Framing kids as “disruptive” or “inattentive” or otherwise having the wrong nature if they feel disengaged. This is after informing them what they’re going to study without consulting what’s relevant or interesting to them, and then using social power to require them to study those things. But the problem is supposedly the student, not the system.
Claiming that they’ll need these math tools later in life, and that this justifies adults pressuring the kids to learn those skills now. (This is more bullshit-flavored than gaslight-flavored, but I think they’re psychological neighbors.)
Pretending that because a word problem touches on a topic kids care about, the math is relevant to what the kids like about that topic.
Insisting that forcing kids to take math classes is for their own good, and if the kids don’t see why or don’t agree, then they should believe the adults over their own sense of things.
It makes me so angry. It’s perfectly antithetical to the essence of math as I see it.
This question might be independent from my other one, so I’m putting it in a separate comment.
What’s your primary solution to the problems that you list? Do you think that it can be mostly solved by teachers—e.g. by not exaggerating the applicability of the course material—or do you think that it requires a systemic solution—e.g. by sending the disruptive and inattentive kids to a class (potentially a quite unconventional one) that they’re more interested in?
I ask because I’m considering changing careers to become a high school math teacher, and I’d like to avoid using insidious psychological techniques on my students—doubly so if the techniques would cause my students to develop a long-term aversion to mathematics.
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.
Would you say the same of most other class subjects? I ask because, with the exceptions of reading and persuasive writing, I don’t think that any conventional school subject is more applicable to the average person’s life than grade-school math.
Yes, people can get through life with an astonishing ignorance of mathematics, but they can get through life with an even more astonishing ignorance of social studies, literature, and thesciences.
In my opinion, the purpose of public basic education is twofold:
Identify the children who are talented at a given subject so that we can rapidly and efficiently develop their skill to a point that it becomes useful to society.
Intellectually immunize the general population against low-effort fraudsters and other bad actors.
Unfortunately, (2) requires most people to spend years learning about subjects that they don’t care about. Do you have a different philosophy of education, a different ranking of subjects’ importance, or something else?
Would you say the same of most other class subjects?
I was homeschooled and then studied math education, so I’m not sure. But my passing impression is (a) yes, it applies to most methods of teaching in schools regardless of subject; but (b) math taught this way is particularly damaging.
I want to emphasize that this is my impression. I’m also not entirely sure why math seems to be more damaging. I have guesses. I just observe that e.g. literature hatred or music phobia aren’t nearly as prevalent as math trauma is. Best as I can tell.
I ask because, with the exceptions of reading and persuasive writing, I don’t think that any conventional school subject is more applicable to the average person’s life than grade-school math.
Yes, people can get through life with an astonishing ignorance of mathematics, but they can get through life with an even more astonishing ignorance of social studies, literature, and thesciences.
Well, sure. But people will also pick up the math they need as they need it for the most part. That’s true of most subjects really.
I didn’t learn to read in school. I went to kindergarten before being homeschooled, and they were teaching us the alphabet and some basic words, but I could already read books by then. I learned to read because I wanted to read.
There’s something very weird in our cultural groundwater around what teaching is. It’s like we start with a prescription of subjects and then default to coercion to get students to “know” those subjects. Why? If it’s relevant to their lives, we could learn to point out the connection in a way that feels alive to them. If we can’t do that, then what makes us so sure that it’s relevant for them?
Do you have a different philosophy of education, a different ranking of subjects’ importance, or something else?
Yeah I do. I think the most imporant function of widespread education is to make good citizens. Which is to say, children put through an education system need to come out of it better able to engage with the system that runs their civilization, including the education process for the next generation.
In the United States, I think that puts civics as the most important subject. It’s really key that citizens understand how their government works, what the checks and balances are, how jury nullification works, what forms of corruption actually do arise even within the current system, etc. Otherwise they don’t know how to participate in the government that’s supposedly “by the people, for the people”. This is vastly more important than learning math they don’t naturally pick up in their day-to-day lives.
I think the two things you named are really good though. I wish public education had those as real goals! That’d be nice. I think (1) happens sort of despite the education methods, and (2) happens more through other cultural channels than it does through formal public education. Just my impression.
A few examples:
Framing kids as “disruptive” or “inattentive” or otherwise having the wrong nature if they feel disengaged. This is after informing them what they’re going to study without consulting what’s relevant or interesting to them, and then using social power to require them to study those things. But the problem is supposedly the student, not the system.
Claiming that they’ll need these math tools later in life, and that this justifies adults pressuring the kids to learn those skills now. (This is more bullshit-flavored than gaslight-flavored, but I think they’re psychological neighbors.)
Pretending that because a word problem touches on a topic kids care about, the math is relevant to what the kids like about that topic.
Insisting that forcing kids to take math classes is for their own good, and if the kids don’t see why or don’t agree, then they should believe the adults over their own sense of things.
It makes me so angry. It’s perfectly antithetical to the essence of math as I see it.
This question might be independent from my other one, so I’m putting it in a separate comment.
What’s your primary solution to the problems that you list? Do you think that it can be mostly solved by teachers—e.g. by not exaggerating the applicability of the course material—or do you think that it requires a systemic solution—e.g. by sending the disruptive and inattentive kids to a class (potentially a quite unconventional one) that they’re more interested in?
I ask because I’m considering changing careers to become a high school math teacher, and I’d like to avoid using insidious psychological techniques on my students—doubly so if the techniques would cause my students to develop a long-term aversion to mathematics.
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.
Would you say the same of most other class subjects? I ask because, with the exceptions of reading and persuasive writing, I don’t think that any conventional school subject is more applicable to the average person’s life than grade-school math.
Yes, people can get through life with an astonishing ignorance of mathematics, but they can get through life with an even more astonishing ignorance of social studies, literature, and the sciences.
In my opinion, the purpose of public basic education is twofold:
Identify the children who are talented at a given subject so that we can rapidly and efficiently develop their skill to a point that it becomes useful to society.
Intellectually immunize the general population against low-effort fraudsters and other bad actors.
Unfortunately, (2) requires most people to spend years learning about subjects that they don’t care about. Do you have a different philosophy of education, a different ranking of subjects’ importance, or something else?
I was homeschooled and then studied math education, so I’m not sure. But my passing impression is (a) yes, it applies to most methods of teaching in schools regardless of subject; but (b) math taught this way is particularly damaging.
I want to emphasize that this is my impression. I’m also not entirely sure why math seems to be more damaging. I have guesses. I just observe that e.g. literature hatred or music phobia aren’t nearly as prevalent as math trauma is. Best as I can tell.
Well, sure. But people will also pick up the math they need as they need it for the most part. That’s true of most subjects really.
I didn’t learn to read in school. I went to kindergarten before being homeschooled, and they were teaching us the alphabet and some basic words, but I could already read books by then. I learned to read because I wanted to read.
There’s something very weird in our cultural groundwater around what teaching is. It’s like we start with a prescription of subjects and then default to coercion to get students to “know” those subjects. Why? If it’s relevant to their lives, we could learn to point out the connection in a way that feels alive to them. If we can’t do that, then what makes us so sure that it’s relevant for them?
Yeah I do. I think the most imporant function of widespread education is to make good citizens. Which is to say, children put through an education system need to come out of it better able to engage with the system that runs their civilization, including the education process for the next generation.
In the United States, I think that puts civics as the most important subject. It’s really key that citizens understand how their government works, what the checks and balances are, how jury nullification works, what forms of corruption actually do arise even within the current system, etc. Otherwise they don’t know how to participate in the government that’s supposedly “by the people, for the people”. This is vastly more important than learning math they don’t naturally pick up in their day-to-day lives.
I think the two things you named are really good though. I wish public education had those as real goals! That’d be nice. I think (1) happens sort of despite the education methods, and (2) happens more through other cultural channels than it does through formal public education. Just my impression.
Your examples fit the definition quite well. Apparently this is in the dictionary now. https://www.merriam-webster.com/dictionary/gaslighting