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

latimes.com

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

#41

Post by pjscott »

dboreham wrote: post #36
novok wrote: post #4

Earlier quoted context omitted.

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've never thought of division as repeated subtraction: it's the inverse of multiplication, or literal division as in I have a pile of beans that I divide equally between N piles. I don't think you're wrong, just seems an odd way to think about it, and fails to account for any remainder.

The remainder is what's left after you've repeatedly subtracted, and can't subtract any more before going negative. (I wish that one of my teachers had said this to me, but they were too busy getting everybody to memorize the steps.)

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

#42

Post by _bxg1 »

LegitGandalf wrote: post #34

The worst part is that female students are more likely to notice the teacher's fearful body language, so you get this never ending cycle of girls developing fear of math, going into teaching and passing the fear on to the next generation.

That seems like a stretch.

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

#43

Post by novok »

_bxg1 wrote: post #17
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 wasn't until I learned about for-loops that I started thinking of multiplication as repeated addition and division as repeated subtraction. Before then I thought purely in terms of geometry.

I think it depends on how you were taught the concepts in elementary school. I think a lot of it is based on things like bar charts[0] and visual representations at first, so it's possible you were never taught how it was repeated subtraction and addition, how powers are repeated multiplication and so on.

https://en.wikipedia.org/wiki/Singapore_math#Bar_modeling

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

#45

Post by [deleted] »

protomyth wrote: post #31
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…

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.

[deleted]

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

#46

Post by dboreham »

chrisseaton wrote: post #33
dboreham wrote: post #32

Earlier quoted context omitted.

>I have a PhD in computer science but I cannot understand long division I think you're trolling us a little: you could sit down with pencil and paper and think about how it must work and 20 minutes later you'd understand it, surely.

I have no intuitive understanding or mental model of the algorithm. I could follow the instructions if they’re written in front of me but I have never managed to understand why they work or to memorise them. I have a similar mental block for standard deviation - I always seem to have another ‘but why?’ question that eventually people answer with ‘because!’ and then we’ve both given up.

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.

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

#47

Post by _bxg1 »

novok wrote: post #43
_bxg1 wrote: post #17

Earlier quoted context omitted.

It wasn't until I learned about for-loops that I started thinking of multiplication as repeated addition and division as repeated subtraction. Before then I thought purely in terms of geometry.

I think it depends on how you were taught the concepts in elementary school. I think a lot of it is based on things like bar charts[0] and visual representations at first, so it's possible you were never taught how it was repeated subtraction and addition, how powers are repeated multiplication and so on. https://en.wikipedia.org/wiki/Singapore_math#Bar_modeling

Yep. I remember in college when I made that connection and realized you could create infinite "levels" of operation, with each repeating the previous one N times.

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

#48

Post by LegitGandalf »

keenmaster wrote: post #15
_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…

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.

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

#49

Post by LegitGandalf »

_bxg1 wrote: post #42
LegitGandalf wrote: post #34

The worst part is that female students are more likely to notice the teacher's fearful body language, so you get this never ending cycle of girls developing fear of math, going into teaching and passing the fear on to the next generation.

That seems like a stretch.

University of Chicago study for you to peruse

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

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

#50

Post by _bxg1 »

aaron695 wrote: post #38

This is because of a lack of men in elementary schools, interesting they skipped the reason. But this is not solvable in the West I guess, it will continue to decrease. Need to offshore it. IE. Produce good external lesson plans that are free to use.

...yikes.
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