Professor Instapundit links to this piece about the teaching of grammar. (If that link doesn't work, try this and then scroll down.)

It's not about how to teach grammar, merely about whether to teach it. **Dennis Baron** apparently believes we shouldn't bother, because other things about writing are, he says, more important. **Ralph A. Raimi** of the University of Rochester, NY, vehemently dissents. Raimi's concluding paragraphs:

Yet Baron's argument is more pernicious than the mere observation that good grammar does not guarantee good writing. This unarguable beginning progresses, and becomes an attack on learning grammar at all. This he is not entitled to do. It is as if a music student were advised against learning anything about scales, arpeggios and modulations, on the grounds that expression and nuance, really, are at the heart of music. And more recently, in the schools, the doctrine that arithmetic is no longer important (now that we have calculators) since mathematics is a science of patterns, big ideas, higher order thinking skills.Then, having demonstrated that learning grammar is a no-no, Baron ends with an attack on testing grammatical competence, with an argument implying that those who would test this competence believe "grammar tests [alone] measure writing ability."

In this last quotation it was I, not Baron, who inserted the "[alone]." I plead guilty, and merely exhibit my take on the general tenor of his article. Read it for yourself, and consider how many such you have read in your time. Arithmetic skill [alone] doesn't lead to better mathematics; music theory [alone] doesn't lead to artistry in composition; Teaching Grammar [alone?] Doesn't Lead to Better Writing. You can cover your flanks by omitting the "alone", sure, but the message is clear: Clean up the curriculum; stick to what's important. No more arithmetic; no more arpeggios; no more grammar. Bah!

So there.

"And more recently, in the schools, the doctrine that arithmetic is no longer important (now that we have calculators) since mathematics is a science of patterns, big ideas, higher order thinking skills."

My wife teaches math to 8th graders (don't know what the English equivalent might be -- this is the year prior to going to "high school" -- i.e., 13 year old kids) and she usually does not allow the use of calculators in class (with certain exceptions) because she feels that simply pushing buttons and copying down the answers prevents students from learning the relationships between numbers and the manupulations performed on them.

Half of her classes are "pre-algebra" or "algebra concepts" -- the other half are actual algebra classes (and students who maintain a class average of 85 and score that well on the final exam will be allowed to skip algebra next year in high school and can proceed to higher level math courses)

Ah, but to return to the topic of grammar -- I happen to hold New York State Permanent Certification in Secondary English, although I've not taught that subject since the mid-1970's) -- I have to concur with Professor Raimi. Dennis Baron starts with an accurate observation (that good grammar does not guarantee good writing) and carries that to an extreme and incorrect conclusion. Just as an aside, however, I would like to note that there are teachers who hammer away at grammar as an end rather than as a means. There are a few of us who may derive amusement from disecting a piece of prose, but the purpose of teaching grammar is to informa and improve the student's writing. It is but a tool. These teachers would, perhaps, be at home in Islamic schools where education seems to mean endless memorizing of verses from the Quoran. I could understand if Baron were proposing the reform of that kind of pedantic waste of time, but it would appear that he is yet another voice pushing for the endless dumbing-down of the curiculum.

The relationship between arithmetic skills and mathematics is more complex than you seem to imagine. It seems to me that if your wife's entire math class could be passed by someone with little real understanding and a calculator, then your wife's class is a very poor class indeed. I well recall getting C's in 7th and 8th grade pre-algebra because of my poor arithmetical skills, or flunking second grade arithmetic exams because I couldn't remember the multiplication tables, etc... I'm now a second-year undergraduate taking graduate mathematics classes, doing research in combinatorics.

I'm also now fairly good with certain kinds of arithmetic operations, but I only gained these abilities after learning more abstract kinds of arithmetic like modular arithmetic. I have a friend who is much brighter at math than I, who cannot accurately add a column of numbers even with paper. He's currently writing a paper on knot invariants and 3-manifold topology. Plainly arithmetic (itself) does not constitute all of mathematics, but "strong arithmetic skills" seem unnecessary for a good comprehension of mathematics as well.

If calculators get in the way of teaching real concepts, fine, get rid of them. However, I rather doubt that your wife succeeds in teaching real mathematics concepts. I (obviously) don't know your wife, but I've yet to encounter a single middle-school (or even high school) math teacher with a good understanding of what these fundamental concepts really *are*. My teachers told me the same "calculators impair understanding" stuff, but on each test, they presented me with a list of arithmetic problems I couldn't solve quickly or accurately enough. I was forced to wonder: what understanding were they keeping me from?

Lucas,

Actually, my wife is a mathematician (undergraduate major in math, M.S. in Systems Science, additional graduate work in computer engineering and in information systems, a successful professional career in computers; and then a mid-life career change to teaching, earning a master's degree in education summa cum laude -- has earned elementary certification grades K-6 plus math certification grades 7-12 plus middle school endorsement -- and has also taught computer programming to college students) -- and the point of banning calculators from classrooom work is exactly because students use the calculator as a crutch and fail to grasp the concepts and relationships. She has found that a significant number of students come into 8th grade without, for example, an real understanding of positive and negative numbers -- and simply pushing buttons on a calculator does not help them with this at all. The point of the course is not the ability to multiply 387 by 264; the point is to understand the basic concepts of algebra and to be able to use these concepts to solve problems. (And she does allow them to be used for certain major tests to relieve student concerns about arithmetic errors.)

I regret that you had such poor math teachers in middle school and high school; that does not imply that all such teachers are incapable of teaching real math concepts.

I didn't say that I thought that calculator-based teaching was necessarily better. I said that the way that mathematics is taught (or at least was taught to me) without them discriminates against students with little ability with arithmetic (i.e. rote memorization and algorithm-following). Furthermore, this is not related to mathematics.

I stick by my assertion that most mathematics teachers don't really understand mathematics, especially in lower levels. Perhaps your wife is an exception, but she's obviously rowing upstream. You said that when children come up from elementary school, they have little understanding of negative numbers or even fractions. My guess (of course based upon my experience as an education consumer) is that this is caused by poor teachers, not calculators. Most teachers don't know how to teach math, so they teach arithmetic. Students didn't learn math, so calculators were introduced. Now even less is being taught, since all the teachers were teaching was something that a calculator can do. It becomes button-pushing instead of number-crunching. I think it likely that calculators might be detrimental to learning mathematics, but their presence is neutral until mathematics is actually being taught.

I go to a college mainly devoted to teacher-training, and so I've had a lot of exposure to math-ed majors. These are mainly people who liked math in highschool, and then hit a wall at college when exposed to proofs and other such abstractions. Their mathematical learning seemed to stop at the end of perhaps first semester-calculus, and hence they have little understanding of mathematics at a higher level. The elementary-ed majors are even worse. Perhaps I'm being unreasonable, but it seems to me that in order to teach something, you must understand it a whole lot better than your students. Most teachers and teachers-to-be that I've encountered don't. These sorts of people objectively make up the majority of teachers, at least in my area. I've no reason to think this is different elsewhere.

hello... i'm from Poland, and I am preparing myself to the math championship... This championship is in English. could someone please send me a www page, on which I could find same excericises? THaks! maciekkowalski@yahoo.co.uk