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Friday, July 17, 2015

Summer Problem-Solving Course

This summer I have the privilege of teaching a problem solving class to mathematically-inclined rising eighth graders. The course is called Math Team Strategies because a big goal is to get kids more ready for contests like MATHCOUNTS and the AMC contests. But we are also looking to highlight problem solving strategies that are broadly useful, whether kids decide to participate in contests or not.

I'm going to make this post pretty nuts and bolts just the facts ma'am - it's the nitty gritty details for people who want the ideas.

I lovingly plucked from the work of, and want to give tons of credit to:

Pacing

Eight days, two hours a day, one focus strategy per day. On the final day, instead of a new strategy, students experience a somewhat-complete MATHCOUNTS contest.

The Strategies

(Most of these are chapter titles in Crossing the River with Dogs - but that book has many, many more chapters. It's awesome. You should check it out.)

The Lesson Flow

For each day, I selected problems that lent themselves to that day's strategy. Some problems are from Crossing the River, some are from old MATHCOUNTS contests, and some I made up. Additionally, we developed a few mathematical shortcuts over the course of a few days, like counting permutations with repetition and the length of a diagonal of a square. I cut the problems up onto slips, so students would only have one problem at a time. (For a longer course, or perhaps for older students, I'd probably elect to use Crossing the River as a text.)

All the students worked on the same problem at the same time, standing at chalkboards. I had anywhere from 6 to 12 students in a class, so this was manageable. I also had a TA who was a math-major undergrad. Nirvana. Before I left home I grabbed a handful of fridge magnets, thinking they might be useful for something, and we used them so students could stick the current problem to the chalkboard.


The Posters

The intention was for the whole class to go over each problem before everyone started the next one. (See this post about group discussions.) Of course, some students took longer and needed support. When I am helping, I tend to make the same suggestions and ask the same questions over and over. This poster was for students to refer to if both the TA and I were busy when they got stuck.


Also, of course, some students finished more quickly than the group. I also tend to always make the same suggestions when students say they are "done," so I made this poster for them, too.


The Self-Assessment

Before we went over each problem, I asked the students to turn in their problem slip with their name and a rating of the problem from 1 through 4. I did compile this data in a spreadsheet, but I'm not sure what to do with it. But I thought the self-assessment couldn't hurt.


The Resources

Will be here until someone holding a copyright yells at me to take them down. Or maybe this is fair use. I dunno. I hope it's good advertising for the publications cited above. Some of the problems turned out to be too easy, and I'll be changing them if I'm back next year. Some were too hard, but I thought it was okay to give kids at most one problem a day that was a big stretch for them. When that happened, I invited the TA to share their solution.

And That's about That

This was a really rewarding course. The kids loved it, I loved it, we all just had a grand old time talking about math for two hours a day! It was refreshing to not feel pressure to cover content at a breakneck speed, or sell kids on math (these kids already like math), or have to assign grades. (This morning when we did a sample MATHCOUNTS Sprint, a girl asked "Does this count? Oh, wait. We don't have grades." And she worked hard on it anyway.)

Questions, feel free to throw them in the comments.