a sketch of the 2 pts first in order to visualize and identify the slope first.

— Andrew Stadel (@mr_stadel) March 18, 2013

Students were prompted to graph a systems that has more than one solution, and one group provided the work above, confident that they had a system with three solutions.

So, how do you respond to the group? What do you say?

Thanks again to Nicole Paris for the submission.

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- Post author By mpershan
- Post date March 7, 2013
- 3 Comments on Solving Systems Algebraically