I’ve developed an instinct against explaining things to students. It’s an instinct I’ve developed for practical reasons. The more I talk, the less students listen. The longer I talk without a break, the more tenuous my hold on what students understand. Students get confused when I spend too much time sharing how I think, and too little time understanding how they think.
I have no philosophical issue with telling students things. In short bursts, when students feel a need, there’s nothing better than a concise explanation that lets them solve a new problem. Then, I ask students to solve the problem, see how it goes, and consider whether there’s something else I need to address or if they are ready to extend their thinking a step further.
Something I’ve found myself doing is finding more and more ways to explain less. Asking students to figure things out for themselves often doesn’t work, and when it does it tends to privilege students with strong backgrounds and positive past experiences in math class. Explaining less might mean breaking a lesson into little chunks, so that I’m only talking for a minute at a time in between having students solve problems, warm calling students after each problem to summarize a key idea for the class. It might mean using worked examples to have students generate an explanation themselves, and listening in to notice their thinking and build from it. It might mean presenting a problem as a puzzle drawing on prior knowledge, figuring out where students are with that prior knowledge, and building my explanation from there.
I read this great post about teaching Computer Science yesterday and couldn’t stop thinking about the elegance of the ways this teacher found to explain less. My favorite:
Here’s an example — the second thing I ever show students, right after
print("hello world"), is this right here:
name = "Tamara" print("Hello" + name)
And then I ask one simple question:
Don’t answer out loud — just think. What will happen when you run this program?
Don’t answer. Just think. What will happen?
Turn and ask your neighbor for their prediction.
Literally every student intuits that this program is going to greet Tamara.
And then after that, we run the program, find out that it prints
HelloTamarawithout a space, and we also do our first round of debugging. High fives all around!
I can imagine myself as a novice computer science teacher trying to explain what this example will do. I imagine it as a complete mess. There will be a time, later, to formalize student knowledge of variables, strings, and more. In the meantime, students learned something , and they’re primed to learn more. This is a beautiful example. It’s not too complex, builds from intuition, and packs in surprise. I’d love to find more ways to do this in a math classroom.
Here are three things that I think matter in finding moments to explain less. First, you can’t force it. I never want to become dogmatic and refuse to explain things. Explanations are valuable, and they’re especially valuable when they’re used at the right time and place. Second, I don’t want to let perfect be the enemy of good. My worst explanations are when I try to explain something with mathematical precision and address every possible case. But that precision can create confusion. Sometimes students are ready for an informal understanding of a concept, but struggle to engage with too much complexity at once. Finally, finding ways to explain less trusts students more, and sends a message about what they can do. If every lesson begins with explanation, students learn that knowledge always moves from the teacher to the student. I don’t expect students to derive centuries of math on their own, but there are plenty of opportunities for students to extrapolate form their knowledge to something new. And every time we do that, students have the opportunity to trust themselves and their ideas a little more.