Trying a bit of “3 Act Math”

Today I decided to try the “3 Act Math” style of modeling mathematics. I had been playing with the idea all year and wanted to try it in algebra II. I was hesitant for a number of reasons. First, this is my first year teaching algebra II, so teaching a topic in an unconventional fashion was a little intimidating. In addition, I wasn’t completely clear on the format of the discussion and how concepts are ultimately tied together in the end. I also struggled to find a good topic/intro to try it out with. With all this making me hesitate, I was inspired by a recent post Dan Meyer made about the detailed structure of his “3 act math” tasks. In this post Dan outlined in detail how each step of his lessons are formatted. This gave me the confidence to try it for myself.

I chose to try it out on the topic of “Heron’s Formula” for the area of a triangle. I believed this topic was straightforward enough that if the lesson crashed and burned I could clean it up fairly quickly the next day.

The first thing I struggled with was coming up with a good visual/problem to start with. I settled on a triangular garden as you can see in the second slide. (Yeah, I know, I didn’t say I was good at this stuff yet…) The picture was simple enough that students did raise many questions during act one. The precise question I wanted to work through wasn’t asked, but we got pretty close in both third and fourth hour. (This was, “How many plants can I fit in my garden?”) I will assume that you have a basic idea of how a 3 Act lesson proceeds, save you the details, and go straight to the reflection.

(You can see the slides to my presentation here. This is after all their questions have been filled in. There was minimal text to begin with.)

The Good

• Simply put: engagement. I had far more engagement in the lesson than I have in a traditional lecture. The intro “task” where students are asked to write any question they have about the garden allows all students to access the material from the beginning. When I asked for feedback at the end of the hour I had a student say “I liked how people that don’t usually talk contributed to the lesson.” I couldn’t agree more.
• Students arguing about math. Students debated what formulas to use, how to measure the sides of the triangle, and whether you could, in fact, plant only half of a green circle tree.
• Act II: The question of “What information do you need?” I especially liked. What matters? Why does it matter? What information do you need from me? What can you get from the picture? I think Act II was largely successful because Act I set the playing field level for all students. Nobody had seen that garden before, so how could any student know more about it than any other student?

The “meh”

• Class size: The lesson went better in my smaller class. A higher percentage of students could get involved. I’m sure with practice I could get better at this.
• Student comfort zone: This style made some students uncomfortable and some didn’t know what to write down. Some thought this style was good for an easier topic, others thought it might be better for a harder topic. I’m not sure which is the case. I certainly enjoyed an easier topic because it was safe; if it bombed, recovering was easy. I do think this would be more difficult to do with a tougher topic. What are your thoughts? How are more difficult topics received by your students?
• Student ownership of their learning: There certainly was more ownership in this style than a traditional lecture. However, I think I got more ownership in my flipped class. I need to try some more 3 act style lessons to come to a verdict here.

Why I’m Excited

I love that everyone could access the lesson from the beginning. I can’t stress that enough! The idea that math becomes accessible to students that generally hate math is enough of a reason to try this technique. I am also excited to apply more “3 act style” structure to my precalculus class. Steve Kelly and I have already set up leading questions for each unit, but I need to do a better job at making the discussion around them more structured. Practicing the 3 Act style will help me do that.

In general I’m just excited that I tried something new and it didn’t bomb. In fact, I would go so far as to say it was successful. Risk-taking paid off and that is a huge take-away from this lesson.