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

#71

Post by mistersquid » Sat, Nov 30, 2019, 6:06 AM UTC

Gunax wrote: post #67

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…

There seems to be a culture of proud ignorance around math more-so than other subjects. While I am sure there is some engineering student out there griping about having to take a psychology course, they don't seem to complain as much as when non-mathy people have to study math. I think it is a mistake for our education system to treat math as something superfluous and abstract from daily life. While neither Laplace t…

> While neither Laplace transforms nor Shakespearen analysis are necessary to live, the former is probably more useful than the latter.

Without context, such an overbroad generalization is at best meaningless.

If someone is choosing between potential spouses, or addressing a dishonest business colleague, or deciding how best to recognize a selfless samaritan, few branches of mathematics would be of any use. Whereas, one of Shakespeare's hundred and an half sonnets might be of direct "use".

Usefulness and utility depend on context. Contextless generalizations about the value of different branches of human knowledge is generally meaningless.

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

#72

Post by Gunax » Sat, Nov 30, 2019, 6:24 AM UTC

> If math knowledge is limited to “when I see this sort of problem, I do that” it’s inflexible; if problems are phrased just a little differently, the student is often stumped. And once students hit algebra, math increasingly demands thinking through a sequence of steps and picking the right mathematical tool for each. That’s hard if you don’t understand what the tools actually do.

That's easy to say, but hard to do. I find in my math experiences that I often don't truly master a concept until I am a level or two beyond it. I learned fractions when I was in grade 5 or 6 and could demonstrate adding, multiplying, reducing, etc. I think if you asked me 'why can you multiply across when multiplying fractions' I may have said I knew, but I don't think I actually mastered that until high school--when I had the skills to derive the fraction operation rules. Ditto with things like FOIL, completing the square, etc which I don't think I mastered until I was out of high school.

And of course, everything seems easy and obvious in hindsight.

I suppose what I mean is: I don't think there is anything new about what the author lauds as a goal. It's what everyone has been trying to do for 50 years. It just isn't easy, and so far no one has found a magic bullet aside for lots of hardwork and practice.

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

#73

Post by threatofrain » Sat, Nov 30, 2019, 6:30 AM UTC

novok wrote: post #4

_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…

Division is a repeated subtraction operation, and the long division algorithm is just a nice way to lay it out. Multiplication = repeated addition Addition = a form of counting

I prefer to think of subtraction as the inverse of addition, and division as the inverse of multiplication. You only need addition and multiplication if you're dealing with rationals.

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

#74

Post by defen » Sat, Nov 30, 2019, 7:20 AM UTC

chrisseaton wrote: post #61

dboreham wrote: post #46

Earlier quoted context omitted.

Try this? https://web.stanford.edu/class/ee486/doc/chap5.pdf Edit: standard deviation is just a fancy name for root mean squared over the sample offsets. The square is there to deal with the fact that there are positive and negative offsets. The mean is the whole point of the exercise, and the root is to negate the fact that we squared earlier.

But why not use the abs function or operator rather than squaring and rooting? This is how I always find maths and particularly statistics - I always just want to answer ‘but why’ and then people lose interest in explaining after a while.

That exists too: https://en.wikipedia.org/wiki/Average_absolute_deviation

Standard deviation is mathematically easier to work with though and has nice properties e.g. you can compute the standard deviation of combining a bunch of independent things by combining their individual standard deviations.

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

#75

Post by ikeyany » Sat, Nov 30, 2019, 7:45 AM UTC

pjscott wrote: post #16

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.

It's almost never explained with such lucidity. If you find a hundred people who can perform long division, I would be surprised if twenty of them have any idea how it works.

Multiplication tables are the most lucid way to explain long division. In order to get from 5 to 40, you need to keep adding 5s until you can't. So to divide 40 by 5, keep subtracting 5s until you can't any longer.

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

#76

Post by copperx » Sat, Nov 30, 2019, 8:59 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...

You linked to the iOS version. Do you have a link to the app webpage, which will surely have both Play Store and App Store links?

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

#77

Post by copperx » Sat, Nov 30, 2019, 9:06 AM UTC

_bxg1 wrote: post #64

buzzkillington wrote: post #59

Earlier quoted context omitted.

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.

I didn't understand why it worked (a comment here pointed out that it's just division-by-repeated-subtraction which does make sense now). But I was still able to perform it, during the time when it was relevant to my life.

What's a red flag is being frustrated by long division and at the same time not being curious or resourceful enough to resolve your frustration. You blame your lack of understanding on other people.

I can understand if most people shared your frustration, but not a PhD holder. Your degree basically says that you're capable of doing long, intensive research on arcane topics.

What am I missing here?

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

#78

Post by copperx » Sat, Nov 30, 2019, 9:12 AM UTC

paganel wrote: post #66

protomyth wrote: post #31

Earlier quoted context omitted.

My response to primary school teachers is that they need some mastery of math so they are not anxious about the subject in front of students. Because if the girls in her class lookup to her and she is anxious, nervous, or dismissive of math then those girls will not go into any STEM field. If you want more females in STEM careers then it starts with elementary school teachers loving STEM.

Primary school maths is not really maths, is arithmetics, asking a primary school teacher to go into some crazy higher-maths details in order to teach arithmetics is just a huge waste of resources.

I would argue that calculus and Laplace transforms aren't math if there are no proofs involved; it's just multi-step arithmetic and symbol manipulation.

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

#79

Post by BrandoElFollito » Sat, Nov 30, 2019, 9:18 AM UTC

I have a hard time explaining to my children how addition of fractions work. Not how to do that, but how to feel the intuitive way. And percentages, to some extend.

The sad part is that I have a PhD in physics and an engineering degree in CS. I used to teach physics at the uni and loved it.

My children like me to explain them physics because I love it so much and they appreciate the analogies, their limits etc. It is just these freaking fractions and their convoluted addition I do not know how to properly convey.

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

#80

Post by ezequiel-garzon » Sat, Nov 30, 2019, 9:49 AM UTC

BrandoElFollito wrote: post #79

I have a hard time explaining to my children how addition of fractions work. Not how to do that, but how to feel the intuitive way. And percentages, to some extend. The sad part is that I have a PhD in physics and an engineering degree in CS. I used to teach physics at the uni and loved it. My children like me to explain them physics because I love it so much and they appreciate the analogies, their limits etc. It is…

To me what is utterly crucial is to use pie pictures to convince children (and adults...) that 1/2 + 1/3 cannot possibly equal 2/5. If they actually buy this that’s a pretty good inflection point in their education on fractions.