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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

#121

Post by alfiedotwtf »

tmh88j wrote: post #65
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…

>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" What university did you attend that Laplace transforms were part of the standard calculus curriculum, let alone a requirement for primary school teachers? From my experience in the US, universities typically offer different sets of calculus…

Nah, not an intro to Calc... it was second year Electrical Engineering calculus, but students were from all different courses (I was doing Compsci at the time).

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

#122

Post by y4mi »

kkarakk wrote: post #86
rahuldottech wrote: post #53

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".

My experience has been the opposite. Indian kids can solve math problems in the "curriculum" quite well but ask them to do anything WITH the math and they're lost. Ask them how the theorem relates to the natural world and they don't know. Ask them what applications it has and they don't know. Ask them to extrapolate their current knowledge base to a theoretical future and they are completely lost on what a "next step…

Try asking the average western student the same question. Most people -be they young or old- aren't able to do that. Nor is that a skill you actually need in real life.

You should also think about if it's more important (to the people you're telling that message) to get a good wage or if they're fine taking a few years to catch up.

"Understanding" concepts is great and all, but unless they're doing that additionally to training the simple application, they'll most likely start having issues once the tests are up.

Having good grades (and being able to prove their ability on the spot) is definitely correlated with good starting wages. Not so much later on, but it's a massive difference at the start.

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

#123

Post by hanoz »

symplee wrote: post #37

A couple examples from the article: >> A colleague told me of vainly trying to persuade a college student that .015 was less than .05; the student insisted “but 15 is more than five.” >> To [students], [the equals sign] doesn’t signify equality, but instead means “put the answer here.” Imagine their confusion when, in algebra, they first encounter problems with numbers on both sides of the equal sign.

>> To [students], [the equals sign] doesn’t signify equality, but instead means “put the answer here.” Imagine their confusion when, in algebra, they first encounter problems with numbers on both sides of the equal sign.

Is this really true? I'm sure I and my children (in the UK) were presented with fill in the box questions like:

7 + [ ] = 10

at the very earliest stages of arithmetic.

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

#124

Post by alfiedotwtf »

v64 wrote: post #57
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.

I took it as an elective that was offered to Electrical Engineering. I'm sad my uni didn't have Number Theory (at least none available to me) :(

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

#125

Post by yorwba »

copperx wrote: post #76
keenmaster wrote: post #52

Earlier quoted context omitted.

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?

They also told us what it's called, which is enough to find the app webpage in this case: https://dragonbox.com/

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

#126

Post by alfiedotwtf »

alfiedotwtf wrote: post #6
_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…

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.

Copied from comment below...

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

#127

Post by pnutjam »

acqq wrote: post #112
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.

> 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 use…

I think you just described the common core method. The main problem is teachers don't understand all the methods they are teaching and kids pick up on this. Then the parents don't understand all the methods and the few intellectually curios help their kids figure it out; but he vast majority of people just tell their kids it's stupid.

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

#128

Post by [deleted] »

chrisseaton wrote: post #119
cjfd wrote: post #104

Earlier quoted context omitted.

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?

[deleted]

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

#129

Post by SamReidHughes »

chrisseaton wrote: post #56
_bxg1 wrote: post #54

Earlier quoted context omitted.

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.

Try again? Long division, dividing A by B, is a for loop that maintains the invariant A = QB + R, where Q is the number written on top (initially 0) and R is the number written on the bottom (initially A), by subtracting values of the form B(C)(10^N) from R and adding values (C)(10^N) to Q to compensate.

    func Longdiv(A, B) {
        // Assume A > 0, B > 0.
        N = floor(log10(A))
        Q = 0
        R = A
        while (N >= 0) {
            // Invariant: A = B * Q + R
            // Invariant: B * 10^(N+1) > R
            C = 0
            while (B * (C + 1) * (10 ^ N)  R because otherwise we
            // would have picked a larger C.
            N -= 1
            // Invariant B * 10^(N+1) > R is maintained.
        }
        // By loop invariants, we have
        // A = B * Q + R and B * 10^0 > R.
        return (Q, R)
    }
This is ten lines, not “astronomically complicated.”

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

#130

Post by username90 »

chrisseaton wrote: post #119
cjfd wrote: post #104

Earlier quoted context omitted.

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?

The standard deviation is not arbitrary, it tells us what the final normal distribution would look like if you averaged a lot of independent distributions.

You can read up on the central limit theorem if you want to understand more.

https://en.wikipedia.org/wiki/Central_limit_theorem

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