# Interleaving and problem writing

It’s official: my shift to problem-based learning has consumed me. It’s all I seem to be thinking and writing about for the last three months. Radical change can do that, I guess.

Like I’ve said before, it has been really fun to think about the algebra 2 curriculum in this new way. Instead of running through units like what is done traditionally, I’ve been nonlinear about my planning. One glaring example of this is how I’m teaching trigonometry and trigonometric functions. In all my previous years, I’ve had one or more isolated units in the spring. Now, instead of doing one big chunk of trig near the end of the year, my kids are learning it in bite-sized pieces over the course of the entire year. I’ve realized that there’s no reason why they can’t explore the unit circle while also learning how to factor or analyze exponential functions.

And this sort of interleaving happens through problems, which is the other reason why I’ve been so excited this year. Specifically, it has been sequencing and writing the problems that has me on the edge of my seat. This is been a challenge that I’m now addicted to.

Before this year, if someone would have asked me to write the problems that I give my students, I would have cried in fear. Why would I want to do that? My life consisted of going to jmap.org or the MTBoS search engine and that was it. The point is that I would find problems, not write them. Besides, even if I wanted to write them, it would have taken waaay too long.

That has changed.

First, I have found the time. Second, PBL requires that I write problems if I want to adequately meet the needs of my kids. That said, I’m not writing all of the problems the kids are doing, but definitely a majority of them. Thanks to Exeter and folks like Carmel Schettino, there are so many problem gems already out there to use and adapt.

As such, I’ve been thinking about problems in new ways. Specifically, I’ve never deliberately thought about the different types of problems that exist and when to throw any given one to the students based on the math that I want them to explore.

Recently, I’ve been especially interested in the student-work based problems, like algebra by example. In essence, they force the kids to analyze math work and then transfer that analysis to a new problem. The work can have mistakes. The problems usually spur some good discussion, too. (Mine haven’t, but I’ve heard they do.)

I don’t claim that they’re great problems and should be used by others, but I’ll close with a few that I’ve written and used with my students.

That’s all for now.

bp

## 4 thoughts on “Interleaving and problem writing”

1. Can’t echo enough how much I agree with your comment about teaching Trig (or other topics) in small snippets over the whole year. I’ve really come to believe that there is no “one day” that a topic is taught / learned or even “one unit”. Ideas evolve and the more we can connect them to other ideas the better for the kids. Thanks for your blog.

1. brian says:

Thanks Joseph for reading and chiming in. I think I took the scenic route in figuring that traditional teaching and learning in the classroom isn’t natural, it doesn’t reflect how we innately come across new ideas and construct knowledge. I’m not there yet, but I’d like to think I’m getting closer to this with PBL.

2. Pingback: PBL v2 | lazy 0ch0
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