UPDATE: Thanks very much for all the comments, which have been very helpful as I try to think this issue through. And I apologize to those of you I angered. There are several points I should have made much clearer:
First: I love math in the abstract, recognize its value, respect its practitioners, and regret very much that I'm not skilled in it and never had the great teachers with which many of you were blessed.
Second: The main reason for writing the diary was to present some possible ways to change the math curriculum so that fewer students will repeat my experience.
Third: I neglected to note a distinction between "basic arithmetic" and "simplistic arithmetic." From reading in recent years, I've learned that arithmetic in and of itself is quite a sophisticated branch of mathematics -- and one of my concerns with students' having to take algebra and geometry two or three years earlier than I did is this: They're being denied the time necessary to master important arithmetical concepts.
Fourth: As some of you have said, our school system needs to adapt some of the approaches common in Europe and Asia. And we definitely need radical changes in teacher preparation. And we need parents' reinforcing with their children how vital it is that they work hard in school. (When my son expressed discouragement about algebra last year and was having great difficulty with it, my wife and I empathized with him, but made sure to get him a tutor.) I never say he doesn't have to try his best because a subject is challenging. In fact, I've tried to communicate to him how fantastic math can be; I've encouraged him (so far without success) to participate in one of Robert Kaplan's Math Circles; once I even assembled my own little math book for him.
Finally: The country, it seems to me, would benefit from a massive overhaul in the way math and science are taught; most reform proposals merely tinker at the edges. If kids are brilliant and love those subjects (like some of your lucky children), they're okay. If they're of average intelligence, but encounter some brilliant teachers, they're okay. What I'm struggling to envision is a way to maximize the chance that average kids with average teachers will yet discover the exhilaration in math (and science) and be able to acquire the skills and discipline that will allow them to excel. Again, your comments have been terrific and I greatly appreciate your reading and taking the time to respond.
(Start of original diary) Another school year is under way and my son the 8th grader grouses like I used to. For example, he says: It’s a waste of time to learn algebra and geometry because I’ll never need them in the real world. And even though I’m now a parent, I have to agree with him.
The painful memory of a 9th grade algebra teacher’s assigning me extra homework over winter break remains vivid. Three years later, the same teacher refused to excuse me from algebra so I could take a special 20th century American history seminar. In general, he was a good guy, but his rigidity caused so much frustration and stress – and for what?
I never used algebra after high school and, if I had Dumbledore’s wizardry, no school (other than math-science magnets) would require it. Ditto geometry – although it was an oasis in my math Sahara: I had a 99 for the year – and calculus.
Instead, let’s require:
- An extra year or two of the arithmetic almost everyone will need in adulthood – when starting a small business, or simply managing a household budget. As part of the curriculum: books such as John Allen Paulos’s A Mathematician Reads the Newspaper and Steve Campbell’s Statistics You Can’t Trust. Citizens should be aware when reporters and politicians employ bogus figures either out of ignorance or malice.
And to exercise the mind in entertaining ways: books such as Martin Gardner’s Mathematical
Carnival: A New Round-up of Tantalizers and Puzzles from "Scientific American."
- A year or two of the history of mathematics. About five years ago, looking through old paperbacks on sale for 50 cents at the local library, I saw Men of Mathematics, by E. T. Bell. Grumbling to myself "I really should learn about this stuff," I bought it.
And my goodness: what a revelation! I’ve since learned that Mr. Bell is occasionally inaccurate,
but he so brings the mathematicians to life. They’re extraordinary people, their careers exciting,
their discoveries thrilling.
I had no more an idea of this extraordinary intellectual tradition than do middle and high
schoolers today. Undoubtedly it would inspire many students to learn the math for themselves;
and for them, there would be algebra, geometry, and calculus electives. And with motivated
students, teachers wouldn’t need to present the material in the current mind-numbing way,
with endless sets of dull problems filling a cinder-block tome containing graphically
repellent pages dense with small type.
- As part of history-of-mathematics courses, discussion of the scientific accomplishments particular kinds of math have made possible: medical breakthroughs, super-fast computers, movie special effects, the Hubble telescope, etc. Math’s ultimate products are not dismal textbooks, but glorious and very cool achievements emblematic of our species at its pinnacle.
- An overview of how the world economy and financial institutions large and small function and interact with one another and other actors in society – in fact, not just in theory, and illegally as well as legally. I’m not talking about some watered-down version of model-heavy traditional economics; the current recession demonstrates the catastrophic limits of models that rely on idealized – rather than actual, often messy – human behavior. Instead, students desperately need insights into how math, both complicated and relatively simple, facilitates both the best and the worst in world finance, with profound consequences for all of us. The most effective means to accomplishing that: the clear and engaging writings of David Leonhardt, Michael Lewis, Matt Taibbi, and others.
I’ll close with a more general comment, then a query. It amazes me that my son’s overall classroom experience – aside from frills such as Macs and smart-boards – is essentially identical to mine of 40-plus years ago. To science fiction aficionados who may be reading this: Could you recommend sf novels and stories that depict truly revolutionary approaches to education that are, well, light years ahead of ours?