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

> It takes a lot of research and work though.

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.

I really enjoyed your link too. So thanks for posting. But I do have some qualms about the article's position.

> Two weeks of content are stretched to semester length by masturbatory definitional runarounds.

That Lockhart describes trigonometry as "masturbatory" I find ironic. Lockhart argues that math is fun for its own sake. Personally, I think that math is fun per se. I.e. patterns and ideas and puzzles are fun. But historically, much of math was invented as engineering-shortcuts. E.g. trig identities for navigation, newton's calculus for friction, etc. The philosophical Greeks and their geometry I think are the exception. So I think most people would rebut that math's actual raison d'etre lies in it's tangible application. The manner in which Lockhart describes math is why physicists joke that theoretical math is nothing more than masturbation.

> In certain of the arts and crafts, we sometimes do precisely this--requiring a child to "express himself" in paint before we teach him how to handle the colors and the brush. There is a school of thought which believes this to be the right way to set about the job. But observe: it is not the way in which a trained craftsman will go about to teach himself a new medium. He, having learned by experience the best way to economize labor and take the thing by the right end, will start off by doodling about on an odd piece of material, in order to "give himself the feel of the tool." [1]

I do agree that math curriculums are excruciatingly insipid. And Lockhart makes some good points. But I think this other link makes a strong argument too, which is contradictory to what Lockhart argues. So I was thinking: for each unit, maybe teachers could explain what problems the unit was actually solved historically. This differs from the article, because 6th graders don't really need to know about Riemann Surfaces if that's not what the unit covers. This differs from your Lockhart, because I don't think it's as "masturbatory". But it still affords students a glimpse of where all this pedagogical grinding is headed, allows students to reify to something relevant, and retains that "puzzle" feeling.

Again, I like puzzles. But teachers have a responsibility to teach everyone, not just the select few who solve rubiks cubes in their spare time. How much of that would be solved by removing the educational mandate on math, I don't know.

[1] http://www.scribd.com/doc/36325362/The-Lost-Tools-of-Learnin...

"great" is a superlative. His statement an opinion. But I imagine he knows what he's talking about since he has a PHD in math. [1]

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

I agree, and I don't see the relevance of 1,000 old findings to an bad math curriculum. The beauty of math is that findings 1,000 years ago are still relevant today.

I think first steps in improving math education are teaching concept instead of calculation, and focus on understanding math principles instead of memorizing.

As a math/CS major, when I wanted to fully understand the basic concepts of pi, pythagorean theorem, I looked back at how they were originally discovered. It gave math a story behind it, and these concepts stuck with me because I understood them. I think we could improve people's understanding of math through telling the story of many of the concepts, rather than throwing concepts at students and hoping that they stick. Stephen Wolfram discusses the concept will on Concept vs. calculation: http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_m...

Memorization is the road to failure in math, and many teachers push memorization rather than understanding.

The irony is that all mathematics up to the high school level was historically motivated by practical problems. Algebra began as a system of rules to fairly partition land, for irrigation or inheritance, for example. But most of the high school math teachers are not actually mathematicians, so they themselves have no clue what algebra and calculus are used for. There ought to be incentives for professionals of all fields to go into teaching.