Many elementary teachers don’t understand math, and it makes them anxious
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Re: Many elementary teachers don’t understand math, and it makes them anxious
#2I 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 linked to a spatial comprehension of the numbers. That underlying grasp is really all that sticks with you into the real world (and it's also what makes math engaging). If students aren't getting that, they're wasting their time in my opinion.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#3On 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 one step. I'm an idiot!
Re: Many elementary teachers don’t understand math, and it makes them anxious
#4I 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
Re: Many elementary teachers don’t understand math, and it makes them anxious
#5I feel like anyone should be anxious if they don't understand math. How does one get through life without understanding math? Probably by getting had a lot.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#6I 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…
It's weird because I was taught long division in primary school that was different to everyone else in class (different maths class). Everyone seems to do some weird subtraction for each digit, whereas I was taught to carry right (i.e almost like how carries work with addition). Way faster, and it works the same all the way to decimal places, no weird remainders. Not sure why that wasn't the standard approach.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#7I 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…
My parents invented a simplified division algorithm so they could teach me the four basic arithmetic operations by third grade, and it was so much easier than long division that I could never remember how to do things the conventional way. I just pretended to follow the teachers' instructions for the next few years.
(All these methods had the same asymptotic complexity. Mine was slower by a small constant factor; on the other hand it actually made sense. It was just repeated subtraction!)
Re: Many elementary teachers don’t understand math, and it makes them anxious
#8I 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…
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.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#9I 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
That makes sense. And actually I think I could re-derive the algorithm from that explanation.
Maybe they need to explain it in those terms. Or use pictures.
Re: Many elementary teachers don’t understand math, and it makes them anxious
#10I 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…
My parents invented a simplified division algorithm so they could teach me the four basic arithmetic operations by third grade, and it was so much easier than long division that I could never remember how to do things the conventional way. I just pretended to follow the teachers' instructions for the next few years. (All these methods had the same asymptotic complexity. Mine was slower by a small constant factor; on…
My mom got in trouble with the teacher for doing that kind of thing with me.