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How our 1,000-year-old math curriculum cheats America's kids

latimes.com

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Re: How our 1,000-year-old math curriculum cheats America's kids

#81

Post by SamuelMulder »

j2kun wrote: post #27

> By hiding math's great masterpieces from students' view, we deny them the beauty of the subject. The problem is that math's great masterpieces are problems and proofs. High school math educators are largely the folks who hated doing proofs during their education, and they're just as uninformed about what the interesting open problems are as their students.

As a mathematician, how much time do you spend studying proofs written by other people?

I'm genuinely curious, because I think that if I wanted to be a novelist, I would spend a lot of time reading novels before trying to write one. I feel like we never have children read the great "literature" of mathematics, but then expect them to write their own proofs and are surprised when they hate it.

Re: How our 1,000-year-old math curriculum cheats America's kids

#82

Post by sitkack »

j2kun wrote: post #27

> By hiding math's great masterpieces from students' view, we deny them the beauty of the subject. The problem is that math's great masterpieces are problems and proofs. High school math educators are largely the folks who hated doing proofs during their education, and they're just as uninformed about what the interesting open problems are as their students.

Teachers should have the place of manager and coach with specialists brought in who are subject matter experts. We had this in art (painting,music), PE and computer programming when I was in public school.

To force or demand that teachers be skilled and have deep interests in everything they teach is not realistic.

Re: How our 1,000-year-old math curriculum cheats America's kids

#83

Post by sitkack »

SamuelMulder wrote: post #80
sitkack wrote: post #75

Earlier quoted context omitted.

Is your work done in the public? It would be nice to put it on a public repo and get others feedback and help.

I'm still struggling with how to handle this. On the one hand, it makes a lot of sense for it to be public. On the other, I've given up a lot to spend time developing it (including going part time on my day job), and I would love to be able to devote more time to it, which would require making some money off of the material in some way. I've been thinking about doing a kickstarter, but I'm interested in exploring oth…

I don't have a lot of knowledge, but there are websites that allow for the monetization of lesson plans. Maybe workbooks and videos to help teachers present the materials?

I do think a kickstarter would definitely help as would getting it out in other teacher's classrooms to get earlier feedback.

I totally support this.

Re: How our 1,000-year-old math curriculum cheats America's kids

#84

Post by gus_massa »

Consultant32452 wrote: post #26
gus_massa wrote: post #19

Earlier quoted context omitted.

The curriculum changed. For example, logarithm tables were a standard topic. I don't know haw many hours in a year were use to explain it. Now that subject luckily has disappeared because it's not necessary. Note: There are some tables that are very similar, for example the voltage of a thermocouple.

I went all the way through differential equations in engineering school and don't know how to do anything with matrices. shrug

Don't worry, Heisenberg discovered the matrix formulation of quantum mechanics without knowing matrices http://en.wikipedia.org/wiki/Werner_Heisenberg#Matrix_mechan... :). More seriously, if you ever want to study quantum mechanics, you should learn matrix algebra before.

Re: How our 1,000-year-old math curriculum cheats America's kids

#85

Post by Patrick_Devine »

dllthomas wrote: post #78
Patrick_Devine wrote: post #73

Earlier quoted context omitted.

You're right, I did state it a little awkwardly, but the statements are correct. I'll give a more concrete example: I'm firing a projectile at 52 degrees and it needs to move 10 units. I'm at (5,7), where does the projectile end up? delta x = cos(theta) * 10 delta y = sin(theta) * 10 So my final position is (5 + 6.16, 7 + 7.88), or (11, 15). If I already knew how far the delta X and delta Y were, I could get the leng…

Yes, I certainly wasn't disagreeing that trig is useful for games. The "if you want to try this out yourself" comes across a little patronizing in this context...

It was more trying to be helpful. A lot of people's heads explode when they see trig, and they stumble on things like radians vs degrees. You can do some really cool stuff with just a little bit of knowledge.

Re: How our 1,000-year-old math curriculum cheats America's kids

#86

Post by WalterBright »

sitkack wrote: post #79
WalterBright wrote: post #39

Math curriculum may be rote and boring, but if you don't master arithmetic, fractions, exponents, etc., you're going to have a lifetime of poor decisions regarding investments, financing, etc., which will be very costly.

You can teach exponential growth, compound interest and ratios before mastery of the mechanics. To many, mastery of the mechanics inoculates them not from darkness but from a scientific mind. I know many people with a mastery of arithmetic and fractions yet still make poor mathematical decisions. Conversely, I see people make projections and use algebra w/o even knowing they are doing it. Learning assembly isn't is a…

I've talked with people who sell finance, and they make bank off of people with a poor grasp of mathematical fundamentals. And that's just a small bit of what it will cost a person to not master it.

Re: How our 1,000-year-old math curriculum cheats America's kids

#87

Post by sitkack »

WalterBright wrote: post #86
sitkack wrote: post #79

Earlier quoted context omitted.

You can teach exponential growth, compound interest and ratios before mastery of the mechanics. To many, mastery of the mechanics inoculates them not from darkness but from a scientific mind. I know many people with a mastery of arithmetic and fractions yet still make poor mathematical decisions. Conversely, I see people make projections and use algebra w/o even knowing they are doing it. Learning assembly isn't is a…

I've talked with people who sell finance, and they make bank off of people with a poor grasp of mathematical fundamentals. And that's just a small bit of what it will cost a person to not master it.

These people also don't understand concepts like exponential growth, I think a lack of fundamentals is a symptom not a cause.

Re: How our 1,000-year-old math curriculum cheats America's kids

#88

Post by minikomi »

Pxtl wrote: post #67
katbyte wrote: post #65

Earlier quoted context omitted.

personally, busy work just never sticks for me, i don't remember almost any of the math i did in HS and uni that was just "do these problems over and over till you remember it" because it just wasn't all that interesting, and this goes for any subject. However some concepts, limits, derivatives and integrals i remember perfectly well (5+ years later) because my math teacher explained how the all fit together, what th…

It's the difference between skills and knowledge. Limits/derivatives/integrals are interesting knowledge so you can discuss them verbally, even if you don't have extensive practice in using them. The basic, core stuff is the opposite. Fractions, bedmas, etc. you don't care enough to talk about, but if I handed a problem that used those concepts you could do it in your head, because they're skills that have been devel…

Dull work can be made fun with a little effort. One of my high school teachers had us form lines, we refactor on the fly, said the factors of a quadratic out loud, and then were able to shoot the opponent (like a duel).. After a few shootouts everyone got very quick at refactoring. That little fun boost made the grind feel meaningful.

Re: How our 1,000-year-old math curriculum cheats America's kids

#89

Post by dllthomas »

Patrick_Devine wrote: post #85
dllthomas wrote: post #78

Earlier quoted context omitted.

Yes, I certainly wasn't disagreeing that trig is useful for games. The "if you want to try this out yourself" comes across a little patronizing in this context...

It was more trying to be helpful. A lot of people's heads explode when they see trig, and they stumble on things like radians vs degrees. You can do some really cool stuff with just a little bit of knowledge.

Yeah, I don't get why more people don't get trig - it's always come very naturally to me, but I have to work to recognize that's not the case for everyone, particularly when confronted with experiences from my past like working on homework with math majors and finding them confused when I applied a trig identity to the problem...

Re: How our 1,000-year-old math curriculum cheats America's kids

#90

Post by j2kun »

SamuelMulder wrote: post #81
j2kun wrote: post #27

> By hiding math's great masterpieces from students' view, we deny them the beauty of the subject. The problem is that math's great masterpieces are problems and proofs. High school math educators are largely the folks who hated doing proofs during their education, and they're just as uninformed about what the interesting open problems are as their students.

As a mathematician, how much time do you spend studying proofs written by other people? I'm genuinely curious, because I think that if I wanted to be a novelist, I would spend a lot of time reading novels before trying to write one. I feel like we never have children read the great "literature" of mathematics, but then expect them to write their own proofs and are surprised when they hate it.

I literally study the proofs of others every working day, for at least a few hours a day. But I am a young mathematician and still inexperienced with research.

I imagine that once you are a professor you can spend less time studying the details of proofs because you can generate them on your own once you understand the big picture. But even so this depends on your field (combinatorics folks, for example, REALLY spend a lot of time studying proofs).

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