Article on Math (and Music!) and how they are taught...

Poststructural Pub
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Ok, I really don’t think I’ve ever read an essay by a mathematician before…ever.

I hated math in school, until I hit Algebra, where I took off like a rocket, because at last, it wasn’t just busy-work. But, even so, the main attraction of math to me was that I got to use a calculator, and that was a pretty cool little piece of electronics. :sunglasses:

Back to the essay, I would’ve suspected that such an activity, reading an essay on the way we teach children math, would have probably been about as exciting as watching your toenails grow, or maybe watching paint dry. I certainly wouldn’t have suspected that I would laugh out loud, many times…or that I would get to the end of the essay and be sorry that it was over.

Here’s the link:

http://www.maa.org/devlin/LockhartsLament.pdf

This is just wonderful. I hope that everyone enjoys it as much as I did. :slight_smile:

Here’s a quote to hopefully tantalize you, on the subject of “if music were taught like math…”

In the higher grades the pressure is really on. After all, the students must be prepared for the
standardized tests and college admissions exams. Students must take courses in Scales and
Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college
when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high
school.” Of course, not many students actually go on to concentrate in music, so only a few will
ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every
member of society be able to recognize a modulation or a fugal passage, regardless of the fact
that they will never hear one. “To tell you the truth, most students just aren’t very good at music.
They are bored in class, their skills are terrible, and their homework is barely legible. Most of
them couldn’t care less about how important music is in today’s world; they just want to take the
minimum number of music courses and be done with it. I guess there are just music people and
non-music people. I had this one kid, though, man was she sensational! Her sheets were
impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful.
She’s going to make one hell of a musician someday.”

–James

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Thanks James! I greatly enjoyed reading Lockhart’s critique on math school teaching (though not on music). I assume he talks about conditions in the US. I had the good fortune to have had some excellent math teachers, and we actually did a lot of real maths, a lot of finding proofs etc. But that was way back and in Hamburg, Germany…

For those too lazy to read all 25 pages here is Lockhart’s concluding summary, enjoy :laughing:

To put the finishing touches on my critique of the standard curriculum, and as a service to the community, I now present the first ever completely honest course catalog for K-12 mathematics:
The Standard School Mathematics Curriculum

LOWER SCHOOL MATH. > The indoctrination begins. Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions. Children are expected to master a complex set of algorithms for manipulating Hindi symbols, unrelated to any real desire or curiosity on their part, and regarded only a few centuries ago as too difficult for the average adult. Multiplication tables are stressed, as are parents, teachers, and the kids themselves.

MIDDLE SCHOOL MATH. > Students are taught to view mathematics as a set of procedures, akin to religious rites, which are eternal and set in stone. The holy tablets, or “Math Books,” are handed out, and the students learn to address the church elders as “they” (as in “What do they want here? Do they want me to divide?”) Contrived and artificial “word problems” will be introduced in order to make the mindless drudgery of arithmetic seem enjoyable by comparison. Students will be tested on a wide array of unnecessary technical terms, such as ‘whole number’ and ‘proper fraction,’ without the slightest rationale for making such distinctions. Excellent preparation for Algebra I.

ALGEBRA I. > So as not to waste valuable time thinking about numbers and their patterns, this course instead focuses on symbols and rules for their manipulation. The smooth narrative thread that leads from ancient Mesopotamian tablet problems to the high art of the Renaissance algebraists is discarded in favor of a disturbingly fractured, post-modern retelling with no characters, plot, or theme. The insistence that all numbers and expressions be put into various standard forms will provide additional confusion as to the meaning of identity and equality. Students must also memorize the quadratic formula for some reason.
> GEOMETRY. > Isolated from the rest of the curriculum, this course will raise the hopes of students who wish to engage in meaningful mathematical activity, and then dash them. Clumsy and distracting notation will be introduced, and no pains will be spared to make the simple seem complicated. This goal of this course is to eradicate any last remaining vestiges of natural mathematical intuition, in preparation for Algebra II.
> ALGEBRA II. > The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects, simply because they have to be
stuck in somewhere, apparently. The name of the course is chosen to reinforce the ladder mythology. Why Geometry occurs in between Algebra I and its sequel remains a mystery.

TRIGONOMETRY. > Two weeks of content are stretched to semester length by masturbatory definitional runarounds. Truly interesting and beautiful phenomena, such as the way the sides of a triangle depend on its angles, will be given the same emphasis as irrelevant abbreviations and obsolete notational conventions, in order to prevent students from forming any clear idea as to what the subject is about. Students will learn such mnemonic devices as “SohCahToa” and “All Students Take Calculus” in lieu of developing a natural intuitive feeling for orientation and symmetry. The measurement of triangles will be discussed without mention of the transcendental nature of the trigonometric functions, or the consequent linguistic and philosophical problems inherent in making such measurements. Calculator required, so as to further blur these issues.

PRE-CALCULUS. > A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of ‘limits’ and ‘continuity’ are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.

CALCULUS. > This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises which do not really apply in this setting, and which will of course not be mentioned. To be taken again in college, verbatim.

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Thanks!
Bad enough having lived through it.

Yep, his summation matches up with my recollections.