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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

#191

Post by pbhjpbhj »

marakv2 wrote: post #132
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.

I looked up long division thinking that I had missed something, I just want to chime in for support of what you said. Afaikr it's just division, how man X are in y.

Long division calculates the multiple at each step; short division just finds the remainder. That doesn't seem that different but when you come to do it algebraically you need to do long division. I did both at primary school (age 10), but it wasn't until 6th form (age 16) that we used long division again, those who hadn't done it at primary struggled a little.

       083.28
         2.26...
       ___
    7 |583.00
That's short division (sometimes called the "bus stop method" in UK), top line is answer [quotient], next line is "remainders". You say "7 in to 5 won't go; 7 in to 58 is 56 [just from knowledge of times tables, it's 56 tens your dividing], with remainder 2 [write remainder down, usually as a superscript to the dividend]; 7 in to 23 goes 3, remainder 2 [write remainder down]". Now you have the answer 583/7 is 83 remainder 2; but you can continue and divide the 20 tenths by 7, and so on.

Long division:

       083.28
         2.26...
       ___
    7 |583.00 [
What we're doing is taking five-hundred and saying can we divide that by seven-hundred, we can't. So then we say well how about fifty-eight tens, can we divide that by seven-tens. The tens cancel each other out ( 10/10==1 ), so 58/7 = 8r2 but this is really saying 580/70 is "80 lots of 7" and 20/7 left over. So now we add that 20 units to the 3 units we have already from the dividend we started with, so now we need to do 23/7. And so on ...

I'd do an algebra example but it's a pain in the arse just using ASCII.

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

#192

Post by zorked »

TeMPOraL wrote: post #109
OscarCunningham wrote: post #105

Earlier quoted context omitted.

> But why not use the abs function or operator rather than squaring and rooting? You can. It's called the mean absolute deviation. Which one you use depends on your application. If you just want to give a summary of how spread out the data is then either would work. Lots of people say that we should use the mean absolute deviation as the default rather than the standard deviation.

And suddenly another small subarea of maths starts to make sense for me. Thank you, and thanks to everyone commenting in this subthread. I too have a problem with math tools passed down without any surrounding context - without telling why are we using this formula, instead of any other variant from the family of formulas that would satisfy the same goals. I'd have much easier time dealing with statistics in school i…

By the way, statistics as its own discipline is taught rather differently from the "here is a toolkit of magic tables and formulas and how to use it" method used when teaching it to non-statisticians. The magical bits actually make sense.

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

#193

Post by marcosdumay »

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.

The abs has a problem in that it has no derivative at 0. I imagine that's why people go with squaring and rooting.

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

#194

Post by pbhjpbhj »

_bxg1 wrote: post #47
novok wrote: post #43

Earlier quoted context omitted.

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.

Up-arrow notation ftw.

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

#195

Post by marcosdumay »

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 mathematical representations and operations people see at school were picked because they are easy to work on most common problems. There is not this "correct math" thing, you pick what works best.

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

#196

Post by barry-cotter »

blt wrote: post #44

If we are serious about trying to "break the cycle", one obvious solution is to pay teachers more. Imagine if teaching paid as well as software development.

This would be true if we had any idea what makes a good teacher, or could reliably determine who good teachers are. Neither of those are true.

TEACHER QUALITY

https://faculty.smu.edu/millimet/classes/eco7321/papers/hanu...

> Perhaps most remarkable is the finding that a master’s degree has no systematic relationship to teacher quality as measured by student outcomes. This immediately raises a number of issues for policy, because advanced degrees invariably lead to higher teacher salaries and because advanced degrees are required for full certification in a number of states. Indeed, over half of current teachers in the US have a master’s degree or more. Teacher experience has a more positive relationship with student achievement, but still the overall picture is not that strong. While a majority of the studies finds a positive effect, only a minority of all estimates provides statistically significant results. Even the subset of studies that use a value added approach and information from a single state produce a highly variable set of results (see bottom panel in Table 1). If anything, the value-added estimates within individual states suggest more strongly that experience has an impact, although still only 41% of the estimates are statistically significant. It is quite likely that a number of these studies lack the statistical power necessary to identify precisely the experience effects.

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

#197

Post by pbhjpbhj »

chrisseaton wrote: post #143
marakv2 wrote: post #141

Earlier quoted context omitted.

What? 35/350 (to simplify) Once is 325, twice is 300, X, X, X, we end up at 10 times is 350 divisible by 35. I'm wondering if I'm missing something (and if I am I'll own up to it lol)

Lol I can't understand any of that. 'Once is', 'twice is' what does that mean? Once what is what? Twice what is what? You aren't even writing coherent English phrases how am I supposed to follow that?

https://news.ycombinator.com/item?id=21670030 maybe that's understandable?

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

#198

Post by pbhjpbhj »

purple-again wrote: post #183
roenxi wrote: post #131

> But many elementary students don’t understand the meaning of the equal sign. Some people might not have made the connection, but by and large programming languages make this mistake too. All the major ones are using the = glyph for assignment.

What mistake is that? The left hand variable equals the right hand value assigned to it. Foo = bar and 1 = 1 are equivalent in my mind.

So 2 = 1?

How do you square that circle, "fine" for assignment; wrong for equality.

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

#199

Post by war1025 »

blt wrote: post #44

If we are serious about trying to "break the cycle", one obvious solution is to pay teachers more. Imagine if teaching paid as well as software development.

You would also then need a feedback mechanism to ensure you were hiring people worth that extra amount of money.

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

#200

Post by theli0nheart »

chrisseaton wrote: post #19
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.

Because the algorithm is so astronomically complicated that people can’t see any pattern or reason in it anymore and it becomes an opaque mystery. I have a PhD in computer science but I cannot understand long division.

This animated image of long division from Wikipedia might help show what’s going on:

https://commons.wikimedia.org/wiki/File:LongDivisionAnimated...

In essence, repeated subtractions. The blank areas to the right of each number are really just zeros.

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