This summer, we had the opportunity to draw up and institute a wholesale program from scratch, using our own lesson plans and providing the PD and support. Following that program, we began some fascinating conversations about how to articulate our vision of excellent math classrooms in more detail. From 30,000 feet, the direction we want everyone to move feels clear: our goal is to help design experiences that give everyone a chance to fall in love with math. But I feel like we’re due for a new articulation of where we’re aiming.

So what does this loving-math classroom actually look like?

1. The Loving-Math Classroom is a Doing-Math Classroom
   The central activity in the class must be the doing of mathematics. Our metaphor here is brain as muscle, and classroom as gym. The instructor needs to launch the activity so that everyone can get started (and won’t injure themselves), but fundamentally, the actual “working out” is done by the students. The students must encounter activities that are difficult enough to be challenging but not debilitating. Most of class time (50 – 80%) should be spent actually doing math, preferably individually or in groups. This might mean playing math games (i.e., Pig), working through complex math tasks (i.e. The Power of 37), and also story problems and more plebeian math worksheets, though it can be problematic to rely too heavily on these.
2. The Loving-Math Classroom is a Thinking-Math Classroom
   In addition to the actual doing of math, which is primary, it’s vital to find moments to take a step back and reflect on the process of doing math. What type of tools are useful to solve problems? How should we organize our data to best find patterns? What are good problem-solving techniques, and which whens are most useful for which kinds of problems? What do we currently know, and what questions do we still have? These times for reflection and discussion are critical for encouraging a depth of thought and development of the habits of mind that are, arguably, the true goal of math education.

What does this look like in real life? Our Summer Staircase classroom had a four-part structure:

1. Warm-up (5-10 min) — keeping with the gym metaphor, a quick game or exercise to get the mathematical thinking started. Number Talks are a prime example.
2. Launch (5-10 min) — this is the only time in lesson structure that doesn’t explicitly include doing or thinking math: the time when the teacher is explaining something new. In general, the teacher should streamline all explanation to the minimum required to allow students to work on their own. Sometimes the launch is time for a mini-lesson, or to pull together ideas from previous lessons. Sometimes it’s simply to demonstrate a new game or activity. In general, the goal of the Launch is to get them to the starting line, not the finish line.
3. Work (30 – 45 minutes) — this is the period when the students actually do the math. For the summer, we used a station model, since younger kids usually have trouble focusing on a single activity for a long period of time. Typically, stations included a math game, a new problem or task, and an activity aimed at helping kids practice to master a technique or get comfortable with a mathematical representation. Starting in 3rd or 4th grade, and certainly by middle and high school, it’s more reasonable for students to be able to focus on a single, more complex task for the duration of this time.
4. Wrap Up (5 – 15 minutes) — this is when the doing-math class has the opportunity to become a thinking-math class. The Wrap Up allows students to articulate their conjectures, counterexamples, arguments, and questions from class. It’s also where the teacher can underline deeper lessons learned, in line with the Common Core Math Practices, for example.

We found that virtually everyone could create a doing-math classroom. All it takes is the teacher belief that student activity is the central function of the classroom, combined with good materials, which we provided. Creating a thinking-math classroom is trickier; it takes more artistry and more practice.

Aside: Last year, we wrote an introduction for our 2015 Summer Staircase curriculum that outlined what we dubbed five principles of extraordinary math teaching that later become my TEDx Talk:

1. Start with a question
2. Give students time to struggle
3. You are not the answer key
4. Say yes to your students’ thinking and ideas
5. Play!

It’s clear that these are all urging teachers toward a doing/thinking/loving math class as well. Principles 1-3 are designed to get kids doing and wondering as quickly as possible, and to avoid short-circuiting the doing/thinking process. Principle 4 is about expanding from doing to thinking. Principle 5 is about creating the atmosphere that actually makes it all jell.

So here’s the goal for us now: we need to articulate and fully formulate a vision, first of the doing classroom that teachers can make their own by a series of small, manageable steps, and second, of a pathway from the doing to the thinking classroom. Here’s a small beginning to that process:

Doing-Math Classrooms ideally involve a Warm Up, as brief a teacher Launch as possible, and then most of the class time devoted to the students working on a deserving problem or task.

Thinking-Math Classrooms are Doing-Math Classrooms that additionally include Wrap Ups for reflection and development of higher order skills, in line with the Common Core Math Practices.

Loving-Math Classrooms are Thinking-Math Classrooms that, at least occasionally, blow kids’ minds.

We’ll try to go forward with sketching a fuller vision of all of this. In the meantime, I’d love to hear your feedback.