I actually think that math teaching might work better if people spent time learning who though what as a result of asking what questions and how they first conceptualized their insights by building on what else.
Memorizing anything anywhere ever except as practice for understanding how memory works is always an indication that something has gone wrong however.
Do you mean “being made to explicitly work at memorizing is always bad, because you should pick up the important parts in the course of doing natural work”?
Memorizing anything anywhere ever except as practice for understanding how memory works is always an indication that something has gone wrong however.
I agree. I can’t recall the last time I had to work on directly memorizing something, after the poetry assignments in high school. In all the other instances, the memorization occurs in the course of understanding the material, thinking or reading in terms of new concepts. This applies even to language learning, where the new words are learned in course of reading with a dictionary (if you are not in a hurry). The concepts learned this way can always be tabooed without hurting the knowledge.
I take it you’ve never studied biochemistry at the senior undergrad level. Evolution doesn’t produce easily systematizable components down at the level of proteins and other macromolecules of like size. I can’t think of a workable alternative to giving things more-or-less arbitrary names and requiring people to memorize them so as to have a common language.
Can you imagine a successful computer programmer who was constantly looking up the syntax of the language they were programming in? Memorization is damn near essential.
I expect a good computer programmer to be effective in a language he has not seen before by looking up the syntax as he needs it, and to increase his effectiveness over time by learning the syntax through use, without any specific effort of memorization. At least, provided the novel language is good.
Good point. Now that you frame things in terms of how knowledge is acquired, the only thing I’m glad to have memorized is math facts in elementary school. But they have been pretty helpful!
When I was in school, we were given proofs of certain geometry theorems, and we were told that we might have to prove the same theorems in the exam. Most of my classmates simply memorised the proof as given; since I’m better at on-the-spot analysis than at memorisation, I used to re-prove the theorems from basic principles instead. The result of this was that my proof, while (usually) correct, would look nothing like everyone else’s proofs. Because of this, the maths teachers would have to actually evaluate my proofs step by step, instead of simply ticking off the well-recognised general proof. Apparently this makes marking slower.
This implies that there may be some pressure from the teachers for memory-learning, as it leads to easier marking.
Understanding the process of extending math theory is essential if you want to be able to tell the difference between being led down a good path and being led down a bad path.
If all you do is memorize theorems without understanding their proofs, you can memorize false theorems and not know the difference until, maybe, a contradiction hits you over the head and demands attention.
Checking a solution is often a lot easier than generating an original solution. If you are not going to be generating original solutions, I would guess that there are better uses of your time than learning how to.
In my schooling in general (at middle school and higher level), I was generally annoyed that most subjects were taught with the assumption that you were going to become a practitioner of that subject, rather than simply a user. Naturally, every teacher thinks their subject is the most important in the world (why else would they have chosen it?), but most of their students do not see it that way. I would have been far better off learning how to communicate effectively rather than psychoanalyzing literature, just as those bound for non-quantitative careers would have been better off learning the math they need to keep their finances in order than constructing geometric proofs.
Most people hate geometry and not only promptly forget it once they’re out of the class but develop an aversion to it.
Also, there’s barely any historical discussion of how the geometrical results were first found, with a few colorful anecdotes as exceptions.
Knowing how to construct a proof has nothing to do with knowing how the ancient Greeks viewed geometry. Knowing how to solve a math problem has nothing to do with knowing how the method was originally worked out.
Memorization is necessary, though it is certainly overemphasized in certain academic contexts. For example, good math teachers know that memorizing multiplication tables and working to improve the speed of recall frees working memory to deal with higher level concepts. Of course it is also important that kids are simultaneously being taught what multiplication represents. I’ve seen teachers err on both sides of the memorization vs. exploration/conceptual development fence. - Wow, its rare to catch Vassar in an over-generalization!
I actually think that math teaching might work better if people spent time learning who though what as a result of asking what questions and how they first conceptualized their insights by building on what else.
Memorizing anything anywhere ever except as practice for understanding how memory works is always an indication that something has gone wrong however.
Do you mean “being made to explicitly work at memorizing is always bad, because you should pick up the important parts in the course of doing natural work”?
I agree. I can’t recall the last time I had to work on directly memorizing something, after the poetry assignments in high school. In all the other instances, the memorization occurs in the course of understanding the material, thinking or reading in terms of new concepts. This applies even to language learning, where the new words are learned in course of reading with a dictionary (if you are not in a hurry). The concepts learned this way can always be tabooed without hurting the knowledge.
I take it you’ve never studied biochemistry at the senior undergrad level. Evolution doesn’t produce easily systematizable components down at the level of proteins and other macromolecules of like size. I can’t think of a workable alternative to giving things more-or-less arbitrary names and requiring people to memorize them so as to have a common language.
Can you imagine a successful computer programmer who was constantly looking up the syntax of the language they were programming in? Memorization is damn near essential.
I expect a good computer programmer to be effective in a language he has not seen before by looking up the syntax as he needs it, and to increase his effectiveness over time by learning the syntax through use, without any specific effort of memorization. At least, provided the novel language is good.
Good point. Now that you frame things in terms of how knowledge is acquired, the only thing I’m glad to have memorized is math facts in elementary school. But they have been pretty helpful!
So, how else do you suggest people learn to speak, read and write?
I’ll give you reading and writing, but learning to speak isn’t memorizing any more than subitizing is counting.
Memorizing is always bad? That seems obviously wrong to me.
When I was in school, we were given proofs of certain geometry theorems, and we were told that we might have to prove the same theorems in the exam. Most of my classmates simply memorised the proof as given; since I’m better at on-the-spot analysis than at memorisation, I used to re-prove the theorems from basic principles instead. The result of this was that my proof, while (usually) correct, would look nothing like everyone else’s proofs. Because of this, the maths teachers would have to actually evaluate my proofs step by step, instead of simply ticking off the well-recognised general proof. Apparently this makes marking slower.
This implies that there may be some pressure from the teachers for memory-learning, as it leads to easier marking.
Most science classes aren’t about practicing science, but memorizing science that’s already done. Most math classes are the same way.
If you’re not going to be extending math theory, is remaining ignorant of the process really a detriment?
Understanding the process of extending math theory is essential if you want to be able to tell the difference between being led down a good path and being led down a bad path.
If all you do is memorize theorems without understanding their proofs, you can memorize false theorems and not know the difference until, maybe, a contradiction hits you over the head and demands attention.
Checking a solution is often a lot easier than generating an original solution. If you are not going to be generating original solutions, I would guess that there are better uses of your time than learning how to. In my schooling in general (at middle school and higher level), I was generally annoyed that most subjects were taught with the assumption that you were going to become a practitioner of that subject, rather than simply a user. Naturally, every teacher thinks their subject is the most important in the world (why else would they have chosen it?), but most of their students do not see it that way. I would have been far better off learning how to communicate effectively rather than psychoanalyzing literature, just as those bound for non-quantitative careers would have been better off learning the math they need to keep their finances in order than constructing geometric proofs.
Even high school geometry requires you to construct your own proofs.
It may be different abroad, but in the UK state system, we were never taught the idea of a proof untill sixth form (age 16-18).
Most people hate geometry and not only promptly forget it once they’re out of the class but develop an aversion to it.
Also, there’s barely any historical discussion of how the geometrical results were first found, with a few colorful anecdotes as exceptions.
Knowing how to construct a proof has nothing to do with knowing how the ancient Greeks viewed geometry. Knowing how to solve a math problem has nothing to do with knowing how the method was originally worked out.
Memorization is necessary, though it is certainly overemphasized in certain academic contexts. For example, good math teachers know that memorizing multiplication tables and working to improve the speed of recall frees working memory to deal with higher level concepts. Of course it is also important that kids are simultaneously being taught what multiplication represents. I’ve seen teachers err on both sides of the memorization vs. exploration/conceptual development fence. - Wow, its rare to catch Vassar in an over-generalization!