Assuming that you like math… would you have preferred to have more lessons focused on the lives of mathematicians? As opposed to only having lessons about mathematics itself.
I found this question on StackExchange, and I was horrified: I loved math, but I hated history, and this sounds like a suggestion to make math more like history.
The problem with school is that it not only tells you things, but it also expects you to memorize them. My memory sucks. I was good at math because I was able to re-derive everything that I forgot. But there is no way to re-derive historical trivia. If my math tests asked me questions such as “which century did Euler live in? in which country? did he have a pet, and what was the pet’s name?”, it would have ruined my favorite subject.
But apparently most people feel the other way round, so my answer was downvoted.
Some teachers argue that many students prefer stories about mathematicians. But I suspect that it’s simply because many of those students hate math, and talking about mathematicians gives them an opportunity to discuss something other than math, which of course they are happy about. I would have been equally happy if a history teacher stopped teaching history, and instead gave us problems like “if the war started in a year X, and ended in a year Y, how many years did the war take?”. But that’s simply because I hated history and loved math. So obviously, people who hate math and love history would prefer to learn about the history of mathematics instead of mathematics itself. And they would probably prefer to learn about history of something else even more.
I don’t mind listening to a good story about mathematicians, in my free time. But I feel like introducing history of mathematics to math lessons at school would be just another step towards dumbification of math education. That it would give people illusion of learning math without actually learning math. Yes, this is a zero-sum perspective, but at school there is a limited amount of time, and you have to split it among the subjects, and among the topics within the subject, so more history of math will inevitably mean less numbers and equations.
I think more technicallly-oriented history would benefit a lot of students. And more stories generally—not just facts, but world models of how individuals who were gifted in some ways and damaged in others navigated their society in order to produce lasting value.
But really, one size doesn’t fit all, and never has. Some students will bounce off some or all aspects of adulthood and competence, no matter how it’s presented. Some will be great, happy people regardless of classes. The really good teachers/professors and a well-fitting curriculum for a lot in the middle will be pivotal for them.
I had a class in college about the history of the atomic bomb. Our text book was Rhodes, and most of the stuff we learned about was the different competing theories of atoms, the experimental methods & math used to distinguish between them, math behind atomic chain reactions, and the scientists who did those things. It was great! Our tests were basically physics tests.
I’d like more history like that, and I’d like marginal movements in that direction in math class. For example, something like Radical Real Analysis but for everything.
Obviously schools won’t do this well, but they won’t do anything well. Any change they make nowadays will be oriented toward making the least common denominator happy, if I understand the current fad among teachers nowadays.
The much more interesting question is how could this be done well, and the more useful is why the current fad & how can it be changed, so saying something like “teach more history in math!” can be expected to go well.
For people who are not very interested in some topic like math, presenting the topic as a story about the struggle of historical figures usually makes it much more palatable. Quanta magazine and Veritasium use this strategy to great effect. But I agree: At school time is very limited, and focusing on historical stories would greatly take away from the available time.
Moreover, I think it’s usually not possible anyway to present technical subjects as engaging historical dramas. For most subjects there simply was no such historical drama, nothing fitting an engaging narrative.
By the way, I think the issue you are pointing at is even worse for philosophy, and probably other subject areas except math and science. Too often popular introductions into philosophical topics (insofar they even exist) get turned into a biography of philosopher X, which is almost never illuminating, and usually ignored by academics for good reason.
I had some lessons on psychology and philosophy, and was extremely disappointed. (Not sure how much of that is general, and how much I just chose a bad school.)
At psychology, most lessons were a combination of learning some things the famous psychologists said, and learning some historical trivia about them. The part that was missing completely was applying any of that knowledge, whether to real or fictional examples.
As an example, when we learned about Freud, we were given a list of ego-defense mechanisms to memorize. What I would naturally expect next, would be a set of exercises, for example to read a written dialogue, and then answer “what ego-defense mechanism was used here?” and to underline the specific sentence; or something like that. But this way of thinking was complete out of every teacher’s mental space. The lessons were simply “here is the list”, and the exams were “give me the list”; if you repeated the list correctly, you passed. (My point is that even if you think that Freud is complete pseudoscience, this is still a wrong way to teach his theories, because you just teach the keywords, not the—actual or imaginary—concepts those words were supposed to refer to.)
Also, if you tried to ask something like “Maslow says that people first need to have their biological needs met, and only then they do things like art; but Freud says that people do art because they are sexually frustrated… so, which way is it actually?”, you would be met by a blank stare. What do you mean by “actually”? We don’t teach any “actually” here! We teach what Freud said. Then we teach what Maslow said. Those are two separate lessons, you are not supposed to mix them together. There is Map#1, which you need to know at Exam#1, and there is Map#2 for Exam#2. There is no territory.
At philosophy, that was also mostly an overview of historical philosophers, and what they said, but just quotes, not even trying to explain the concept, explore its boundaries, thinking about whether the actual world actually works that way. Plato said that specific things were imperfect reflections of ideas. What specifically did he mean by an “idea”? Is there a general idea of a “dog”, and also a more specific idea of a “poodle”? And a more general idea of an “animal”? A hierarchy of ideas? Is there also an idea of a “black poodle”, or is that too specific? I don’t know. All we learned was to quote that Plato said that “specific things were imperfect reflections of ideas”, full stop.
It’s not like subjects other than STEM are inherently bullshit, it’s just… most people who study and teach those subjects simply don’t care about making sense. None of my humanities-oriented classmates saw a problem with that. Learning means memorizing words. What else could it possibly mean?
...and then I see people complaining that teaching math is not more like this, and I get triggered.
If those stories were about pursuit of truth, like Archimedes’s eureka in a bathtub, they could motivate students and teach some lessons of rationality thinking.
And the history itself could be much more interesting subject if it were teaching some real wisdom rather than demanding stupid memorization of dates and places.
Assuming that you like math… would you have preferred to have more lessons focused on the lives of mathematicians? As opposed to only having lessons about mathematics itself.
I found this question on StackExchange, and I was horrified: I loved math, but I hated history, and this sounds like a suggestion to make math more like history.
The problem with school is that it not only tells you things, but it also expects you to memorize them. My memory sucks. I was good at math because I was able to re-derive everything that I forgot. But there is no way to re-derive historical trivia. If my math tests asked me questions such as “which century did Euler live in? in which country? did he have a pet, and what was the pet’s name?”, it would have ruined my favorite subject.
But apparently most people feel the other way round, so my answer was downvoted.
Some teachers argue that many students prefer stories about mathematicians. But I suspect that it’s simply because many of those students hate math, and talking about mathematicians gives them an opportunity to discuss something other than math, which of course they are happy about. I would have been equally happy if a history teacher stopped teaching history, and instead gave us problems like “if the war started in a year X, and ended in a year Y, how many years did the war take?”. But that’s simply because I hated history and loved math. So obviously, people who hate math and love history would prefer to learn about the history of mathematics instead of mathematics itself. And they would probably prefer to learn about history of something else even more.
I don’t mind listening to a good story about mathematicians, in my free time. But I feel like introducing history of mathematics to math lessons at school would be just another step towards dumbification of math education. That it would give people illusion of learning math without actually learning math. Yes, this is a zero-sum perspective, but at school there is a limited amount of time, and you have to split it among the subjects, and among the topics within the subject, so more history of math will inevitably mean less numbers and equations.
I think more technicallly-oriented history would benefit a lot of students. And more stories generally—not just facts, but world models of how individuals who were gifted in some ways and damaged in others navigated their society in order to produce lasting value.
But really, one size doesn’t fit all, and never has. Some students will bounce off some or all aspects of adulthood and competence, no matter how it’s presented. Some will be great, happy people regardless of classes. The really good teachers/professors and a well-fitting curriculum for a lot in the middle will be pivotal for them.
I had a class in college about the history of the atomic bomb. Our text book was Rhodes, and most of the stuff we learned about was the different competing theories of atoms, the experimental methods & math used to distinguish between them, math behind atomic chain reactions, and the scientists who did those things. It was great! Our tests were basically physics tests.
I’d like more history like that, and I’d like marginal movements in that direction in math class. For example, something like Radical Real Analysis but for everything.
Obviously schools won’t do this well, but they won’t do anything well. Any change they make nowadays will be oriented toward making the least common denominator happy, if I understand the current fad among teachers nowadays.
The much more interesting question is how could this be done well, and the more useful is why the current fad & how can it be changed, so saying something like “teach more history in math!” can be expected to go well.
For people who are not very interested in some topic like math, presenting the topic as a story about the struggle of historical figures usually makes it much more palatable. Quanta magazine and Veritasium use this strategy to great effect. But I agree: At school time is very limited, and focusing on historical stories would greatly take away from the available time.
Moreover, I think it’s usually not possible anyway to present technical subjects as engaging historical dramas. For most subjects there simply was no such historical drama, nothing fitting an engaging narrative.
By the way, I think the issue you are pointing at is even worse for philosophy, and probably other subject areas except math and science. Too often popular introductions into philosophical topics (insofar they even exist) get turned into a biography of philosopher X, which is almost never illuminating, and usually ignored by academics for good reason.
I had some lessons on psychology and philosophy, and was extremely disappointed. (Not sure how much of that is general, and how much I just chose a bad school.)
At psychology, most lessons were a combination of learning some things the famous psychologists said, and learning some historical trivia about them. The part that was missing completely was applying any of that knowledge, whether to real or fictional examples.
As an example, when we learned about Freud, we were given a list of ego-defense mechanisms to memorize. What I would naturally expect next, would be a set of exercises, for example to read a written dialogue, and then answer “what ego-defense mechanism was used here?” and to underline the specific sentence; or something like that. But this way of thinking was complete out of every teacher’s mental space. The lessons were simply “here is the list”, and the exams were “give me the list”; if you repeated the list correctly, you passed. (My point is that even if you think that Freud is complete pseudoscience, this is still a wrong way to teach his theories, because you just teach the keywords, not the—actual or imaginary—concepts those words were supposed to refer to.)
Also, if you tried to ask something like “Maslow says that people first need to have their biological needs met, and only then they do things like art; but Freud says that people do art because they are sexually frustrated… so, which way is it actually?”, you would be met by a blank stare. What do you mean by “actually”? We don’t teach any “actually” here! We teach what Freud said. Then we teach what Maslow said. Those are two separate lessons, you are not supposed to mix them together. There is Map#1, which you need to know at Exam#1, and there is Map#2 for Exam#2. There is no territory.
At philosophy, that was also mostly an overview of historical philosophers, and what they said, but just quotes, not even trying to explain the concept, explore its boundaries, thinking about whether the actual world actually works that way. Plato said that specific things were imperfect reflections of ideas. What specifically did he mean by an “idea”? Is there a general idea of a “dog”, and also a more specific idea of a “poodle”? And a more general idea of an “animal”? A hierarchy of ideas? Is there also an idea of a “black poodle”, or is that too specific? I don’t know. All we learned was to quote that Plato said that “specific things were imperfect reflections of ideas”, full stop.
It’s not like subjects other than STEM are inherently bullshit, it’s just… most people who study and teach those subjects simply don’t care about making sense. None of my humanities-oriented classmates saw a problem with that. Learning means memorizing words. What else could it possibly mean?
...and then I see people complaining that teaching math is not more like this, and I get triggered.
If those stories were about pursuit of truth, like Archimedes’s eureka in a bathtub, they could motivate students and teach some lessons of rationality thinking.
And the history itself could be much more interesting subject if it were teaching some real wisdom rather than demanding stupid memorization of dates and places.