How our 1,000-year-old math curriculum cheats America's kids • Hacker News Board

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

#21

Post by j2kun » Mon, Mar 03, 2014, 3:14 PM UTC

Spooky23 wrote: post #4

I don't think that you can appreciate this stuff until you actually have the mechanical background in math. Unlike most subjects in K-12, you can't BS math. You're right or wrong. There's no subjectivity in evaluation, and no opportunity for lazy students like me to BS a tired teacher with flowery prose that doesn't say much. Why not make math accessible in easier or more practical ways? My trigonometry teacher walke…

This is the viewpoint of an engineer. The salient difference in thought is that the goal is rarely to be right (initially), but to get insight about mathematical stuff.

Mathematicians do (and students should) focus on proofs over computations, and there is an extreme amount of subjectivity there. If you produce a false proof, it can nevertheless be beautiful and yield fantastic insights. Likewise, a correct proof can be unsatisfying and ugly. Your goal then is to revise it (or completely rewrite it) to make it more beautiful and insightful.

Here is an example: the 7 Bridges of Konigsberg problem is one of the most famous (solved) problems in all of mathematics. One can easily give a proof by exhaustion, but that is wholly unsatisfying and perhaps the ugliest possible proof. A much better proof involves some insight into graph theory, and a satisfying and elegant proof would give you a characterization of these kinds of trails in graphs.

You don't need a mechanical background to start trying to solve such puzzles (I know because I've taught it that way), and you don't need any mathematical background to appreciate the very elementary proof. But as you let students flounder with puzzles like these, you can slowly introduce technical matter. The point is that it has a context they care about (people like working on puzzles!).

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

#22

Post by j2kun » Mon, Mar 03, 2014, 3:16 PM UTC

gus_massa wrote: post #19

jerf wrote: post #5

Focusing on the age is probably the wrong approach. Math true then is still true now. The problem is that the curriculum is now held sacred (and I mean that fully as nastily as possible), and it is being held there by people who are now the blind-leading-the-blind unto the sixth or seventh generation. I've gotten around in the math world a lot since primary school, and what I was taught vs. any actual modern mathemat…

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.

And yet, we somehow think that being able to draw an accurate picture of an ellipse given its equation is useful, along with knowing the derivative of every inverse trig function, and countless other things.

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

#23

Post by j2kun » Mon, Mar 03, 2014, 3:21 PM UTC

dalke wrote: post #2

It sounds like a return to the "new math" of the 1960s. Compare this article: > If we are to give students the right tools to navigate an increasingly math-driven world, we must teach them early on that mathematics is not just about numbers and how to solve equations but about concepts and ideas. > It's about things like ... clock arithmetic — in which adding four hours to 10 a.m. does not get you to 14 but to 2 p.m.…

Any attempt to force a particular mathematical subject matter on students will undoubtedly be ruined by a committee.

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

#24

Post by drakaal » Mon, Mar 03, 2014, 3:27 PM UTC

Ok. First I'm not taking lessons from anyone who plagiarizes. This is a re-write of:

http://j2kun.svbtle.com/you-never-did-math-in-high-school

Which may also be someone's work, but it was one I read recently.

Second, I learned some Calculus in school, how about you? That is not a subject a 1000 years old. So we haven't been teaching it that way for 1000 years.

Third, did this guy not have story problems? Applied Math is basically what this author is claiming we don't have.

Fourth, Graphing is pretty new. We didn't use to visualize plots because we didn't have the resources, I can't tell you when that became part of algebra, but it was in the past 100 years.

I can't believe LA Times ran such a poorly informed piece.

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

#25

Post by geebee » Mon, Mar 03, 2014, 3:27 PM UTC

I read that article over the weekend. I agree completely, but it's downstream of a bigger problem. Think of it this way - when we file the bug fix, the report will reference a different bug fix that solved this one downstream.

We need to draw math teachers from the top tier of math majors (or physics, stats, etc). And if we do that, it's very likely that people with real insight into math will teach it very effectively but less mechanically.

One thing I've noticed is that the US system loves a "plan". This might be a result of the career ladder - a teacher is on the bottom rung, whereas someone who sets the curriculum for all teachers has moved beyond that lowly spot. But what we really need is an armada of accomplished math majors in actual teaching positions.

Without that, the plan won't really matter. With it, the plan? It matters, sure, but I'd personally be inclined to give quite a bit of latitude and autonomy to people who were in the top tier of their class and majored in math and who are inclined to teach.

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

#26

Post by Consultant32452 » Mon, Mar 03, 2014, 3:27 PM UTC

gus_massa wrote: post #19

jerf wrote: post #5

Focusing on the age is probably the wrong approach. Math true then is still true now. The problem is that the curriculum is now held sacred (and I mean that fully as nastily as possible), and it is being held there by people who are now the blind-leading-the-blind unto the sixth or seventh generation. I've gotten around in the math world a lot since primary school, and what I was taught vs. any actual modern mathemat…

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

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

#27

Post by j2kun » Mon, Mar 03, 2014, 3:28 PM UTC

> 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.

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

#28

Post by ghaff » Mon, Mar 03, 2014, 3:28 PM UTC

j2kun wrote: post #21

Spooky23 wrote: post #4

I don't think that you can appreciate this stuff until you actually have the mechanical background in math. Unlike most subjects in K-12, you can't BS math. You're right or wrong. There's no subjectivity in evaluation, and no opportunity for lazy students like me to BS a tired teacher with flowery prose that doesn't say much. Why not make math accessible in easier or more practical ways? My trigonometry teacher walke…

This is the viewpoint of an engineer. The salient difference in thought is that the goal is rarely to be right (initially), but to get insight about mathematical stuff. Mathematicians do (and students should) focus on proofs over computations, and there is an extreme amount of subjectivity there. If you produce a false proof, it can nevertheless be beautiful and yield fantastic insights. Likewise, a correct proof can…

I guess I have an engineering viewpoint as well--which may not be surprising because I, well, was one. I never especially connected to geometry with its proofs in high school. What I did learn was lots of basic trig and algebra and the beginnings of calculus (which I took more of in college). The result is that while I've never had much of an interest or flair for advanced math, I did develop most of the math skills I needed both for school and, more importantly, through career and life.

I've had stats as well. As I was just discussing with someone in a different context, I think stats, accounting, and similar applied math would be far more useful to most students than either most calculus (past simple differentiation which is used in a lot of contexts), proofs, or set/group theory. And, arguably, could be linked a lot better to real-world applications.

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

#29

Post by jcampbell1 » Mon, Mar 03, 2014, 3:29 PM UTC

Steuard wrote: post #13

I'm very much a math person, but I think this author is being rather naive. In the current political climate surrounding education, it seems like madness to say, "Teach math more like we teach art!" After all, art classes in the US are pretty much first on the chopping block for the many, many people who think education should be all about test scores and checklists. I would love to see more kids exposed to "real mat…

Not to mention, "The curriculum is 1000 years old" is a terrible argument from a logical perspective. I have no idea if that means math is timeless or dated.

There are other funny gems.

"A mathematical statement is either true or false"

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

#30

Post by belovedeagle » Mon, Mar 03, 2014, 3:29 PM UTC

jerf wrote: post #5

Focusing on the age is probably the wrong approach. Math true then is still true now. The problem is that the curriculum is now held sacred (and I mean that fully as nastily as possible), and it is being held there by people who are now the blind-leading-the-blind unto the sixth or seventh generation. I've gotten around in the math world a lot since primary school, and what I was taught vs. any actual modern mathemat…

As a student in my first /real/ real analysis course (called "Advanced Calculus I" by the registrar, predictably), I have a slight quibble with your characterization of high school "calculus" as real analysis. What we did in high school, which I now think of as nothing but "calculus" in scare quotes, is to real analysis as arithmetic is to mathematics proper---because that's all it was, glorified arithmetic. Even though I had a great teacher and an understanding principal who allowed me to just go and study math on my own for two years, even then I was misled into the glorified-arithmetic world of studying "calculus" for advanced standardized tests. That's all high school math ever was, and when I scored in the 99th percentile on all the standardized tests, it was because they quite literally just asked arithmetic questions (sometimes disguised as "plug this into the quadratic formula", sometimes as "take the derivative then plug in this value").

TL;DR: high school math, and even much of what's taught in an undergraduate degree now (in math!), is just glorified arithmetic.