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

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.

Seriously, as a video game programmer, you use trig _every day_. If you want to find the distance between two points when you have the angle (eg. I'm firing a projectile at a certain angle), use cosine for the length of the x axis and use sine for the y axis. You get the hypotenuse from using pythagoras' theorem. If you want to find the angle between two points, use arc tangents.

Once kids have mastered all of that, you can teach them law of cosines and get into linear algebra; simple rotational matrices which can let you do collision detection and a whole bunch of other really, really cool stuff.

So yeah, Bob the builder might be boring as shit as a word problem, but Bob the builder might be a pretty cool video game. Without trig, as a game, Bob the builder is probably going to be boring as shit too.

You can also throw in some economics: Bob would be fired and/or get better equipment.

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.

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 they represented wrt the real world and how they can be useful and that actually got me interested.

Yea you need to know the basics, but i daresay busy work isn't the best way to teach them.

Of course it's not enough to state something, but making the students reiterate what you've stated a hundred times is only marginally better.

Another problem is that no student really learns ANYTHING until they need to use it to do something else. No student learns fractions until they need to use it to do algebra, and they don't learn algebra until they need it to do calculus. And they don't learn calculus until they need it to do engineering/physics or higher mathematics (real analysis, which they don't really learn until they do measure theory...).

Yeah, absolutely. In fact, I'd say that it's just as important that students receive confirmation of this history and motivation in their other subjects. For example, in various history classes, we learn about kings and wars and important philosophers. But we rarely learn about mathematicians and why their contributions were important, of if they were polymaths, we discuss their non-mathematical contributions, but omit their mathematical ones entirely.

Then in writing and literature we spend endless hours on appreciating tiny non-relevant symbols, but don't read something like Ringworld and spend part of a session calculating and relating the size of it. Conversely, in Math class, writing a paper on the history and influence of Platonic solids or similar would have been an interesting break and let kids struggling with crunching numbers take an interest and shine a little.

Or imagine a math course that analyzes things like agricultural output from Roman times to modernity, involving geometry, arithmetic, algebra, percentages (taxes to the king!), nutrition, etc. Extend out to how greater agricultural output per unit land produces surpluses that enable people to take up other labors like politics or art or music.

Off the cuff examples that would need more careful thought, but hopefully the idea is sound.

Bringing math into other non-math subjects, and bringing arts into non-art subjects I think helps prop up what students see as isolated subject "silos" that have nothing to do with anything.

Literature and history courses mutually reinforce each other, and math and science course mutually reinforce each other, but there's a tremendous gap between these two groups of courses where they don't reinforce each other.

This really needs to end because it all is connected and builds relevance for students.

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.

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.

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.

I'd guess most kids hate puzzles.

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.

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

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).

[1] http://jeremykun.com/about/

I can't say how many times my 'teaching concentration' colleagues would look at a basic linear algebra problem (which requires a proof) and whine saying things like, "I don't care about this stuff, it's so stupid and pointless, I just want to get my degree so I can go teach high school math."

All irony aside, these are the students who actually enjoyed the structure of high school math, and were rudely awakened when they were asked to apply their minds to reason. As a result, 'teaching concentrations' in undergraduate and graduate school usually provide mathematically watered down courses and automatic passing grades, and the teachers-in-training don't learn anything new. They certainly don't learn, for example, any mathematics that has been done since 1900, or any open problems that aren't Millenium Prize Problems. And god forbid they ask and try to answer an original question (as they expect their students to do when they're confused).

This is what they mean by the "blind leading the blind."

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).

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.