I imagine this is pretty high on whatever hierarchy of question you ascribe to, but it’s one that sure speaks to me. Malcolm Swan references Creating Problems (p.28) as a way of students demonstrating mastery. I’ve had mixed result with having students do just that.

Below is an attempt at streamlining the process, using a sort of “walkthrough” template. It begins by asking the students to describe the math we’ve been doing recently, followed by copying a recent prompt. Along the way are some (hopefully) helpful hints and key words that may be useful.

Feel free to use & modify as you see fit. Better yet, tell me how it goes.

Note: scribd doesn’t play well with some formatting, so here’s the original doc and PDF.

Problem Creation Walkthrough (PDF)

Problem Creation Walkthrough (doc)

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Cool idea. I’ve encouraged, but never formalized this. Thx for a great post.

Just hit me that this might be a higher level of mastery demonstration, perhaps in standards-based learning or something similar. Very intriguing set-up…

Huh, I hadn’t thought of that either but yeah, I could easily see this being tied to something SBG-like:

Level 1: Apply the math in a different context.

Level 2: Design a problem using similar math.

Level 3: Design a problem under the same content umbrella with multiple solution paths.

… or something. Great thoughts!

I’ve incorporated a limited version of this into my “test corrections” policy this year. Instead of a retake policy like I had previously, students can earn partial or even full credit back on their tests in the week after getting them back by solving each problem they missed correctly (fixing their mistakes), then creating a similar problem and also solving it correctly. They moan about having to write and solve the similar problem, but they agree that it supports their learning.

I don’t require the corrections to be done solo, so I help them with the process if they ask me to.

I have not figured out a way to make it general, but an example I have used at the Algebra 2 level is to have them select a complex conjugate and then create a quadratic using their selection as roots. Students then had to solve the problem by factoring (which it won’t) , by completing the square and the quadratic formula. I then had my students exchange their quadratics with another student to evaluate another persons work. This allows for creation and evaluation.

We tried this (in a more informal way) with our fifth graders, an experience I relate in the latest post on my blog: exit10a.blogspot.com

I like the addition of a “word bank” on the problem creation walk-through, I will use that next time.

Also thanks for reminding me about Malcolm Swan! Lots in there to think about and use.