Math education is living under a spell. Most classes and curricula operate under a pervasive and unspoken assumption; its benefits are widely accepted, but its flaws are all too hidden. Making math classes welcoming to students should be an important consideration in addressing some of these flaws.

The assumption is that you learn math by solving strings of successively harder problems, which does not particularly make math class welcoming. At each stage, the teacher decides how hard to make the problems; that is, where to set the “difficulty dial.” The ideal is to gradually turn the difficulty dial from left to right, easy to hard, at just the right speed. For example:

First: Add 19 + 12. Then, later: Add 1989 + 1272.

First: Solve 2x + 1 = 9. Then, later: Solve 2x + 9 = 1.

First: Graph y = x2. Then, later: Graph xy + 25 = x2 + y2.

Welcoming and Challenging Aren't Opposites in Math Education

There’s truth in this way of thinking, but when I start treating that slice as a whole loaf — when I catch myself thinking of where to set the difficulty dial as the only choice, or even the primary choice, that a math teacher faces — that’s when I slap my face, dump ice water on my head and write two crucial inequalities on my hand:

Easy ≠ Welcoming.

Difficult ≠ Challenging.

Focusing on “easy” vs. “difficult” can become a trap. The two appear to stand opposed, and so teachers can fall into the idea that we must pick one or the other.

But who really cares about “easy” and “difficult”? They are only proxies for two higher virtues, the actual qualities of successful instruction.

First, math class should be welcoming. Students need to feel comfortable in the intellectual work of mathematics. Teachers need to help them feel capable not just of solving an “easy” or dumbed down problem, but of tackling the real stuff.

Second, math class should be challenging. It should sharpen and deepen students’ thinking. They should master new skills and practice solving unfamiliar problems.

Unlike easy vs. difficult, welcoming and challenging aren’t opposites. We don’t need to choose between them. The best math education is welcoming and braids the two together, in puzzles that are clear yet subtle. A good math lesson, like a good sudoku, can welcome and challenge students simultaneously — welcome them by challenging them.

Read the full article about making math class welcoming by Ben Orlin at The Hechinger Report.