November 14, 2006

Fuzzy Math Must Cause Fuzzy Logic

Constructivist educators say the kookiest things sometimes. Here's a good example in today's NYT.

Many parents and teachers remain committed to the goals of reform math, having children understand what they are doing rather than simply memorizing and parroting answers. Traditional math instruction did not work for most students, say reform math proponents like Virginia Warfield, a professor at the University of Washington.

Have you ever read an article on education that didn't contain enough false dilemmas to fill an undergraduate logic text?

There's reform math on one hand that has "children understand what they are doing" though no one has ever been able to prove that this is in fact the case since students taught using typical constructivist math programs tend to score just as poorly as the more traditional math programs which simply require "memorizing and parroting answers." Oddly enough, if constructivist taught students were better at "parroting answers" we might not have a math war going on now would we. But, the sad fact is that they are not any better than the traditionally taught kids in this regard which tends to give one pause when constructivists parrot the "children understand what they are doing" meme. No doubt such sentiments were learned by rote.

There is some truth in the "[t]raditional math instruction did not work for most students" meme that traditional math proponents should take to heart. Same holds for proponents of traditional phonics instruction. Most traditional math and phonics programs weren't and aren't any good, though constructivist heavy math and balanced literacy programs offer no improvements other than rosy rhetoric.

One area where reform math programs do fall down is in computation skills. All those hide-the -ball problem solving lessons that chews up mucho class time come at the expense of the all important practice that all but the looniest constructivists recognize is still needed to learn math. Understanding math (whatever that means) may be beneficial, but if that understanding doesn't translate into computational fluency, then the hapless students are not going to have a fun time in algebra or anything else that comes later.

Moving right along.

"It produces people who hate math, who can't connect the math they are doing with anything in their lives," Dr. Warfield said. "That's why we have so many parents who see their children having trouble with math and say 'Honey, don't worry. I never could do math either.'"
Any program that does not result in students learning math is going to cause those students to hate math. Those who can't do math (and by do, I mean compute) won't be able "connect the math they are doing with anything in their lives."

If constructivist taught students hate math any less than traditionally taught students it is not because they understand or are any better in math. Such has never been shown in any legitimate study. Only possible explanation is the "ignorance is bliss" theory that might be causing all this unexplained happiness. Kids who are never asked to do long division or manipulate fractions aren't going to be too upset that they can't do those things.

In part, the math wars have grown out of a struggle between professional mathematicians, who say too many American students never master basic math skills, and math educators, who say children who construct their own problem-solving strategies retain their math skills better than those who just memorize the algorithm that produces the correct answer.
Talk is cheap. Educators can say whatever they want. But, no one has ever proven that "children who construct their own problem-solving strategies retain their math skills better."

Remember, these kids who've constructed their own problem-solving strategies aren't scoring any better in test of simple math skills. They might be retaining something better, like maybe all the bad strategies they discovered along the way, but it's not math skills.

Memorizing the algorithm isn't going to do squat either. Practicing the algorithm until it can be performed with automaticity is what's needed. And, if it can be taught in an efficient way so that it is learned with understanding, all the better. It is a conceit of constructivists that they believe they are the only ones teaching with understanding. That and the inability to distinguish between memorization and practice leads one to the conclusion that they really have no idea what they are talking about.

9 comments:

Mr. Person said...

[It] tends to give one pause when constructivists parrot the "children understand what they are doing" meme. No doubt such sentiments were learned by rote.

NICE turn of phrase. [Applause.]

Anonymous said...

I agree that educators present a false dichotomy between constructivist learning and rote learning. They also misrepresent the history of math education.

I have a fourth grade math textbook from the 1950's called "Seeing Through Arithmetic" by Scott Foresman. It explains concepts, and then provides ample practice. The children did not learn "by rote." In fact, it has many more word problems than Everyday Math.

It is easier than Everyday Math, but also better in many ways. I would imagine that the kids who took this program had a thorough understanding of arithmetic by the end of fourth grade. For the top third of the kids, however, it is probably too easy.

RobynW

SteveH said...

I hate articles like this. The journalist has no clue or basis for asking the right questions of the right people. Dueling quotes. Throw it away.


"There is some truth in the "[t]raditional math instruction did not work for most students" meme that traditional math proponents should take to heart."

Remember that it is a strawman to say that those who dislike fuzzy math want to go back to "traditional" math, whatever that was. There really is no such thing as a "traditional math proponent". The fuzzies use this to put others on the defensive or as a basis to negotiate a "balance". However, they can't even define what understanding means.

SteveH said...

"Talk is cheap. Educators can say whatever they want. But, no one has ever proven that 'children who construct their own problem-solving strategies retain their math skills better.'"

Their talk also distracts everyone from the fact that they don't get the kids where they need to go. They hide behind understanding and a very broad ("but we do statistics") coverage of the material. They try to come to the table as equals when deciding balance. However, all you have to do is to lay out Everyday Math workbooks next to Singapore Math workbooks to EASILY see the difference. It's not a matter of understanding. It's a problem of low expectations.

The problem is also not constructivism. The problem is that they don't get kids from point A (counting numbers in Kindergarten) to point B (a proper course in algebra in 8th grade). The problem is that they don't believe in mastery. The problem is that they allow kids to get to fifth grade without knowing their times table. The problem is basic competence. They don't make sure the kids learn anything.

Constructivism and understanding are just ruses. It's the only thing they can grasp on to, and they can't even define it. They don't know when it happens, and they can't test for it.

The hard part in all of this is coming to grips with the fact that so many people are so wrong. At the very best, it's all about philosophy and opinion, but they have no hesitation in forcing their opinions on everyone else. Ignorant or arrogant. Which is it?

Dr. P. said...

The Zhou study showed U.S. teachers scoring at the 30% level on tests of knowledge of fractions, whereas Chinese teachers scored at the 90% level. Clearly something was very wrong with how the U.S. teachers learned math.

"Ma (1999) speculated that the generally low-quality of mathematics education in the U.S. contributes to the low-quality of teachers’ knowledge of school mathematics in the U.S. Unfortunately, teachers who do not acquire mathematical competency during schooling are unlikely to have another opportunity to acquire it. Most U.S. teacher preparation programs focus on how to teach mathematics rather than on the mathematics itself. Later when they become teachers, they typically do not have the opportunity to improve their subject matter knowledge."

Anonymous said...

Interesting post. While the Times showed parents who do care, it's obvious that math scores are dropping, but parents aren't flinching. Overall, parental concern over math and science education has fallen since 1994, with 64% stating that math and science education is not a problem in their public school systems. In addition, 70% of those parents surveyed believe that their child's high school is teaching the right amount of math and science. For more information on "Reality Check 2006," go to http://www.publicagenda.org/research/pdfs/rc0601.pdf.

SteveH said...

"Overall, parental concern over math and science education has fallen since 1994, with 64% stating that math and science education is not a problem in their public school systems."


Is there a point here?

That because a poll shows that many parents don't care (or are ignorant), there isn't a problem?

That education policy should be based on poll results?

That education should be based on opinion or averages, rather than expertise and individual student needs?

Perhaps we should design curricula and tests by poll.

It's like nightly TV news. Polls as a substitute for critical knowledge and analysis.

Anonymous said...

Is there a point here?

That because a poll shows that many parents don't care (or are ignorant), there isn't a problem?


One point might be that if 2/3 of parents believe that everything is fine, it will be difficult to improve things.

I have believed this for a while. The public schools aren't going to get much better/rigorous any time soon because most parents believe that the school their child attends is doing well.

-Mark Roulo

SteveH said...

"One point might be that if 2/3 of parents believe that everything is fine, it will be difficult to improve things."

It depends on how you ask the questions.

The real reason it's difficult to improve things is that schools and teachers don't want to change. It doesn't matter what the parents think. Schools aren't waiting for parents to tell them what they want. It would take a mass uprising to get schools to change. Parents have no leverage. Schools do what they want. Polls don't matter.