[HN Gopher] How to Teach Math? ___________________________________________________________________ How to Teach Math? Author : LittlePeter Score : 17 points Date : 2021-05-06 08:56 UTC (1 days ago) (HTM) web link (rjlipton.wpcomstaging.com) (TXT) w3m dump (rjlipton.wpcomstaging.com) | atoav wrote: | One important thing is: create realistic problems that need | certain math. I had to calculate integrals for a _year_ before | our teacher for a brief moment glossed over what problem it might | be needed for. | | In fact I only understood why integrals were useful, when I | started learning for the final exam. | | This stuff can be really cool, but if even your teacher does as | if it is the most boring and useless thing in the world, if even | your teacher is unable to explain beforehand why you want to know | this, how would you? | jrib wrote: | One of my best memories from high school math was our teacher | taking us outside to measure the height of our building after | teaching us trigonometry. | | We took a triangular ruler outside, leveled the base and lined | it up by eye with the top of the building. Then we measured the | distance to the point where we were standing and the distance | from the ground to the ruler. | | I really wish education reduced the amount of rote learning | involved and focused more on letting students explore and make | mistakes with the educator as a guide. | dfdz wrote: | I am really confused by this article. The section "First An | Issue" is a great example of how NOT to teach math. | | First, the class of sequences under consideration is not clearly | defined. (I am not going to invest time solving a problem, if I | am not sure about the definitions involved, constant | coefficient/variable coefficient etc). | | Second, a question is asked "Is a product of two such sequences | also of the same form?" and the meaning of product is also not | clearly defined. | | Third, the author links to an article whose PDF on the publishers | website is unreadable, and does not seem to answer the question | from what I can tell. The only purpose linking to this article | serves is intimidation. | | There is a happy ending to my rant. I googled the topic alluded | to by the author and found a clear post explaining the solution. | In this stackexchange post the question and solution are both | clearly stated. | | https://math.stackexchange.com/questions/1348838/sum-and-pro... | this-pony wrote: | I think the point the author tries to make in the section | "First An Issue", as you say, is exactly to give an example of | bad teaching. | quacked wrote: | I don't know how to teach math, but I know how not to teach math. | | 1. Don't teach that math is a "ladder". Trigonometry is not | "harder" than geometry, although many concepts in trigonometry | are expressed as geometry. Calculus is not "harder" than algebra, | although many concepts in calculus are indeed expressed as | algebra. Teaching that math is a ladder allows people to believe | that once they've covered the "basics" of a field of math (as if | you could ever learn all of "algebra"), they shouldn't have to | think about the basics again. Try telling a pianist that once | they've learned a set of scales they don't need to study them any | more, or try telling Richard Feynman that once he understood the | standard atomic model there was no need to continue examining it | in greater depth. | | 2. Don't teach that math was "discovered" in its current form. | What most students think of when they think "math" is in fact | western notation for patterns observed in reality, handed down by | a bored teacher as universal law. A sheet full of squiggles isn't | "math", it's just a set of the most-predictable and best-notated | patterns made up by past mathematicians. "Math" is the process of | discovering and refining those squiggles. The relationship | between the length of the two perpendicular sides of a right | triangle and the hypotenuse exists outside of human knowledge, | but the Pythagorean Theorem is a only a certain method for | expressing that relationship. The numbers 1 through 9 are one | possible code for counting, but the quantities I through | IIIIIIIIII and onward exist outside of the notation of Arabic | numerals. | | 3. Don't immediately move on from concepts once a student has | mastered them. Imagine if every time you figured out how to do | your job correctly, your boss moved you to a completely new task | requiring a completely new set of skills, giving you no time to | enjoy applying your prior mastery. If you've just learned how to | factor quadratic equations, why move on? Why not explore programs | that factor equations? Why not dig up old exams and show how | factoring would have solved earlier problems faster? This is | always met with cries of "but they're supposed to use what | they've learned to go on to even harder problems!" Sure, I agree, | but how can you possibly enjoy any task if the only thing you can | really expect is that even if you master your task, you'll be | struggling again within the week? Would you join a rec basketball | team if every time you started hitting three-pointers | consistently, they moved the rim higher and farther away without | giving you any time to feel what it's like to be good at | basketball? | | 4. Don't teach that you need to know math because your grades | have to be high. For nearly every profession available, grades | are immediately forgotten as soon as you start receiving wages. | Teach that you need to know math because the world is constructed | and controlled by mathematicians and those acting on the advice | of mathematicians. If you don't know math you'll be taken | advantage of by those who do, whether it's in advertising, | gambling, banking, medicine, insurance, politics, entertainment, | engineering, programming, or any of the many other fields driven | entirely by math. | | Of course, not teaching those four lessons becomes difficult, | because those lessons work in opposition to the central tenets of | mandatory state education, which necessarily operates as a giant | brainwashing factory working to justify its own existence. Modern | ediucators spend most of their time trying as hard as they can to | teach people that knowledge is best bestowed by authority and | then proven through certificates, that various fields of inquiry | exist separately from one another (for instance, that physics and | biology can or should be studied independently of history, | mathematics, grammar, semantics, or art), and that failure to | live up to expectations must necessarily lead to shame and | corrective action. | | Don't send your kids to school if you can avoid it. | tediousdemise wrote: | The human brain is like a self-compiling compiler. You can teach | people math by teaching them how to read, and then suggesting a | good math book. | rahimnathwani wrote: | I'm trying that with my son (who is not yet 5). He has no | trouble reading anything in his math book[0], but 'suggesting' | that he work through the book isn't enough. He'd rather play | with lego, read a story book, or do pretty much anything else. | | My solution: short sessions of a few pages at a time, with me | sitting by his side, ready to intervene when he gets | sidetracked. | | [0] | https://shop.singaporemath.com/index.php/product/dimensions-... | dboreham wrote: | I'm a strong proponent of learning things yourself, and have | done so life long, but I suspect there may be something | different about Mathematics, at least up to undergraduate | level. At least based on my experience helping my kids. Even | today's rich kahnsphere doesn't seem to adequately stand in for | a good teacher. | royaltjames wrote: | Can you suggest me a good math book to read? | hansvm wrote: | Tons, but it really depends on where you're starting. Is | there anything in particular you'd like to learn? | | Every time I've recommended Calculus Made Easy [0] it's been | a huge success. The writing is lively and full of motivating | examples, and it's an enjoyable read. | | [0] https://news.ycombinator.com/item?id=17185577 | teeray wrote: | I started high school in a program that was more focused on | "applied math learning." (IMP [0]) We'd throw dice and figure out | probabilities and stuff. I transferred out of it within two | months because it was so focused on finding applications that it | completely missed the mechanics of manipulating expressions. | | It was boring at times, but after three years I had a rock-solid | base on how to turn one expression into any other. The | applications of those skills came later once I got into Physics | and Stats. | | I don't know if it worked out better that way, but I think | there's kind of a chicken-and-egg situation. To really understand | the applications, you need the math background. To appreciate the | math background, you need the applications. | | [0] | https://en.wikipedia.org/wiki/Interactive_Mathematics_Progra... ___________________________________________________________________ (page generated 2021-05-07 23:00 UTC)