Comments on: Old math

By: Mary Ann

Mary Ann — Sat, 28 Feb 2004 14:45:22 +0000

Thank you for your math wisdom which gives me the courage to bring a math workbook which I’m developing to fruition. –Mary Ann

By: J.Mason

J.Mason — Thu, 26 Feb 2004 16:31:56 +0000

…required to take a course in “teaching K-7 math” to renew certificate.

…NCTM is all that is being taught… “fuzzy math”, “new-new math” etc. is the garbage being taught to teachers of math. what a crok!

…Bobbs Merrill Algebra (book 1 and book 2) found at College library … Copyright 1927 -1934
These are perfect for 7th -9th Algebra and not a word about a calculator or even slide-rule.

By: jv

jv — Mon, 29 Dec 2003 22:20:33 +0000

I’m late to this post but one point that anti-old math advocates are missing: The best teaching would teach concepts and so-called math facts. But in the absence of IDEAL teaching, drill and kill works better. In a real world with real world teachers, the average teacher — given real world salaries and constraints anywhere in the world — will botch the New Math. Drills guarantee some degree of knowledge and force hard work.

In Taiwan, China, Japan, etc, the best teachers do go beyond sheer drill, but the main thrust of the teaching guarantees that all students will learn something. Most of all, teachers in the Far East are under no illusion that students should necessarily see math work as “easy” or “fun”.

It can be, but students need to learn that much of life is dealing with material that could be better taught but which needs to be learned, no matter how dull the experience.

By: Julie

***Julie*** — Mon, 29 Dec 2003 18:11:03 +0000

The problem is worse, I fear. We have high school students who don’t know how to do simple double digit multiplication problems without a calculator!
I believe that technology has it’s place - but elementary school is not the place. We have to start at the root of the problem - get them to use their brains first - understand the concept of math, then show them the short cuts with a calculator. (to top it off, some kids don’t even know how to do long division even with a calculator…which number do they put in first???)

By: D. Cooper

D. Cooper — Mon, 29 Dec 2003 02:24:34 +0000

Ah … Williams indicates that ‘demanding assignments’ and ‘hard work’ are key components in what has worked … now there’s a revelation !!!! All you have to do is get that out of them and you’ve got something … anyone who believes that that’s easy has never been in a classroom working with todays teens and all their distractions (too numerous to mention here but to include MTV, VH1, et. al.). Although not impossible to be sure, it is one of the factors that has become more and more difficult to achieve over the years. I’ve been doing it for 35 years and it doesn’t get any easier. I never give up but I swear there’s a ‘math gene’ .

By: Brenda

Brenda — Fri, 26 Dec 2003 03:09:44 +0000

Underwood Dudley, a marvellously entertaining expository math writer, wrote an article about calculus textbooks. One thing he pointed out is that they keep getting longer and longer, presumably because authors think that the reason students aren’t learning calculus is because their textbooks don’t have enough topics, or enough examples, or enough applications…he mentioned something to the effect that if the trend continues at this rate, in around a hundred years, the average calculus textbook will be around 2000 pages. And students STILL won’t get calculus.

From what I’ve seen of middle school textbooks, in a hundred years we can expect a typical one to be a pop-up book illustrated with holograms. And students STILL won’t understand fractions.

By: Wacky Hermit

Wacky Hermit — Fri, 26 Dec 2003 01:50:19 +0000

I hate with a passion those busy algebra books. They send the message to students that (A) they are way too stupid to do any actual algebra, (B) that actual algebra consists largely of social studies problems, and (C) that the objective of a textbook (and school by extension) is to keep them entertained. I’ve always maintained that kids are smart, and that they pick up on these kinds of messages, even if only at a subconscious level.

They gave me one of these to teach algebra to 7th graders with. There are about 6 problems in any given section that I would even consider assigning, and they are all easy problems. The textbook encourages “guess-and-check” solutions, even when they take longer than standard solving algorithms. The problems have all been carefully selected for this purpose, since it is unlikely a student would guess an answer like 11/2. They all have nice integer answers. The pages are so busy that I can’t even look at them, they make me dizzy. It looks like the sort of textbook you’d get if math textbooks were written entirely by graphic arts designers.

By: Jim C.

Jim C. — Fri, 26 Dec 2003 00:10:41 +0000

Richard Cook: I don’t think that’s the problem. To continue your analogy, the students don’t know that 2+2=4. They need a calculator to find out.

On the other hand, too much memorization isn’t good either. Richard Feynmann described the situation in Brazil in one of his books. The students could recite the law connecting refraction and polarization, but they couldn’t apply it to the real world and were astounded when he showed them a simple demonstration.

By: Robert Wright

Robert Wright — Thu, 25 Dec 2003 18:00:46 +0000

This is one of those odd situations were opposing arguments are both right.

Vern Williams is right about the text books. Gosh, they’re terrible. Too many pictures, not enough practice problems.

Math books need to be written by good math teachers, not by a subcommittee of the Human Relations Task Force.

Oh, and they need to be written in two colors. Black and white.

However, contrary to widespread opinion, knowing math facts is not necessary for learning math concepts. Most math teachers can tell you that from experience (not from new age teacher training.) Most parents will not understand.

One pitfall of school choice is that parents will place their children in schools that emphasize memorization over learning. I’ll take drill and kill over the gobbledy-gook promoted by current textbooks, but they’re both off the mark.

Memorization never killed anybody, but when an 8th grader isn’t allowed to take algebra because he can’t do 75 multiplication problems under 60 seconds, well, that’s a crime. A crime of ignorance–but not his.

By: Richard Cook

Richard Cook — Thu, 25 Dec 2003 14:20:41 +0000

I’m not a teacher but, boiled down to my level, teaching math seems more concerned, or is settling for students knowing that 2+2=4 instead of teaching the student why 2+2=4. Parents and teachers that support this are doing such a grave disservice to students its a crime. This nicely dovetails with the entry above on “old math”.