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

#51

Post by dhruvmittal » Mon, Mar 03, 2014, 4:19 PM UTC

kens wrote: post #49

bane wrote: post #47

Earlier quoted context omitted.

> Algebra is problem solving. You have a formula describing the problem, and want to re-arrange it to find one of the variables. It has a lot of useful and logical applications. It does, but for average Joe and Carla, who's day job involves making sure the box of sprockets sitting on the loading dock matches the P.O., and who's most pressing math problem is balancing their check book every few days and using turbo ta…

What motivated trig functions for me was writing 5 line BASIC programs as a kid to draw circles, spirals, etc. Realizing that COS was the X coordinate and SIN was the Y coordinate made it all clear. Unfortunately there's no easy, low-friction way for kids today to do that with their PC.

I had the same experience, but with a TI-83.

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

#52

Post by Pxtl » Mon, Mar 03, 2014, 4:19 PM UTC

bane wrote: post #33

I was a terrible math student in school. Looking back, it wasn't because the material was hard, or boring, but because it was completely unmotivated. They may as well have been asking me to organize piles of toothpicks or count ceiling tiles to fill up the class periods. There was simply no sense to it. I think this is partially understood, and the attempted solution is to try to find applications for the math you're…

The problem is that if you don't fill the period with busywork? The students don't build up the intuitive, gut-level skills they need to handle the higher-level stuff.

Math requires building muscles in your head, and muscles take reps. Lots of reps. Let's look at the elementary level: it's not enough to simply introduce BEDMAS or least-common-denominator and write a few problems that get the student to check off "okay, I know that" from the list of stuff they know.

The student has to be so practiced at these concepts that they could do it while trying to juggle 9 other extremely complicated brand-new concepts in their head because that's what you need to do when you build calculus upon factoring upon algebra upon fractions upon arithmetic.

If you fail to do this, you get kids walking into grade 9 math class who've forgotten everything they were supposed to know about fractions and teachers have too much new material to cover to re-teach fractions (my wife is a math teacher. This happens way, way too much - too many students enter her class missing necessary prerequisite skills). Students struggling with applying the basics cannot properly grasp the new material - so the basics have to be rock solid.

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

#53

Post by Pxtl » Mon, Mar 03, 2014, 4:21 PM UTC

kens wrote: post #49

bane wrote: post #47

Earlier quoted context omitted.

> Algebra is problem solving. You have a formula describing the problem, and want to re-arrange it to find one of the variables. It has a lot of useful and logical applications. It does, but for average Joe and Carla, who's day job involves making sure the box of sprockets sitting on the loading dock matches the P.O., and who's most pressing math problem is balancing their check book every few days and using turbo ta…

What motivated trig functions for me was writing 5 line BASIC programs as a kid to draw circles, spirals, etc. Realizing that COS was the X coordinate and SIN was the Y coordinate made it all clear. Unfortunately there's no easy, low-friction way for kids today to do that with their PC.

I feel like the educational and software worlds have failed to work together to provide a modern, powerful, 21st century answer to the TI-83.

Being able to animate and play with your math helps a lot. GeoGebra is a good example, but it's not the holy grail.

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

#54

Post by rayiner » Mon, Mar 03, 2014, 4:38 PM UTC

belovedeagle wrote: post #30

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 tho…

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

Is this a bad thing? You can design and build airplanes with what doesn't amount to anything more than glorified arithmetic. I don't see the value in teaching kids more than that.

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

#55

Post by SamuelMulder » Mon, Mar 03, 2014, 4:42 PM UTC

bane wrote: post #33

I was a terrible math student in school. Looking back, it wasn't because the material was hard, or boring, but because it was completely unmotivated. They may as well have been asking me to organize piles of toothpicks or count ceiling tiles to fill up the class periods. There was simply no sense to it. I think this is partially understood, and the attempted solution is to try to find applications for the math you're…

I think you're absolutely right that math has to be motivated. A lot of the effort to motivate it is to provide problems that students understand relate to the real world. Most of them come across as contrived.

You hit on a good concept with the idea of incorporating the history of math. I'm working on a Geometry curriculum that does just that. Understanding math in the context of a grand story of mankind trying to understand the world around us is a lot more interesting than as a set of received wisdom that must be memorized.

I would love to see more math material along these lines, but there isn't much out there, and it takes a long time to produce. I've been working on mine for around 6 months and am just up through looking at how the discovery of incommensurable lengths influenced Plato's philosophy. The idea is to work through the history and philosophy in parallel with Euclid's Elements, relating points back and forth where possible.

I've tried teaching a history of math class to local homeschool kids along those lines, focusing on Egyptian - Greek history, with some success. It takes a lot of research and work though.

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

#56

Post by chrisBob » Mon, Mar 03, 2014, 4:44 PM UTC

DerpDerpDerp wrote: post #48

chrisBob wrote: post #12

Earlier quoted context omitted.

That was a fun read, but no one can teach that way. You can't become a teacher by studying math, physics, chemistry, biology, literature, french, programming, history, geography or english. You become a teacher in the US by getting a teaching degree. I believe that is the biggest problem we have in the US education system. Teachers only need minimal knowledge of their subject, and if someone discovers that they don't…

I know a number of math teachers who have undergraduate degrees in math, and then attended a 2 year masters program to get their degree in teaching. I also know a number who came from a humanities background, and "learned enough math" in the single, poorly taught math-for-teaching class they had in getting a masters. One of these groups makes better teachers (and likely has a wider career path, because of the undergr…

I also know some smart teachers that started with something else and ended up teaching high school. I have more examples of people who got a degree in something else and wanted to teach, but then found out how hard and expensive that transition is.

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

#57

Post by rayiner » Mon, Mar 03, 2014, 4:45 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…

> The point is that it has a context they care about (people like working on puzzles!).

I'd guess most kids hate puzzles.

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

#58

Post by 6d0debc071 » Mon, Mar 03, 2014, 4:54 PM UTC

Pxtl wrote: post #52

bane wrote: post #33

I was a terrible math student in school. Looking back, it wasn't because the material was hard, or boring, but because it was completely unmotivated. They may as well have been asking me to organize piles of toothpicks or count ceiling tiles to fill up the class periods. There was simply no sense to it. I think this is partially understood, and the attempted solution is to try to find applications for the math you're…

The problem is that if you don't fill the period with busywork? The students don't build up the intuitive, gut-level skills they need to handle the higher-level stuff. Math requires building muscles in your head, and muscles take reps. Lots of reps. Let's look at the elementary level: it's not enough to simply introduce BEDMAS or least-common-denominator and write a few problems that get the student to check off "oka…

To a certain extent that's a product of a bad curriculum though. If you teach something, tick it off, teach something else, tick that off. And build a large number of things ticked off in that manner - that don't reuse the things taught earlier - then of course you're not going to get the reps in.

As compared to, say, the syntax in a programming language. Where you don't write out hello world sixty times to get the bracket rules, you just reuse the rules in other things you're doing often enough that they become ingrained.

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

#59

Post by arbitrage » Mon, Mar 03, 2014, 4:56 PM UTC

jcampbell1 wrote: post #29

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"

Gödel might have something to say about that. Then again, he might not.

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

#60

Post by arbitrage » Mon, Mar 03, 2014, 5:01 PM UTC

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.

Wow, that's a really bold statement. Do you have a proof of that?