[HN Gopher] How to Teach Math?
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How to Teach Math?
Author : LittlePeter
Score : 17 points
Date : 2021-05-06 08:56 UTC (1 days ago)
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| 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...
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