Mathematics As the Most Misunderstood Subject 680
Lilith's Heart-shape writes "Dr. Robert H. Lewis, professor of mathematics at Fordham University of New York, offers in this essay a defense of mathematics as a liberal arts discipline, and not merely part of a STEM (science, technology, engineering, mathematics) curriculum. In the process, he discusses what's wrong with the manner in which mathematics is currently taught in K-12 schooling."
Why math is worth doing in the first place (Score:5, Informative)
I've seen the following link in many a Slashdot thread before, but it certainly bears repeating here: "A Mathematician's Lament" by Paul Lockhart [maa.org] It's mostly known as an insightful critique of what's wrong with K-12 math education, but I've always liked it as an explanation of why people who enjoy math do it in the first place: it's satisfying in an artistic way. I think it would be great if more students saw math as something worth doing for its own sake, like art or athletics, and hey, it lets you do science and engineering too.
In fact, this summary sounds similar enough to "Lament" that I wouldn't be surprised if this Dr. Lewis was inspired by and/or cited it. But this is Slashdot, so I'll let someone else check that out.
Re:Why math is worth doing in the first place (Score:4, Informative)
As a part-time college math teacher, I almost totally disagree with Lockhart's Lament. (Ironically, the K-12 school where he teaches is close to the neighborhood where I live.)
It's not that it's bad to see that math can be an art and a pattern-finding exploration (some part of the time), but someone has got to teach and be held accountable for the nuts-and-bolts of how to read and write mathematical vocabulary, notation, and justification (algebra and geometry, for starters). Knowing about the scientific method is necessary, but exclusively spending your K-12 time re-inventing the wheel is inefficient at best. It's the same problem as in English nowadays -- I was told last weekend that teachers in junior high schools are forbidden from teaching the rules of grammar. That is, it's exclusively about expressing "big ideas", no matter how poorly-formed or unreadable. The more this produces crippled students, the more we seem to run deeper in the same direction -- if you abandon teaching the basic structure of our shared communication systems, then we thereby just generate more and more unreadable nonsense as time goes on.
The remedial math I teach (basic algebra; about half my assignment load) is almost entirely about just reading & writing. Even the first unspoken step of simply transcribing symbols (i.e., an expression) from one page to another is almost impossible for about half my students, because no one has ever asked for any level of precision in their reading, writing, or observation skills (whether in English, math, or anything else). To me, basic math is an opportunity to focus on precision in thinking and writing -- applications belong in other classes! No, that's not what a professional mathematician works at on a daily basis, but frankly, not every K-12 class can be an independent research opportunity. At some point you've got to eat your vegetables, and if you run entirely away from that, then it truly is a monumental waste of time.
Re:he's right (Score:5, Informative)
>>I doubt philosophers give a rats ass about pointers, let alone fill up books on the subject.
From the Stanford Encyclopedia of Philosophy:
* Almog, J., J. Perry, and H. Wettstein (eds.) (1989), Themes from Kaplan, New York: Oxford University Press.
* Bach, K. (1987), Thought and Reference, Oxford: Oxford University Press.
* Bach, K. (2004), 'Points of Reference,' in Bezuidenhout & Reimer (eds.) 2004. [Preprint available online]
* Barcan Marcus, R. (1947), "The Identity of Individuals in a Strict Functional Calculus of Second Order," Journal of Symbolic Logic, 12(1): 12-15.
* Barcan Marcus, R. (1961), 'Modalities and Intentional Languages,' Synthese, 13(4): 303-322.
* Barcan Marcus, R. (1993), Modalities, Oxford: Oxford University Press.
* Bezuidenhout, A., and Reimer, M. (eds.) (2004), Descriptions and Beyond, Oxford: Oxford University Press.
* Brandom, R. (1994), Making it Explicit. Cambridge MA: Harvard University Press.
* Brueckner, A. (1986), 'Brains in a Vat,' Journal of Philosophy, 83: 148-167.
* Davidson, D. (1984), Inquiries into Truth and Interpretation, Oxford: Clarendon Press.
* DeRose, K. (2000), 'How can we know that we are not Brains in Vat?,' Southern Journal of Philosophy, 39: 121-148.
* Devitt, M. (1981), Designation, New York: Columbia University Press.
* Devitt, M. (1990), 'Meanings just ain't in the head,' in Meaning and Method: Essays in Honor of Hilary Putnam, Cambridge: Cambridge University Press, pp. 79-104.
* Devitt, M. (1996), Coming to our Senses, Cambridge: Cambridge University Press.
* Devitt, M. and Sterelny, K. (1999), Language and Reality (2nd edition), Cambridge MA: MIT Press.
* Devitt, M. (2004), 'The Case for Referential Descriptions,' in Bezuidenhout and Reimer (eds.) 2004.
* Donnellan , K. (1966), 'Reference and Definite Descriptions,' Philosophical Review, 75: 281-304. [Post-print online version]
* Donnellan, K. (1972), 'Proper Names and Identifying Descriptions,' in D. Davidson and G. Harman (eds) The Semantics of Natural Language, Dordrecht: Reidel.
* Evans, G. (1973), 'The Causal Theory of Names,' Proceedings of the Aristotelian Society, Supplementary Volume 47: 187-208.
* Evans, G. (1982), The Varieties of Reference, Oxford: Oxford University Press.
* Field, H. (2001), Truth and the Absence of Fact, Oxford: Oxford University Press.
* Fodor, J. (1990), A Theory of Content and other Essays, Cambridge MA: MIT Press.
* Frege. G. (1893), 'On Sense and Reference,' in P. Geach and M. Black (eds.) Translations from the Philosophical Writings of Gottlob Frege, Oxford: Blackwell (1952).
* Kaplan, D. (1989), 'Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals.' In J. Almog, J. Perry, and H. Wettstein (eds.), Themes from Kaplan, Oxford: Oxford University Press.
* Kripke, S. (1977), 'Speaker's Reference and Semantic Reference,' Midwest Studies in Philosophy 2: 255-76.
* Kripke, S. (1980), Naming and Necessity, Cambridge: Harvard University Press.
* Meinong, A. (1904), 'The Theory of Objects,' in Meinong (ed.) Untersuchungen zur Gegenstandtheorie und Psychologie, Barth: Leipzig.
* Mill, J. S. (1867), A System of Logic, London:
Harry Chapin (Score:4, Informative)
The mindset of the teacher reminds me of the Harry Chapin song "Flowers Are Red."
Teachers that are that narrow minded should be transferred to places where they can't do any damage to students. Perhaps a prison environment would be best for them. They could at least try to help some of the people they screwed over.