Tuesday, August 08, 2006

Why Students Fail at Math & Math as a Different Language

In Washington state, almost half of 10th graders failed the Math part of the WASL, as state superintendent Terry Bergeson confessed, "We have to change our course of action in math. I don't have any brilliant schemes today, but I clearly know we have a challenge."

So how hard or obscure are WASL math problems? From a recently posted sample test - here's one: Caprice dries to work 5 days a week. In the morning, she takes a 10-mile route. In the afternoon, she takes a 12-mile route home to avoid traffic. Caprice's car gets 20 miles to the gallon. How many gallons of gasoline will Caprice use each week driving to and from work?

Not that bad, right? It's even a practical scenario, especially with gas prices these days.

Why do students struggle with problems like these? From the cognitive perspective, the most common problems we see are: a lack of automaticity regarding basic math facts, working memory overload (that can be due to a primary limitation in working memory, or other factors like dysgraphi), language problems, and spatial and / or sequential memory weakness.

The practical dilemma for teachers - is that if a student struggles with any of these problems he or she may vary widely in how much they learn depending on the pace and style in which they're taught. Often these kids make more progress with individualized instruction (i.e. tutors) that takes into account their relative memory strengths and weaknesses.

Recently, a Stanford study suggested a cause for added math meltdowns in the early elementary grades. Look at how much easier it is for older students to do simple mental math calculations than their younger counterparts (blue indicates lower levels of activation for the older students).

This does not necessarily mean mental math manipulations only turn on at the older ages - it could also mean that older folks have had so much practice with number manipulation that they've internalized number relationships as representations in the parietal lobes so that thinking about them has become more "automatic."

It is also true, too, that many teachers feel poorly prepared to teach mathematics. Conventional classroom teaching may attract more verbal learners than mathematical - so math may be like a hard foreign language for them.

In fact, because mathematics is its own distinctive language, some outstanding mathematical thinkers have had trouble explaining themselves to verbal thinkers. This may be true of many dyslexic-mathematical folks. From Hadamard's The Psychology of Invention in the Mathematical Field, here's a quote from Galton (a Victorian polymath, statistician): "It is a serious drawback to me in writing, and still more in explaining myself, that I do not so easily think in words as otherwise. It often happens that after being hard at work, and having arrived at results that are perfectly clear and satifactory to myself, when I try to express them in language I feel that I must begin by putting myself upon quite another intellectual plane. I have to translate my thoughts into a language that does not run very evenly with them. I therefore waste a vast deal of time in seeking for appropriate words and phrases..."

These folks have a hard time showing their work.

Developmental Changes in Math
Failing the Math WASL
Practice Tests for High School Math WASL
Eide Neurolearning Blog: Problem Solving and the WASL
Eide Neurolearning Blog: East meets West: Fundamental Differences in Math Teaching
ComputerUser.com - Insights - The dyslexic CEO, John Chambers

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