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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

#251

Post by esmi »

nopinsight wrote: post #227
nopinsight wrote: post #115

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. Regar…

For those curious, below are some kinds of primary math questions we model after to test teacher applicants. In my experience, many kids are much more enthusiastic about this kind of "challenging" problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well. Note that although they do require a little arithmetic to solve, the ch…

Is the answer to the second question allowed to be in engineering form? :)

What grade level is question 3 considered?

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

#252

Post by chongli »

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.

Now you’re talking about something different. The proof of the division algorithm is built up from a bunch of other machinery. It relies on the fact that the ring of integers is a Euclidean domain.

Take a course in ring theory if you want to see how all of this machinery gets built up.

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

#253

Post by nopinsight »

esmi wrote: post #251
nopinsight wrote: post #227

Earlier quoted context omitted.

For those curious, below are some kinds of primary math questions we model after to test teacher applicants. In my experience, many kids are much more enthusiastic about this kind of "challenging" problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well. Note that although they do require a little arithmetic to solve, the ch…

Is the answer to the second question allowed to be in engineering form? :) What grade level is question 3 considered?

What do you mean by 'engineering form'? Using variables in the answer?

It would be suitable for students between grades 4 and 6 (the highest level we currently teach), depending on how talented the kid is.

To be clear to other readers, these are hard questions that most people, including older kids and adults, probably can't answer without proper learning and practice.

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

#254

Post by tasty_freeze »

garmaine wrote: post #167
cptskippy wrote: post #155

Earlier quoted context omitted.

Then you never knew it? Perhaps what you were taught wasn't long division. My kids were not taught the same math that I was taught in the 80s. My 17 year old was struggling with the division algorithm they were teaching in Elementary school at the time (late 2000s). I can't remember the details but it was something I had never seen before that was a step up from throwing poop at the wall. I showed her how to do long…

It is nothing to do with book publishers, but new federal mandates for "Common Core" curriculum as part of the No Child Left Behind legislation.

It isn't a federal mandate, which can be seen because not all states adopted Common Core. There were federal incentives for states adopting a standard which has been recognized as effective, including Common Core.

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

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

#255

Post by klyrs »

leetcrew wrote: post #223
nopinsight wrote: post #115

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. Regar…

I always found it amusing that most of my math and cs professors in college seemed to have terrible arithmetic skills. I'm sure part of it is just that it's hard to concentrate on the work when you're also narrating the process to the class, but I suspect it's also that basic arithmetic is a relatively unimportant skill in most advanced research. hiring this sort of person to teach/tutor grade school math might be li…

I'm a mathematician, not a calculator. Mathematicians spawned an entire field, computer science, to alleviate the tedium of computation!

Back when I thought I was going to be an engineer, I went through a brief phase of doing everything by hand. Indeed, my brain is capable of "rapid" arithmetic, but it requires practice and discipline to achieve and maintain what amounts to a billion-time slowdown.

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

#256

Post by fractaled »

leetcrew wrote: post #228
darkerside wrote: post #139

Earlier quoted context omitted.

I've looked at both Wikipedia pages and still can't really understand the difference. Is it anything more than notational? Either way, you're calculating divisors for each component of the problem, and it only seems to matter whether you calculate it on paper or in your head.

the way I learned it, it's just a notational difference. either way, you are dividing the divisor into each place of the dividend (starting with the most significant digit) and carrying over the divisor to the next place. short division is just a more implicit way of doing this that saves space. the shorthand version doesn't really work for divisors with more than one digit though.

What doesn't work with short division and multi-digit divisors?

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

#259

Post by Shivetya »

nopinsight wrote: post #227
nopinsight wrote: post #115

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. Regar…

For those curious, below are some kinds of primary math questions we model after to test teacher applicants. In my experience, many kids are much more enthusiastic about this kind of "challenging" problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well. Note that although they do require a little arithmetic to solve, the ch…

and here I sit totally flummoxed by the questions yet later on you state these were suitable to grades up to sixth?

So for those who have let their math skills lapse or need help to get back in the right frame of mind to learn, where online is the best resource? Khan Academy?

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

#260

Post by hackermailman »

chrisseaton wrote: post #161
SamReidHughes wrote: post #153

Earlier quoted context omitted.

> But why? Why are we doing things in decimal? We’re subtracting off multiples of 10^N because that’s easy when you write your numbers in base 10. Try subtracting off multiples of 9^N, or multiples of N!, or some other choice, and you’ll see why.

Ok, but do you see what I mean about how that part was just sitting there without any explanation? That's why I find it hard.

Wildberger has a channel that explains this from scratch, also shows a different method of long division https://m.youtube.com/playlist?list=PL5A714C94D40392AB

His method for polynomials/derivatives is also interesting if you watch until the end, dead simple calculus.

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