Trigonometry Problem Sets

J. M. — Fri, 28 Mar 2008 18:47:38 +0000

A couple years back a colleague and I decided to start using journals in our precalculus classes. Our idea was to periodically assign challenging problems for the students to solve in their journals. The catch was that they would also need to explain their thought process and reasoning as they solved the problem. Just knowing the steps wasn’t going to be good enough. Students hated these journals.

I hated the journals as well. As a person who struggles to stay organized, a stack of 25 journals was a major problem. So this year I’ve continued with the same idea, but I’ve abandoned the novelty of journaling. Students still hate explaining themselves, but they do see the value in the activity.

Recently, rather than assign these “journal” problems as homework, I created a set to do in class. The motivation was threefold:

Working on the problems in class would allow me to coach them through these difficult problems that I knew would cause them to struggle some. Doing these problems as homework would not have worked.
Working on the problems in class would allow them to collaborate.
I wanted them to receive feedback on their work from someone other than their teacher.

How it Works

I created a set of five “problem sheets” (I’ll include these as pdfs the end) and the class divided themselves into groups. Each group received one problem sheet to work on. The activity moved in rounds:

Work on problems.
Look at another group’s work.
Comment on that group’s work by writing notes to them on Post-its.
Return the work with comments to the original group.
Get a new problem to work on.
Repeat.

I should also note that before class I created a set of “hint cards” which they could ask for if they found themselves stuck. The hint cards nudged them toward a key insight or suggested a good place to begin. These cards ended up working out much better than I anticipated, mostly because I didn’t have to answer the same questions over and over and over. Instead I was able to move around the room and help with questions that went beyond, “Um, I don’t know what I’m supposed to do.”

Did it Work?

Yes. The problems I presented were right in the sweet-spot — challenging, but not so hard that they didn’t know where to start. If a group was feeling lost, then they got a hint card. Also, once everyone got down to business, they were really doing some fine work and having good discussions about math, and that’s exactly what I wanted.

The feedback portion of the lesson started out weak. Once I saw a few Post-its that said, “Awesome!” I knew I needed to clarify the purpose of the Post-its. By the end of class I saw some really specific and useful student-to-student feedback.

Finally, I should note that at the end of class I reiterated my intentions and the purpose of the activity. I explained my hope that they would have a better understanding of the math by trying to explain their process and their thinking. I then passed out some scraps of paper and asked them to evaluate the effectiveness of the activity. My prompt was, “I know that you hate writing about math. I understand. However, devised this activity to help you understand the math more deeply? If a deeper understanding is the goal, is this a good activity? No names on the papers, hand it to me on the way out of class.” About 70% of the class said, “I don’t like writing in math class, but yeah, it helped my understanding.” I even had a few students come up to me after class and say, “I really do understand things better now.” Only one student said, “This is the perfect marriage between English and math! I love it!” (She left class early to go to an interview with Harvard. Seriously.)

What Would I Change?

The organization of the different rounds is taxing. I was trying to watch the clock, shuffle papers, and teach. I need to come up with a way for them to manage the paperwork. In/out boxes? Envelopes? Let me know if you have ideas.
I always assume that my students know how to give each other feedback. They don’t. Directions about feedback need to be really clear. If you give them a few examples beforehand it will help.
It might be fun to make them do something crazy to get a hint card… sing a song, act like a cat, etc.

Handouts

Finally, the problems: Trigonometry Problem Set (pdf). Enjoy.

Purpose

J. M. — Tue, 18 Mar 2008 21:23:40 +0000

Dan Meyer:

So my advice is this: you have to make stories out of your lesson plans, collapsing resources into anecdotes. It’s easy to blog stories. They’re cathartic and satisfying where resource posts feel expensive. Plus people are more inclined to read stories than rubrics. (link)

The problem I’ve found with collections of lesson plans, materials, and ideas is exactly what Dan and his readers hit on here — I’m not inspired to use them. Without context, the information isn’t very helpful to me. I always try to give my students a context for their own learning, so I shouldn’t be surprised that the only lesson plans I’ve actually adopted come from friends and colleagues. These people sell me on the value of their ideas and inspire me to try something new.

So the purpose of this project is two-fold:

Provide some teaching ideas and the stories that go with them so that you might find some new idea that you connect with. If you do, we’ll provide materials so that you can easily try in your own classroom.
Make sure these ideas are coming from people you trust. In the art world these people are called curators.

That’s my vision for this project. We’ll start small and see what comes.