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Whatever Happened to New Math? (1990)

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Re: Whatever Happened to New Math? (1990)

#91
post #78
post #62

Earlier quoted context omitted.

Any math higher level than arithmetic doesn't actually require doing arithmetic. If you want to find the hypotenuse of a triangle with side lengths A and B, the answer is sqrt(A^2 + B^2). It shouldn't matter how long it takes you to multiply A with itself because you shouldn't actually be doing that. Even if one insists on getting a numerical answer for say a word problem, you can use a calculator. If knowing your ti…

> Any math higher level than arithmetic doesn't actually require doing arithmetic. That's not really true. If you're doing calculus, solving some integral, you end up doing a bunch of addition and multiplication along the way. That's not the part you're trying to learn, which is my point—by having your arithmetic down pat, you can focus on the important things, rather then having to think about the low level details…

My point is explicitly that you should not be doing that addition and multiplication.

Re: Whatever Happened to New Math? (1990)

#92
post #62

Earlier quoted context omitted.

Any math higher level than arithmetic doesn't actually require doing arithmetic. If you want to find the hypotenuse of a triangle with side lengths A and B, the answer is sqrt(A^2 + B^2). It shouldn't matter how long it takes you to multiply A with itself because you shouldn't actually be doing that. Even if one insists on getting a numerical answer for say a word problem, you can use a calculator. If knowing your ti…

The mathematics itself might not require doing arithmetic, but human psychology forces us to approach the abstract via the concrete. A facility with arithmetic helps with building a pile of concrete examples as a springboard for the leap to the abstract. For example, the usual example of a cyclic group is {0,1,2,3,4,5} with addition modulo 6. Maybe we start with 12 rather than 6 because it is familiar to old people u…

I don't know what kind of mind finds it easy to go from such a "concrete" example to the abstract, but I don't have one.

Now let's consider taking just the first sentence on wikipedia for the Klein Four group:

> In mathematics, the Klein four-group is a group with four elements, in which each element is self-inverse (composing it with itself produces the identity) and in which composing any two of the three non-identity elements produces the third one.

Starting with the abstract definition, now it's clear what we're talking about.

The problem with math education generally tends to be that the teacher knows the concept that the students are meant to learn, but the students don't, and thus logical jumps which appear obvious to the teacher are not at all so to the student. Concrete examples which the teacher thinks clearly illustrate the concept just add noise that the student must cut through.

Consider for example the pattern 1, 2, 3, 5, 7... what is the sequence I am trying to convey? I bet you're thinking the next number is 11, but you would be wrong. It's 9. The sequence is n+1 = floor((n + n+2)/2). Of course there are an infinite number of patterns that would fit the data. Expecting you to pick the specific one of those infinite I had in mind would be absurd. So to is the number of potential truths in mathematics infinite - expecting a student to get the one a teacher has in mind from a finite number of concrete examples is likewise woefully impractical.

Re: Whatever Happened to New Math? (1990)

#93
post #82

Earlier quoted context omitted.

I'm curious about this too. My best guess is that they're measuring household income and there are a lot of kids with low household incomes (more than adults with low household incomes, especially when you have more kids than adults in a household). /shrug

With all due respect, there are quite literally hundreds of well written papers that explain this. The number isn’t controversial in the slightest and it’s based on one of the most basic statistical observations in economics. Honestly, I can’t understand why HN is having so much trouble with this. The answer is that in child poverty research, a child is considered to live in poverty if that child lives in a household…

That does not answer how the child is poorer than its parents, though.

I don’t think people have difficulty with the concept of child poverty, but your original assertion sounds super weird (and yet it sounds official, not a personal opinion, so a paper detailing that would be a better answer).

Re: Whatever Happened to New Math? (1990)

#94
post #34

Earlier quoted context omitted.

You're assuming that "math problems" is a well-defined set of problems. But depending on what you want to test/teach, there's also going to be different problems that students will do well on. As an example: do you consider solving 579×46 quickly a "math problem"? I will solve it (relatively) quickly, since I was thought how to solve that exact problem algorithmicaly. But if you hadn't thaught that algorithm (you cou…

Being able to do arithmetic like 579x46 is foundational arithmetic, not some esoteric thing. Furthermore, teaching arithmetic while relying on a calculator is not teaching arithmetic. It's second or third grade material. It's reasonable to expect teachers to teach it and kids to learn it. It's easy to create tests for it.

At least for me, the issue was being able to do arithmetic by hand fast enough to meet the time limit of the test.

I don't think that ability necessarily has a great deal in common with understanding mathematics or the ability to do higher level math.

Re: Whatever Happened to New Math? (1990)

#95
post #82

Earlier quoted context omitted.

I'm curious about this too. My best guess is that they're measuring household income and there are a lot of kids with low household incomes (more than adults with low household incomes, especially when you have more kids than adults in a household). /shrug

With all due respect, there are quite literally hundreds of well written papers that explain this. The number isn’t controversial in the slightest and it’s based on one of the most basic statistical observations in economics. Honestly, I can’t understand why HN is having so much trouble with this. The answer is that in child poverty research, a child is considered to live in poverty if that child lives in a household…

So a much less confusing way to say the same thing would be that people in households with children are poorer than people in households without children? Or even simply "poor people have more children than average"?

Re: Whatever Happened to New Math? (1990)

#96
post #82

Earlier quoted context omitted.

With all due respect, there are quite literally hundreds of well written papers that explain this. The number isn’t controversial in the slightest and it’s based on one of the most basic statistical observations in economics. Honestly, I can’t understand why HN is having so much trouble with this. The answer is that in child poverty research, a child is considered to live in poverty if that child lives in a household…

That does not answer how the child is poorer than its parents, though. I don’t think people have difficulty with the concept of child poverty, but your original assertion sounds super weird (and yet it sounds official, not a personal opinion, so a paper detailing that would be a better answer).

The child is probably not poorer than its parents, but instead, I'm guessing households with children are poorer on average, and even more so the more children they have. This would then mathematically result in children being poorer on average if this is determined by the household they live in. If poor people have more children, then children are going to be poor overall.

I agree it's very confusing.

Re: Whatever Happened to New Math? (1990)

#97
post #91
post #78

Earlier quoted context omitted.

> Any math higher level than arithmetic doesn't actually require doing arithmetic. That's not really true. If you're doing calculus, solving some integral, you end up doing a bunch of addition and multiplication along the way. That's not the part you're trying to learn, which is my point—by having your arithmetic down pat, you can focus on the important things, rather then having to think about the low level details…

My point is explicitly that you should not be doing that addition and multiplication.

You gotta do it sometimes—jumping between paper and a calculator is a pain in the butt.

Re: Whatever Happened to New Math? (1990)

#98
post #82

Earlier quoted context omitted.

I'm curious about this too. My best guess is that they're measuring household income and there are a lot of kids with low household incomes (more than adults with low household incomes, especially when you have more kids than adults in a household). /shrug

With all due respect, there are quite literally hundreds of well written papers that explain this. The number isn’t controversial in the slightest and it’s based on one of the most basic statistical observations in economics. Honestly, I can’t understand why HN is having so much trouble with this. The answer is that in child poverty research, a child is considered to live in poverty if that child lives in a household…

With all due respect, that's quite literally exactly what I said:

> there are a lot of kids with low household income

I think maybe you meant to reply to someone else.

Re: Whatever Happened to New Math? (1990)

#99
post #87

Earlier quoted context omitted.

Is it not the "teach a man to fish" problem? Sometimes, welfare can cause more problems than it creates. So what should "people in power" do? Setup welfare programs, and in turn welfare dependence? Education was seen a cure for poverty, which in turn is why Johnny isn't fed.

The shortest answer is that it’s far cheaper to feed two families than to incarcerate one adult. The longer answer is that you don’t necessarily need welfare programs to help people out of poverty. Rather, a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. Edit - Also, fuck no, it’s not a teach a man to fish…

Sure, but only short-term. And if you only care short-term, because you are a politician with a short term, then fine (for you).

But that's a different plan from "the government" in general.

> a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence.

You are describing "safety-net" welfare, but how do you ensure any form of welfare remains a safety-net, and doesn't become a norm? welfare for those not in poverty is much more likely to work this way. If you specifically set out to tackle poverty, the most important thing are educational programs, and limited welfare programs.

I'm not against welfare in any case, but I see it as a double-edged sword that is too often seen as a "throw money at the problem" solution.

> Also, fuck no

It's a metaphor, the difference between men and children aren't relevant. The abstract meaning is dependence vs self-dependence. Giving a child food solves their food, but not their poverty.

The way it was originally stated:

  what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly
I could just as well say "what if instead of spending so much time wondering why a man can't fish, we spent that money and effort on making sure that man is fed properly", and the answer is the same: because then they will be dependant on us (the government) to provide food. This doesn't mean we shouldn't provide food, but that both are required, since the original post post specifically proposed providing food should displace education i.e. we spend money elsewhere. In fact, what we spend on food is a problem in itself, but unrelated to what we spend on education, we should not cannibalise one in favour of the other as if they are competing solutions - they are both solutions to the same problem, but do not compete because they have different scope: one long term (poverty) the other short (hunger).

Re: Whatever Happened to New Math? (1990)

#100
post #87

Earlier quoted context omitted.

The shortest answer is that it’s far cheaper to feed two families than to incarcerate one adult. The longer answer is that you don’t necessarily need welfare programs to help people out of poverty. Rather, a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. Edit - Also, fuck no, it’s not a teach a man to fish…

Sure, but only short-term. And if you only care short-term, because you are a politician with a short term, then fine (for you). But that's a different plan from "the government" in general. > a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. You are describing "safety-net" welfare, but how do you ensure an…

> Sure, but only short-term. And if you only care short-term, because you are a politician with a short term, then fine (for you).

Feeding children so that they can be stable adults is one of the most long-term policies I can think of.

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