Many elementary teachers don’t understand math, and it makes them anxious • Hacker News Board

Re: Many elementary teachers don’t understand math, and it makes them anxious

#51

Post by jknz » Sat, Nov 30, 2019, 5:24 AM UTC

_bxg1 wrote: post #2

I still don't know why long-division works. I don't think I even remember how to do it as an adult. I've always had a very intuitive grasp of math, which meant I excelled at solving things in my head but struggled with (and resented) having to show my work in the arbitrary algorithms we were taught. I understand division despite my education. They really should try to come up with algorithms that are more intuitively…

Dividend is 123456 and divisor is 37.

37>1, 37>12 but 37*3Write down 3 (meant for 3000) and start again with 123456-37x3000 as the new dividend.

I wish the algorithm was taught by writing the full 3000 instead of only the digit 3; this appears to be a source of major confusion and to hide the underlying additions/multiplications.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#52

Post by keenmaster » Sat, Nov 30, 2019, 5:24 AM UTC

LegitGandalf wrote: post #48

keenmaster wrote: post #15

Earlier quoted context omitted.

That’s a good point. You know what, it’s way easier to teach how to solve for x when y + x = 3x + 3 and y = 4 than it is to teach long division. As far as I could tell, that basic algebra is also much more important than long division, so why not teach it at an earlier age? The symbology of algebra is probably great for developing minds. Just show long division for “proofs” while introducing the concept of division,…

Some guys in Norway made an app that teaches algebra concepts to 5 year olds using pictures, as the game levels up it slides variables and numbers in.

Are you referring to Dragon Box? This looks awesome.

https://apps.apple.com/us/app/dragonbox-algebra-12/id6344441...

Re: Many elementary teachers don’t understand math, and it makes them anxious

#53

Post by rahuldottech » Sat, Nov 30, 2019, 5:25 AM UTC

Huh. I'm from India, and from what I can tell, maths is taught much better here than in the US, at least till 10th grade, after which it's no longer compulsory. It's actually taught in a very intuitive manner, and most students "get" it quite well.

Edit: the textbooks are freely available on the web, if anyone wishes to take a look. Look up "NCERT class 10 maths textbook".

Re: Many elementary teachers don’t understand math, and it makes them anxious

#54

Post by _bxg1 » Sat, Nov 30, 2019, 5:26 AM UTC

chrisseaton wrote: post #19

geomark wrote: post #8

Earlier quoted context omitted.

I don't understand why long division would be a mystery. It's just repeated subtraction - you are finding how many times you can subtract the divisor from the dividend, in a systematic way.

Because the algorithm is so astronomically complicated that people can’t see any pattern or reason in it anymore and it becomes an opaque mystery. I have a PhD in computer science but I cannot understand long division.

Bud, I really hope you can grasp more complicated algorithms than that if you have a PhD in computer science. It's one thing to call it unintuitive and not worth your time, but let's not be hyperbolic.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#55

Post by Gunax » Sat, Nov 30, 2019, 5:28 AM UTC

elchief wrote: post #22

My ex taught grade 6 geography. Is a principal now. Thought the seasons were due to earth tilting back and forth. Didn't get that the tilt was the same, but the position around the sun was different

While I am also appalled, I imagine everyone has some fundamental misunderstanding about something that is 'obvious' to everyone else. Something akin to 'today's 10,000"

Re: Many elementary teachers don’t understand math, and it makes them anxious

#56

Post by chrisseaton » Sat, Nov 30, 2019, 5:29 AM UTC

_bxg1 wrote: post #54

chrisseaton wrote: post #19

Earlier quoted context omitted.

Because the algorithm is so astronomically complicated that people can’t see any pattern or reason in it anymore and it becomes an opaque mystery. I have a PhD in computer science but I cannot understand long division.

Bud, I really hope you can grasp more complicated algorithms than that if you have a PhD in computer science. It's one thing to call it unintuitive and not worth your time, but let's not be hyperbolic.

No I have genuinely tried to learn it and I have no understanding why I am doing any of the steps in the algorithm.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#57

Post by v64 » Sat, Nov 30, 2019, 5:29 AM UTC

alfiedotwtf wrote: post #3

On the flipside, I was in a Calculus lecture at uni and turned to the girl next to me who was crying. I asked her if she was ok, and she said she didn't understand why she had to sit in the lecture learning Laplace transforms when she "only wanted to be a primary school teacher". From the sounds of it, it was a prerequisite? Edit: Oh :) I just worked it out - I was taught to fold the subtraction and carry right in on…

This comment surprised me, as I have a BS in math and Laplace transforms were not something I was required to learn for the degree (although I had the option to take courses as electives that covered them). My university offers a math degree intended for those who want to go into teaching that doesn't get any hairier than Number Theory for required courses.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#58

Post by LegitGandalf » Sat, Nov 30, 2019, 5:29 AM UTC

keenmaster wrote: post #52

LegitGandalf wrote: post #48

Earlier quoted context omitted.

Some guys in Norway made an app that teaches algebra concepts to 5 year olds using pictures, as the game levels up it slides variables and numbers in.

Are you referring to Dragon Box? This looks awesome. https://apps.apple.com/us/app/dragonbox-algebra-12/id6344441...

Yeah,it's amazing, I've hooked multiple friends on this app. It turned my friend's girls math fear around, which is really important given that girls are learning to fear math from teachers who are themselves afraid of math.

https://news.uchicago.edu/story/female-teachers-can-transfer...

Re: Many elementary teachers don’t understand math, and it makes them anxious

#59

Post by buzzkillington » Sat, Nov 30, 2019, 5:29 AM UTC

_bxg1 wrote: post #26

buzzkillington wrote: post #20

Earlier quoted context omitted.

You should probably read about it as an adult: https://en.wikipedia.org/wiki/Long_division Children are mostly idiots. Education is the process of painfully breaking them out of their idiocy. Bonus points if you implement a long division algorithm that works on strings in your favorite language.

Thing is, even now I find it useless. I can do nearly any division in my head whose digits themselves fit in my head (Miller's Law). For anything bigger, I have a pocket supercomputer with me at all times. You're right that it could be a fun programming exercise, though

If you do code in any capacity not being able to understand long division is a huge red flag. In terms of difficulty it's somewhere between regex and being able to write a recursive function.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#60

Post by buzzkillington » Sat, Nov 30, 2019, 5:32 AM UTC

analog31 wrote: post #27

buzzkillington wrote: post #23

Earlier quoted context omitted.

>Also in the states, engineering students ask the same question about Laplace transforms. ;-) Because I want you to build things that don't fall apart because of resonance?

I'm playing devils advocate here, but the argument you'll get is that there's software for that. Also, in a typical department, there may be one or two engineers who handle the quantitative problems for the team. Many engineering students go through their education, having heard from someone, that they won't need their math after they graduate. And things do fall apart.

>I won't need math, so I'll blindly trust this 20 year old 32 bit half precision floating point thing someone coded up in an afternoon before their holiday break.

Don't get me started on engineers who think floating point numbers can be treated like real numbers for equality testing.