One of my goals this year is to add different “evergreen” activities to my teaching toolbox that can be for used for basically any topic, especially ones that are less open to application and need drill type skill practice. Especially for these topics, I always feel like I need things to break up the routine and find ways to get students more involved. Here is one that we did today which the class really enjoyed:

FOLDING STORIES:

A real Folding Story is one where you start out by writing two lines of a story. Then, you fold the paper so the next person can only see the second line and pass it on. Based just on this last line, they write the next line of the story. You keep going for a while and then in the end open up to read the whole thing. They are usually very funny because the story quickly veers in different directions.

The idea in the math classroom is similar, but using a step by step math problem instead of a story. I put them in groups of three and gave them derivative problems involving negative and fractional exponents. The first person rewrote the expression to put it in a power-rule friendly form, the second person differentiated it, and then the third person rewrote the expression back into one with exponents in the denominator or radicals instead of fractional exponents. They folded the paper down each step of the way so that they could only see the step above theirs. Then in the end, they opened up and checked the final answer with the answer I gave them at the top. As a group of three, they attempted to find and fix their errors.

I had three rounds ready that got progressively harder, so when a group finished I would just hand them the next round. The groups worked at their own pace, but most did 2 rounds in about 15 minutes and then got partway through round 3 when class ended.

REFLECTIONS:

1. Students are often really bad at diagnosing their own errors, but I think this is because we have never trained them. They had a tough time at first finding their errors in this exercise, but I think the step by step nature of it helped them figure out which part of it that was wrong and follow it up to the step where it got messed up. I want to do this more often to help them diagnose their own mistakes.
2. My role was reduced to “person who hands out the next round of three when the group finishes,” which I loved. I answered a few questions individually, but for the most part, people helped each other and talked math.
3. Lots of students cheated by opening up the paper to make sure the step above theirs was correct. Don’t know how to avoid this, but maybe it’s not the worst thing in the world.
4. I think that next time I might hand out colored pens too so that when they get to the mistake stage, they correct it with a different color and can more easily see where they went wrong. The correcting stage this time just involved lots of scribbling all over the strips (as you can see above).
5. The only thing I didn’t like is that the students left with nothing in their notebook to review afterwards. Some students took the completed strips, and I will post the whole exercise on our course website, but that is always less than ideal for me.
6. FINAL REFLECTION: Keep this one in my toolbox.