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

#41

Post by dalke » Mon, Mar 03, 2014, 3:44 PM UTC

j2kun wrote: post #23

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.

Such cynicism. What do you have against Feynman's presence in the California committee to select, among other things, math books?

Ahh, I see. If you are the person behind "Math ∩ Programming" then I can see what you have against that committee. Feynman wrote, arguing against new math:

> It will perhaps surprise most people who have studied these textbooks to discover that the symbol ∪ or ∩ representing union and intersection of sets and the special use of the brackets { } and so forth, all the elaborate notation for sets that is given in these books, almost never appear in any writings in theoretical physics, in engineering, in business arithmetic, computer design, or other places where mathematics is being used. I see no need or reason for this all to be explained or to be taught in school.

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

#42

Post by gus_massa » Mon, Mar 03, 2014, 3:47 PM UTC

j2kun wrote: post #22

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.

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.

I agree that the exact form of an ellipse is not useful, but some general idea is.

Other example is the method for long multiplication. I think that it's not 1000 years old, but I can't find a source. One of the formed methods was to use square tables and the identity xy = ( (x+y)^2 - (x-y)^2) )/4. It guesses it was explained in schools, but now it's almost a curiosity. To use it, you must have a book with the tables of the squares, and the last edition of those books is from 1888: http://en.wikipedia.org/wiki/Multiplication_algorithm#Quarte...

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

#43

Post by dalke » Mon, Mar 03, 2014, 3:47 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.

When I was in school there was still the giant slide rule on the wall, from when the teacher used to teach how to use it.

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

#44

Post by DerpDerpDerp » Mon, Mar 03, 2014, 3:48 PM UTC

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 don't see how teaching the motivations, history, context, and future uses of the current topic of study on Mondays (while using the other four days for more traditional teaching) would be significantly worse than what we do now.

It actually sounds a lot better.

> If students are going to succeed in his college-level courses then they need the basics down cold, which means memorization, repetition, and application to concrete problems

Further, the only time I ever needed it "down cold" was when college professors were insisting I not use a calculator on exams. The rest of the time, I was better off knowing about the context and motivation behind what we were doing, not calculating faster.

This experience is shared by friends of mine who are now pursuing PhDs in the hard sciences or working in finance: the computer does the calculating, but you need to know how to write mathematics, not how to manipulate numbers (by hand).

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

#45

Post by jerf » Mon, Mar 03, 2014, 3:48 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…

"I have a slight quibble with your characterization of high school "calculus" as real analysis"

Yeah, I know, but if that's not what high school math is, what is it? As hostile as I am I'm not quite ready to write it off as "entirely not math"... there's some math content in there, after all.

I do want to point out that I am in contact with reality and do not expect students to start with number theory, nor do I realistically expect high school to ever cover what you covered in "real" real analysis. (Real numbers are terribly complicated things and I don't think high school should cover all the endless, endless corner cases of those either; time is short and the fields are vast.) What I'm really looking for is dropping a lot of stuff that is both practically and theoretically pretty useless, and replacing it with a lot of stuff that is, well, both more practical and more theoretically useful. Some of the core will survive (integration and differentiation aren't going anywhere, those really are fundamental to any reasonable math education, though we might spend several fewer weeks walking through all the special cases of each), but there's a lot of room for improvement.

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

#46

Post by wisty » Mon, Mar 03, 2014, 3:58 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…

> Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to.

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.

Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protractor, and can only measure a few of the lengths." Seriously?

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

#47

Post by bane » Mon, Mar 03, 2014, 4:06 PM UTC

wisty wrote: post #46

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…

> Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to. 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. Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protr…

> 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 tax once a year, they'll never encounter anything more complicated than very basic arithmetic.

I think the hardest math problem most people encounter is figuring out percentages so they can fill out the "tip" on the credit card receipt when they eat out. Yeah it's "algebra" but it's a very limited class of problem and people just use a calculator or a tip calculator to do it these days.

>Trig

Yeah, trig really requires good motivation. The answer to most trig questions really is "buy the appropriate measuring tool" not "do a bunch of calculations and look up the result of the trig functions in a table". I don't ever remember having the calculations for cos(), sin() explained to me, they're just magic functions, number goes in, number comes out.

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

#48

Post by DerpDerpDerp » Mon, Mar 03, 2014, 4:11 PM UTC

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…

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 undergraduate degree).

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

#49

Post by kens » Mon, Mar 03, 2014, 4:13 PM UTC

bane wrote: post #47

wisty wrote: post #46

Earlier quoted context omitted.

> Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to. 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. Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protr…

> 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.

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

#50

Post by trothoun » 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.

Fortunately, TI continues to provide this to many students.