Tuesday, September 27, 2005

Klein and Marple on Math Education

While you're over at the Los Angeles Times website, you can check out this op-ed from yesterday's edition. The article is by David Klein and Jennifer Marple, an education professor and high school math teacher respectively. The subject is math education in the Los Angeles Unified School District:

What accounts for the low achievement in middle and high school mathematics in the district? A standard explanation is lack of funds. Certainly more money could — if spent wisely — improve education in the LAUSD, but unfortunately the district uses scarce resources in ways that undermine student achievement.

Take professional development. The district requires math teachers to attend in-service meetings to learn more math and better ways to teach it. No one would quarrel with those goals, but the quality of professional development programs is often so poor that they are likely to cause more harm than good.

LAUSD teachers and math coaches are wrongly instructed not to use time-tested, standard methods of arithmetic. High school teachers are steered away from conventional and powerful techniques in algebra and directed to use unreliable “guess and check” methods and physical objects instead. Even elementary school teachers are discouraged from following their high-quality state-approved math books and from teaching the best methods of calculation, the standard algorithms of arithmetic.

Confirming our own observations, the head of one of the stronger LAUSD high school math departments lamented: “The mandatory 40-hour algebra training was worthless. We had to teach the trainers how to do algebra … the people in charge of making final decisions on math [in the LAUSD] don't know math!”

Too often, the math that teachers are taught at district training sessions is just plain wrong. For instance, middle school teachers are erroneously taught that fraction division is repeated subtraction. This makes sense only for special examples such as 3/4 divided by 1/4 . In this case, 3/4 may be decreased by 1/4 a total of three times, until nothing is left, and the quotient is indeed 3. Understanding division as repeated subtraction, however, is nonsensical for a problem like 1/4 divided by 2/3 because 2/3 cannot be subtracted from 1/4 even once. No wonder students have trouble with fractions in high school.

All of this matches well with my own experiences.


At 3:29 PM, Anonymous Kevin said...

"Understanding division as repeated subtraction, "

Huh? what about multiply and simplify?

1/4 * 2/3 = 2/12 = 1/6

At 3:31 PM, Anonymous Kevin said...

Oh its division, err flip and clip?

3/4 / 1/4 = 3/4 * 4/1 = 12/4 = 3

At 3:46 PM, Anonymous Kevin said...

1/4 / 2/3 = 1/4 * 3/2 = 3/8 or a bit less than a half.

At 5:32 PM, Anonymous Joe Shelby said...

nearest i can figure is that for *some* students, the ability to remember the short-cuts doesn't seem to work, no matter how much rote one tries to put into it (the fact that the schools seem to be decreasing the amount of rote for the average student may also be a factor). so instead of trying to find alternative ways to teach alternative students, the system, bent on trying to keep everything "the same", tries to change the rules for how they teach *all* children, even those who never had a problem with the old methods.

Math isn't alone in this (though my mother as a teacher has seen the effects as well). History is also being "lost" in the way its being taught.

At 9:30 PM, Anonymous Anonymous said...

Brad DeLong has a good post and comments on this. In short, Klein and Marple don't know what they're talking about. Division is repeated subtraction and the concept works for fractions, too.

At 11:23 AM, Anonymous Anonymous said...

It is a shame that school districts do not allow more funding for math programs. It is amazing at the number of math teachers in schools that are not qualified to teach the subjects they are teaching. Of course, there are always other resources (internet) to help re-educate these teachers.

Wishing you luck, Crystal


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