Reform math - we need a BALANCE

Recently Spunky wrote about reform math, and I feel I want to say something about it, too.

She was critizing the movement heavily. Some people call reform math 'new new math' or 'fuzzy math' (in a degrading way) - and like you can read in Spunky's post, sometimes when new ideas are implemented, it can cause math to become 'fuzzy' to the children.

But that is not necessarily a fault of the reform on a whole - maybe the teacher in question didn't understand how to implement the methods, or for some reason (unwisely) totally abandoned 'traditional' math fact drills.

I would say not all of the IDEAS that have come from this mathematics education reform are bad.

For example, encouraging kids to explore and investigate mathematical concepts, or discovering their own rules, can be a good thing. Group work CAN be a good thing.

The reformists promote understanding of concepts, problem solving, critical thinking. They try to distance themselves from the "drill ' n' kill" and rote memorization parts of traditional math education.

If kids "learn" math as a set of disconnected rules, they soon forget those since they never learned WHY they worked. (Well that can easily happen. I just witnessed it this past week; a youngster didn't know how to multiply two two-digit numbers since it had been so long that he had done it.)

The key is a BALANCE. Truth is somewhere in the middle. Kids absolutely need to learn their addition facts and memorize their multiplication facts. Otherwise, they're going to go about learning math without a FOUNDATION.

But, I feel it is very important to teach them also WHY the rules and procedures work.

For example, let kids learn how to multiply 2-digit numbers by 2-digit numbers. Let them practice. But also show them what it is based on (distributive property). They need to know that anyway in algebra class!
(For example: 34 x 58 is based on doing it in parts: 4 x 8, 4 x 50, 30 x 8, and 30 x 50, and adding all those. Compare to (x + 1) (2x - 5) which is done using distributive property.)

Learning to estimate and critically look at your final answer is very important, I feel. (For example, 34 x 58 is about 35 x 60, which is same as 70 x 30 = 2100. Exact answer is: 1972. OK.)

Let them SOMETIMES explore and investigate, find real-life connections. Occasional "math labs" can do much good in motivating and showing where math is useful in real life, letting them gain confidence, etc.

But if all the class time is spent on letting the kids find their own division methods and forgetting all about memorization, the pendulum has swung WAY too far to the other direction.

Memorization is needful, very needful. But let us not forget the 'reform' aspects of math altogether.

And like was pointed out in the comments to this post, it is the TEACHER that decides what is done in the math class and how it is done.

I feel the NAME of this reformist website summarizes it all: Mathematically Sane.

P.S. Here's a nice piece Newer Math by Jack Lee about what is going on at Seattle.

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Anonymous said…

I appreciate your generally balanced comments about reform mathematics and your positive reference to the web site I helped start and maintain, However, I need to make a number of comments to specific things you said. As to the blogger "Spunky" who prompted your post, I can say that at best she is misinformed and at worst she is dishonest in her comments about the current reform movement in mathematics education.

First, when you use language, you need to be very clear about its connotations. Those of us who advocate and teach more progressive approaches to teaching mathematics do not refer to ANYTHING as "new new math" or "fuzzy math." Both are terms that are used to degrade what it is we do. The first is an attempt to pin the alleged failures of the New Math era (basically the late 1950s to mid 1960s) on the current efforts to bring about reform. While I don't want to explore here the history of the New Math, I should point out two things: there were many projects that collectively were labeled "New Math," and no one of them was implemented nationally. In fact, what most people today think of as "New Math" was the result of one publisher getting the Dolciani textbook series into a lot of school systems. While Dr. Dolciani was a respected mathematics educator, her work is NOT representative of the movement as a whole, and what appeared in print (and still does: those Dolciani books are still very popular) was not THE New Math, but one very particular set of books that grabbed the turf before anyone else did. I suspect that the folks who ran SMSG and the Wisconsin project and other "New Math" projects would NOT have been in agreement with Prof. Dolciani on many, many aspects of her books.

The phrase "fuzzy math" is clearly meant as a put-down, to imply that the math is inaccurate, unclear, or just plain wrong (when used to describe the numbers behind a new government plan, it is clearly meant completely negatively, with the added notion of purposeful misrepresentation). Ironically, "fuzzy logic" is a real and highly important area of engineering mathematics that is used widely, especially in Japanese manufacturing circles, to build more sophisticated controls for things like air conditioning. It is a serious aspect of contemporary engineering courses at, for example, the University of Southern California, where Lotfi Zadeh, who is called the father of fuzzy logic, is on the faculty.

That said: there are a wide variety of books and methods currently thought of as reform mathematics. No one of them represents all the ideas. We're really in just the beginning of the second wave of such books, with the earlier ones coming out with second editions. Regardless of grade band, there are differences in these books, and regardless of which one is selected, these books should NOT be viewed as bibles. Unfortunately, many teachers are adopting these books, gladly or otherwise, without any understanding of many or most of the key components. In addition, many elementary and middle school mathematics teachers, and indeed, some high school mathematics teachers, are seriously lacking in their own mathematics education for teaching purposes. This shortcoming is a huge handicap when trying to use less traditional programs that are geared towards looking at the WHY of mathematics as well as at the HOW.

Unfortunately, some of those who willingly adopt the books do a less-than-stellar job teaching with them. They use the same rigid approaches to teaching math with a "progressive" spin as they used for whatever they taught out of before. The results are not necessarily WORSE than what their students did in the past, but it's unlikely that the results would be much better.

I applaud your call for a balanced approach. I would point out, however, that balance is EXACTLY what NCTM and independent reformers have been asking for, nay, BEGGING for, since at least the late 1980s. Irresposible individuals and groups have twisted calls for shifts in emphasis towards more balance as calls for "throwing the baby out with the bathwater." For example, the idea that less time should be spend on traditional drill and practice methods isn't a call for doing away with either drill or practice. However, some teachers may have seen it as an excuse to eschew what they themselves may have experienced as mindless drill. That's unfortunate, but it is not what most reformers advocate. And in reaction to the misrepresentation of what reform is actually about, some teachers many indeed dug in their heels and said, "I'm not going back to being a work-sheet distributor," and refused to be balanced because they feel then need to protect the positive aspects of reform teaching that they and their students really value. This is an understandable counter-counter-revolutionary attitude, but any extreme is likely to hurt kids in the long haul.

I could speak on this and related topics at more length, but I hope this will suffice for now. I invite you or any interested reader to feel free to email me if you have comments or questions.


-michael paul goldenberg Co-founder of Mathematically Sane
Anonymous said…
I think the biggest problem with reform math is also the biggest problem with traditional math: most of the teachers don't know what they're talking about! (See Liping Ma's Knowing and Teaching Elementary Mathematics.) If the teacher doesn't understand mathematics, then how can he/she make the student understand? How can a teacher who never understood long division, for instance, guide a student in creative ways of understanding it? Yet there are good alternatives to long division, such as multiplying in chunks, that can help a student understand what is going on -- and then the teacher can guide the student's transition to the traditional form, if the teacher knows what division means to begin with.

I love reading your blog, Maria. Keep up the good work!
Maria Miller said…
I heartily agree that the TEACHER is the key component, no matter what the book.

As to 'fuzzy math', reading Spunky's post, it sounds like math has become fuzzy to some kids... Maybe in the hands of some teachers, math education does become "fuzzy"...

Thanks for the clarification about the term, Michael. I sincerely agree that we should not degrade movements or ideas based on what happens in any particular school.
Margo said…
I agree with balance- in math and in life. Tradition and modern ways in math should be used in tandem, as long as the methods are proven to work. "Don't fix it if it works."

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