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As part of the Math Blogger Initiation Project, Sam Shah, in his classic avuncular style, offered us the prompt to share anything that we are proud of.  Wait – of which we are proud.  Whatever.  Anyway, I’ve decided to share the very first random problem idea that I ever had.  Here it is – pay no attention to the horrid diagram, not to mention the ridiculous context.  (And here’s the google doc version, which is where all my work resides).

This was an introductory problem to a unit on circles, and the goal was simply to review basic concepts like radius, diameter, circumference, and area of a circle.  It is by no means the greatest problem, and it would be vainglorious to claim it as such.  However, I am proud of it for this reason: it marked a personal turning point for when I finally started to “get it.”

I mean “get it” in two ways.  First, I realized that it is far better to create your own problems than to steal them wholesale.  Believe me, I am not creative and I spend a great deal of time taking Henry Wong’s advice to beg, borrow, and steal.  I steal a ton of ideas from all over – colleagues, the interwebs, books, strange cloud formations…but there are some things that are so much better if you create them yourself.  And problem ideas are one of those things.  (To avoid turning this into a white paper, I think another post may be in order for this topic).

Second, I started to understand what it takes to make a good problem – things like multiple entry points that are accessible to all learners, multiple solution paths, allows opportunities for extension, etc.  If I could take a mundane review topic and create a decent problem out of it…well I can do anything, right?  And the thing is, the problem is almost Hemingway-esque in its simplicity.  I mean, there’s not much to it…and there doesn’t need to be.  (By the way, if you’ve never read Hemingway’s “Cat in the Rain”, do it.  It takes all of three minutes and is the best short story of all time according to this math teacher).

Since that time, my mind has shifted to be on a constant quest for problem ideas.  Most of them hit me at the most inopportune times…which means just at the moment that I’m about to fall asleep.  At first it was kind of a rare occurrence, but now I see them all over the place: the label on a bottle of Mountain Dew, some fried okra, a dirty windshield.  Not to sound trite, but math really is everywhere…especially when you’re on the lookout for random problem ideas.

#### 7 Comments

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1. ray_emily / Aug 28 2012 3:00 am

You get double rainbow bonus points! (I am *thoroughly* impressed. I tried and failed.)

2. Bryan Meyer / Aug 29 2012 12:34 am

I couldn’t agree more with the importance of creating your own problems. I think there are multiple benefits:

1. the creative process engages us (as teachers) in being mathematical along with our students
2. the problems are designed in response to a specific community of learners
3. I have found that reflecting on the struggle to design good problems has made me a much better teacher in many ways.

Nice post…thanks.

• Jeff d. / Aug 29 2012 10:07 am

Well now I don’t need to write a post about it! You bring up three excellent points, and I agree with all of them. The value of engaging in the process alongside our learners probably can’t be overstated. It takes a few months before the kids believe me that I don’t know the “answer” – that we’re figuring it out together.
Reflecting on the struggle to design good problems is important as well, especially combined with efforts to improve my own questioning and helping learners become better question-askers.
Thanks for your input.

3. druinok / Sep 1 2012 3:42 pm

This is one area that I definitely need to work on. I would love to hear more about how you brainstorm these problems.

• Jeff d. / Sep 2 2012 6:48 pm

I struggle with it too (I always say it’s because I’m not creative, but I think there’s more to it than that). I definitely plan to continue posting problems and where they came from, and I think a post about brainstorming might be beneficial as well. Thanks!

4. Katie / Sep 2 2012 8:28 pm

Great post! I attended a CCSS inservice this week where we spent some time creating our own problems for problem based learning!

5. Jeff Brenneman / Sep 2 2012 9:53 pm

This sounds like a really cool problem! It would be awesome if the students would get the opportunity to actually build the cylinder for the winch and test it out.