You ask a good question. I have a lot of thoughts about it. Different answers at different levels. Like, what should a civilization do vs. what should a parent do vs. what should a teacher do? Different answers.
The overall theme, though, is to remove coercion and appeal to native fascination instead. If you have something of value to the student to offer, then in practice there’s a way to either (a) show the student that value or (b) earn the student’s trust that you’re tracking what they care about such that when you say “Trust me” they know there’s something good there even if they can’t see it for themselves just yet.
If you’re aiming to be a teacher… well, it’s tricky because last I checked, the systems you’re embedded in impose mandatory coercion. You have to cover certain topics, often in a certain order, within a certain window of time, etc. Especially since “No Child Left Behind” tied funding to test scores. And parents get mad and start rattling sabres if their kids come back from math class with a bunch of weird stuff the parents don’t recognize. Although maybe that was just the Boomers.
But that said! There are clever ways of working within these social constraints. If you can do that, the overall thrust for a teacher is to prioritize being curious about how the students are thinking rather than on getting them to understand certain concepts.
The lion’s share of work for a really good math teacher is in identifying zinger questions. You have to see how a student is thinking about a problem, and follow their contours of reasoning, and notice where it’s going to run them into trouble. You could just tell them about the trouble, but it’s far more effective to ask them to explain something or figure out something that will lead them right to the paradox spot.
After a while you’ll probably develop a really rich repertoire of such questions. And maybe more preciously, you’ll be familiar with a vast library of thinking styles that students actually use in the parts of math that you teach. This is what the education literature refers to as “pedagogical content knowledge” or “PCK” (which is where the CFAR class on “Seeking PCK” came from).
That’s my main answer. Two other points worth mentioning:
By the time they’re in high school, the basis of their math trauma will probably have already formed. You’re not likely to be the tipping point into horror for them.
Math trauma is way more reversible than most people realize.
So don’t worry about that part too much. Just zoom in on what you love about the subject, stay in contact with the kids’ wonder, and aim to be a guide facilitating their exploration of what fascinates them. I think good things follow pretty naturally from that.
You ask a good question. I have a lot of thoughts about it. Different answers at different levels. Like, what should a civilization do vs. what should a parent do vs. what should a teacher do? Different answers.
The overall theme, though, is to remove coercion and appeal to native fascination instead. If you have something of value to the student to offer, then in practice there’s a way to either (a) show the student that value or (b) earn the student’s trust that you’re tracking what they care about such that when you say “Trust me” they know there’s something good there even if they can’t see it for themselves just yet.
If you’re aiming to be a teacher… well, it’s tricky because last I checked, the systems you’re embedded in impose mandatory coercion. You have to cover certain topics, often in a certain order, within a certain window of time, etc. Especially since “No Child Left Behind” tied funding to test scores. And parents get mad and start rattling sabres if their kids come back from math class with a bunch of weird stuff the parents don’t recognize. Although maybe that was just the Boomers.
But that said! There are clever ways of working within these social constraints. If you can do that, the overall thrust for a teacher is to prioritize being curious about how the students are thinking rather than on getting them to understand certain concepts.
The lion’s share of work for a really good math teacher is in identifying zinger questions. You have to see how a student is thinking about a problem, and follow their contours of reasoning, and notice where it’s going to run them into trouble. You could just tell them about the trouble, but it’s far more effective to ask them to explain something or figure out something that will lead them right to the paradox spot.
After a while you’ll probably develop a really rich repertoire of such questions. And maybe more preciously, you’ll be familiar with a vast library of thinking styles that students actually use in the parts of math that you teach. This is what the education literature refers to as “pedagogical content knowledge” or “PCK” (which is where the CFAR class on “Seeking PCK” came from).
That’s my main answer. Two other points worth mentioning:
By the time they’re in high school, the basis of their math trauma will probably have already formed. You’re not likely to be the tipping point into horror for them.
Math trauma is way more reversible than most people realize.
So don’t worry about that part too much. Just zoom in on what you love about the subject, stay in contact with the kids’ wonder, and aim to be a guide facilitating their exploration of what fascinates them. I think good things follow pretty naturally from that.