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

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

#31

Post by kaitai »

gus_massa wrote: post #18

Math is like knitting. It's not useful to read about it. You must do it. When reading an advanced math book for the fist time, I can spend 1 hour per page, because I must copy the proof, try a few "improvements" that are dead ends, do some exercise, and understand what is the main idea of that part. It's very difficult to mixing some modern subjects without calculation. Most of the time, the idea is to just hide the…

Since you mentioned knitting (and I agree with your analogy), check out the great intuition you can get about hyperbolic geometry via crochet and knitting.

See how "parallel" lines act and the angle sums of triangles end up smaller than 180 degrees: http://theiff.org/oexhibits/oe1e.html

A TED lecture is linked: http://geknitics.com/2010/11/sunday-knitting-science-hyperbo...

Hyperbolic baby pants also convertible into a 2-holed torus (not while on baby I guess), with added note that on 2-holed tori you can make maps that require 8 colors instead of just 4 like maps on the plane or sphere: http://www.ravelry.com/projects/smbelcas/hyperbolic-pants-2

Geometry, topology, map-coloring theorems, crafts: all things many kids never get to do anymore.

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

#32

Post by ronaldx »

w1ntermute wrote: post #10

The biggest problem in education isn't the curriculum or method of teaching or the teachers, it's how motivated the student is (which is usually a product of their home environment). Trying to solve this social issue with "technical" fixes is not going to succeed.

>The biggest problem in education isn't the curriculum or method of teaching or the teachers, it's how motivated the student is (which is usually a product of their home environment)

While I get what you're saying, the motivation of the student is highly influenced by the curriculum and the teacher.

Having a meaningful curriculum content with a teacher who presents it in a way which the student can relate to is surely possible (but woefully rare). Good teaching can change things around.

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

#33

Post by bane »

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 learning. Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to. So they go home, ask their parents "what do you use Algebra for?" and get "I don't." and that's that.

I think, along with application concepts, the history of these maths...why were they created, about the creators who came up with the concepts, what were they trying to solve, let's solve the same problems with these new techniques, etc. This would have grabbed me and pulled me in. Instead you sometimes get a little box in the reading quickly going over all this (if you are lucky) before a hundred problems are dumped on you to drill through. It's rarely talked about in class, and if it is, it's by a teacher who doesn't know or appreciate the value of this history at all.

By doing this you show applicability to entire fields, even if the child doesn't understand what's involved in the field. Those kids that say "when I grow up I want to be a biologist" will encounter stories about people who learned to apply logic or math or fractions or whatever to solve difficult problems in biology or whatever, and then relive those moments as they try to solve the same or similar problem using the tools they were just given.

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

#34

Post by teach »

j2kun wrote: post #16
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…

Low standards for math teachers is a huge concern, and Lockhart addresses it too, I believe. Some possible ways to help: give teachers less class time and more time to prepare interesting lessons, pay teachers more, raise the standards of training and hiring.

And that's the real problem: those things all cost money. Quite a bit, actually.

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

#35

Post by j2kun »

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…

I think one problem is that mathematicians would have high school students focus on solving puzzles and slowly introducing technical content and proof-technique, while the rest of the world cries out that they need real-world applications and preparation for calculus.

The truth is that the puzzles and proof techniques are what develop mathematical thinking skills. Every mathematician knows this, but no administrators are publicly willing to believe it.

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

#36

Post by j2kun »

geebee wrote: post #25

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 effective…

Latidude? Autonomy?! If only you were in charge teachers would get something done!

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

#37

Post by kaitai »

bhixon wrote: post #20

This is like learning art history instead of how to draw. How does the "majestic harmony of Platonic solids" help a middle schooler actually do some math? Why should the average sixth grade class learn about Riemann surfaces when most of them haven't even learned what an exponent is yet? An occasional lecture on a 'fun' topic (or even better, an assigned reading and short essay -- expository writing should be practic…

I've taught a lot of enrichment seminars on Saturdays. They involve "clock arithmetic," or Fermat's little theorem and the basics of RSA encryption for older students, or fractals and ways of computing fractal dimension (and exploring polynomials and iteration and Newton's method), or the differences between geometry on a beach ball, a paper towel center tube, and a piece of paper, or even a bit of Mill and Frege's ideas on how to define a number... Kids love this stuff and they get really excited and they start asking questions about infinity and making connections with their other learning. They have fun, but the topics aren't fun -- they are important and useful! Learning about solids has applications (if that's what you value) to proteins and polymers and all sorts of funky stuff. Check out http://phys.org/news/2014-02-years-mathematicians-class-soli... for some new solids mathematicians have just discovered, inspired by biological research.

Seems better than just learning to hate math. Our current system is certainly not effective in teaching young people to add fractions, which I see as the single greatest indicator for competence in college mathematics (sigh).

Ok, after another moment's thought your argument seems similar to "Why should kids read stories and books? To succeed in writing dissertations they need grammar. All that extra reading of literature should be confined to the side..."

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

#38

Post by DerpDerpDerp »

geebee wrote: post #25

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 effective…

> 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.

Then don't pay me 25%-33% of what I'd make working in industry.

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

#40

Post by btilly »

chrisBob wrote: post #12
dabrowski wrote: post #3

This reminds me of Lockhart's Lament, which I highly recommend reading http://www.maa.org/sites/default/files/pdf/devlin/LockhartsL...

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…

Not only do you have to get a teaching degree, but smart people don't want to do that.

See http://www.statisticbrain.com/iq-estimates-by-intended-colle... and note that, relative to other college majors, education majors tend to be dumb.

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