Thread by @benjamindickman, Where do math problems come from? I write lots of them, and [...]

Where do math problems come from?

I write lots of them, and I have shared a fair number that I really like. Below is one that I think is awful. And: I wrote it [at age 24].

This is a problem that I sent to an MAA journal for undergrads. How would you respond to this email?

Where do math problems come from? I write lots of them, and I have shared a fair number that I really like. Below is one that I think is awful. And: I wrote it [at age 24].This is a problem that I sent to an MAA journal for undergrads. How would you respond to this email?

If you made your way through a math major or have solved enough recreational math problems, then the names Alice and Bob (A and B) will be unsurprising to you.

What expectations should we have in 2020 (and in 2011!) for a problem section editor? Here's the response & the result.

If you use twitter to follow math educators or #MTBoS or #iTeachMath, then you probably know why this problem is trash.

It's not the "math structure" (so to speak). It's

- teachers controlling bodies
- reenforcing gender binary
- general creepiness
- baked in misogyny
& more

I sent the problem to three professors beforehand. (All of whom are cishetero white men...)

What expectations should we have in 2020 (and in 2011!) for professors who read problems phrased like the one that I formulated?

Here are their responses (diff names). What's missing?

Notice above that I tried a gender-equitable

extension in which *boys* choose first in *math* class then *girls* choose first in *English* class.

The problem had now been seen by 3 professors and 1 problem section editor. Sum feedback?

Change: Alice & Bob

Amanda & Bill

Notice above that I tried a gender-equitable extension in which *boys* choose first in *math* class then *girls* choose first in *English* class. The problem had now been seen by 3 professors and 1 problem section editor. Sum feedback?Change: Alice & Bob Amanda & Bill

Those were the solutions that were eventually published. If anyone found the context to be problematic, it wasn't remarked on. And the context wasn't ignored: Note the remark (purple parentheses) from the Cal Poly group who solved it.

How many

s saw this & felt it was good2go?

Fast forward: I meet @joeykelly89 and @xyu119 at a professional development session at @BUWheelock ("SED" at the time) and find out about their @playwyourmath project: https://playwithyourmath.com/

I suggest my problem but by 2015 my thinking shifted:
https://misteristhisright.com/2015/03/01/12-space-race/

Excerpt:

(Background note: Joey & I were both math majors at the same college.)
It is very easy to write an awful problem that you push from your

to professors to an editor to a journal w/o anyone objecting. Fortunately, PWYM reformulated the problem as follows:
https://playwithyourmath.com/2017/07/27/12-space-race/

(Background note: Joey & I were both math majors at the same college.)It is very easy to write an awful problem that you push from your to professors to an editor to a journal w/o anyone objecting. Fortunately, PWYM reformulated the problem as follows: https://playwithyourmath.com/2017/07/27/12-space-race/

Besides the vastly improved aesthetics* (tx to @xyu119) note that the problematic elements are gone yet the mathematical structure remains.

More than removing the bad – the PWYM version looks [to me] like a significant improvement!

*as @ddmeyer notes in a comment on Joey's blog

I also suggested this problem (modified) for a math competition that my college gives to freshmen/sophomores.

Here it is in the 2012 exam (more Walker Exams: https://www.amherst.edu/system/files/media/walker2012_0.pdf).

So from 2011

2012 my thinking shifted.
Yes, we still have Alice & Bob; but coloring vertices!

I also suggested this problem (modified) for a math competition that my college gives to freshmen/sophomores.Here it is in the 2012 exam (more Walker Exams: https://www.amherst.edu/system/files/media/walker2012_0.pdf).So from 20112012 my thinking shifted.Yes, we still have Alice & Bob; but coloring vertices!

Where do math problems come from?

In general? They *can* come from all over.
Specifically? *I* have written a lot of them.

Rather than hiding past problematic instances, one technique I now use is to have students actively consider contexts. For example: https://twitter.com/benjamindickman/status/1124817171375374336

https://twitter.com/benjamindickman/status/1124817171375374336

No attempt to tie this up with a neat Moral Of The Story, and I wish I could say with confidence that this Terrible Problem marks, in fact, the worst Math Education Decision that I've made. (No way...)

But we all – me clearly included! – need to get better.
#MTBoS

#iTeachMath

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