How Math Class Works

If your last math room ran on random groups and vertical whiteboards, this will feel like coming home. If it did not: you will spend most of class standing up, working at whiteboards, in groups you did not choose — because that is how people think best, and thinking is the whole point.¹ This is the calculus room, and calculus is far too good to be dictated.

graph LR
    A["Number talk"] --> B["Random groups"]
    B --> C["Thinking task at the whiteboards"]
    C --> D["Consolidate together"]
    D --> E["Notes to your future self"]
    E --> F["Check your understanding"]

Number talk

We open with ten minutes of mental mathematics — a number talk — done in heads, defended out loud. No pencils, no calculators, no single right method. The method you defend today becomes the method someone else reaches for tomorrow.

Random groups, every day

Groups of three, drawn visibly at random at the door — cards, not choices. Nobody owns a seat, nobody gets stuck being “the one who writes”, and within a few weeks you will have thought hard alongside everyone in the room. It feels strange for about a week; then it feels like the obvious way to run a room.

The thinking task

The heart of class: a problem worth standing up for, worked at the vertical whiteboards — often an exploration, often a problem you have NOT been shown how to do. That is deliberate. The idea gets its name and its clean statement after you have wrestled with it, not before — the shrinking secants before the word “limit”, the slopes conjectured from data before anyone says “power rule”. Marker in hand, one rule: the person holding the marker writes only other people’s ideas.

Stuck is expected and useful — it is where the learning is (Getting Unstuck is a whole tutorial on being stuck well). I answer questions that keep thinking alive and decline the ones that would end it.

Consolidate together

We tour the boards and rebuild the key ideas from what groups actually did — starting from the simplest approach and climbing. Seeing four routes to one answer is how you learn to choose routes; your route being on a board matters more than it being finished.

Notes to your future self

Then, and only then, notes: a few sentences and one worked example in your own words, written for the version of you who opens the binder in exam week having forgotten today. The concept pages hold the clean, complete statements — your notes hold what YOU need to remember about them.

Check your understanding

Class ends with two or three questions you try alone, and your Math Journal. Not collected, not marked — they exist so that you, not the quiz next week, are the first to know what stuck and what needs another pass.

If you were away

Check the class page in All Classes, try the thinking task before reading anything else about it, then do the check-your-understanding questions. A genuine attempt teaches more than a perfect summary.

Footnotes

1. The structure of this classroom — random groups, vertical whiteboards, tasks before technique — comes from Peter Liljedahl’s research in Building Thinking Classrooms in Mathematics (2020), which measured where and how students actually think. ↩