When I sit down and focus on planning for this coming school year, I find myself planning for problems rather than planning for sequence, presentation, or activity. I think this is one of the fundamental growths I’ve had between my first-year self and my current teaching self – around this time last summer, I was outlining day-by-day sequences of what I would cover and scripting specific lessons. I had grandiose ideas and felt like I needed a very specific road-map before I could start the year. I was only barely paying attention to the specific problems I was assigning for homework. This philosophy has changed – now I feel like a loosely defined road-map based on groups of skills and a collection of related problems is sufficient to keep me on track for the year. Based on how much I threw away last year, I’m almost afraid to plan a concrete lesson more than a week in the future. Having a collection of meaningful problems to pull from, though, is incredibly soothing to my nerves and is also a better reflection of my teaching style.

This all might be a bit abstract for now, so here are some things that might give a better idea of what I’m talking about:

Procedural Problems: Pretty much anything generated by Kuta Software and anything that can be put on my Wall of Remediation. Also, here are some concrete Parallel Line Problems I might do:

Discussion Problems: Parallel Line Mazes

Building Cities in Geometry

What I think all of these have in common: They are problems that require procedural fluency in order to be successful, but where the answer to the problem is practically meaningless without process to accompany it. These are problems where the meaning is in doing the problem, not in having the correct answer at the end. In fact, for many of these, incorrect answers could also be incredibly interesting. These are problems that could last an entire class period with the right group structure and questions. These are problems that naturally encourage discussion and justification and arguments. These are also problems that I definitely do not want to solve for them – I want them to try it on their own first. Maybe there’s some productive struggle. Maybe they work with their neighbor for a bit. Maybe at some point, we regroup and I ask the group to clarify a few things. I act as more of a facilitator and guide during these problems rather than an explicit model. These are problems that are the gateway for writing in my classroom.

Stained Glass Project

When I taught area, I gave my students meter sticks and had them go outside to measure the surface area of the parking blocks. The prompt was: if the school wants to repaint the parking curbs, how much paint will they need to buy and how much will it cost?

These are hard to come by and I’m still developing them. They’re not perfect and I’m still trying to figure out the best way to incorporate them into my curriculum. But for right now, I think I want at least one mostly hands-off task/project per unit.

How It’s Influenced My Planning: I’m starting to feel that having a collection of these types of problems will help me more effectively plan assessments, activities, and remediation. It all comes down to having problems to pull from. And not just the procedural ones – the really magical ones are the discussion problems. Some of my favorite moments from last year were during class periods that began with some sort of scenario and guiding my students towards finding the answer. This is where my focus has been: collecting problems and searching for meaningful problems to lead discussions and problems that could become a meaningful task or project for my students. I’m hoping this is a better use of my summer time than what I did last year.

Soon to Come: A review of sources I’ve been looking at for these problems. Spoiler alert: Park Math and James Tanton have some amazing problems to pull from.