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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

#111

Post by nathanwh »

layoutIfNeeded wrote: post #107
_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…

Long division is just polynomial division with x = 10.

This comment is hilariously on the nose for how a lot of math texts read (at least in my experience)

$SIMPLE_CONCEPT that you’re trying your best to understand is easy if you think of it as a specific example of $MORE_COMPLICATED_CONCEPT that you surely can’t understand without understanding $SIMPLE_CONCEPT

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

#112

Post by acqq »

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.

> 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.

Unless you try to solve more problems yourself, you won't understand the advantages or disadvantages of some methods in solving the problems. So the real answer is: construct the examples, compute and compare, don't approach it "philosophically."

All the methods used today survived because they were the solutions to some problems. It doesn't mean that everybody applies them properly: for that you have to get some experience yourself.

Learning about the historical development of the methods is also for me satisfying experience: e.g. logarithms aren't a concept devised for philosophical purposes, Napier developed them to save astronomers time and limit "slippery errors" of (their) calculations:

https://www.thocp.net/reference/sciences/mathematics/logarit...

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

#113

Post by watwut »

mistersquid wrote: post #71
Gunax wrote: post #67

Earlier quoted context omitted.

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,…

If you are using sonnets to decide that, everybody would be better off if you did study Laplace transformations instead. It is harder to be confused with real life.

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

#114

Post by jiggawatts »

nathanwh wrote: post #111
layoutIfNeeded wrote: post #107

Earlier quoted context omitted.

Long division is just polynomial division with x = 10.

This comment is hilariously on the nose for how a lot of math texts read (at least in my experience) $SIMPLE_CONCEPT that you’re trying your best to understand is easy if you think of it as a specific example of $MORE_COMPLICATED_CONCEPT that you surely can’t understand without understanding $SIMPLE_CONCEPT

Wait till you get into Theoretical Physics, where the same thing is being explained by people who don't even have a firm grasp of $MORE_COMPLICATED_CONCEPT, but know just enough to be dangerous with it.

E.g.: I distinctly remember that many of the original articles about the Amplituhedron spent like a page explaining what a triangle was, then jumped straight into functions over higher-dimensional analogues without explaining any of the intermediate steps. Something-something-logarithm-of-a-simplex.

I can grok what a simplex is, but they literally just hand-waved over the bit where they take a logarithm of it in some way.

The page of explanation of what a triangle is was of zero assistance.

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

#115

Post by nopinsight »

For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels.

We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regardless of major, we always test them for math aptitude. The test includes competitive exam questions focused on mathematical understanding and problem solving skills, rather than advanced math knowledge. (The other part of teacher selection is interviewing for teaching skills and trial teaching with student and expert evaluation.)

Somewhat surprisingly, even some PhD candidates in engineering may fail these tests, while a few liberal arts degree grads passed the lower levels of these tests. So math aptitude is not limited to those who majored in math, science, or engineering. (Note that many of our elementary school students who have studied with us for a couple of years also pass them at a high level.)

It seems that countries with successful math programs, like Singapore, also utilize a rigorous teacher selection process that favors subject matter specialists even for teaching at an elementary level.

This is crucial for math, which is particularly hard to catch up later on with shaky foundation.

(In fact, kids are great at absorbing their teacher’s attitude toward the subject. It is no surprise many kids may sense “math fear” from their teacher. Having a teacher with positive attitude toward the subject they teach is essential!)

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

#116

Post by jacobush »

Tomte wrote: post #103
abakker wrote: post #90

Earlier quoted context omitted.

What is short division? I only remember being taught long division and having a calculator. Is there another method?

Fascinating. I didn't know, either. After looking at the English Wikipedia I found that a) what I learned in school is long division b) the notation with the dividend and the divisor separated by a parenthesis and the result on top of a horizontal bar is totally alien to me c) I've never seen short division before d) the German Wikipedia doesn't even have an article about short division

Thanks! What you said, except my own point d) that Swedish Wikipedia tells that apparently short division is also used in Swedish elementary schools now.

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

#117

Post by username90 »

_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…

This is the problem with rewarding conscientious kids, they just follow instructions without ever asking themselves why. If you were more rebellious and refused to follow steps you didn't understand then you'd get worse grades but you'd learn more.

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

#118

Post by alfiedotwtf »

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…

Wow. I edited the wrong comment ️

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

#119

Post by chrisseaton »

cjfd wrote: post #104
chrisseaton wrote: post #61

Earlier quoted context omitted.

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.

Okay, we have deviations from the mean. They are (0.1, 0.1, -0.1, -0.1). Or we have deviations from the mean (0.2, 0, 0, -0.2). I think is is pretty intuitive that in the second case the deviation is larger. In the first case there are only two differing values that are 0.2 apart. In the second case there are three differing values and some are 0.2 apart and others are 0.4 apart. Also, in the first case there are two…

I still don’t understand why we pick a metric because it’s easy to work with. Isn’t it either the right metric or not?

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

#120

Post by chrisseaton »

smabie wrote: post #97
chrisseaton wrote: post #61

Earlier quoted context omitted.

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.

Because the derivative at 0 of abs is undefined.

Why do I care about that though?
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