Monday, September 15, 2008

Individual Differences in Math Sense: "Give me the child at 7, and I will show you the man..."

"Give me the child until he is seven and I will show you the man" - Jesuit maxim

From the Washington Post:

Excerpt -

"Scientists have for the first time established a link between a primitive, intuitive sense of numbers and performance in math classes, a finding that could lead to new ways to help children struggling in school.

A study involving 64 14-year-olds found that the teenagers who did well on a test that measured their "number sense" were much more likely to have gotten good grades in math classes.

"We discovered that a child's ability to quickly estimate how many things are in a group significantly predicts their performance in school mathematics all the way back to kindergarten," said Justin Halberda, an assistant professor of psychological and brain sciences at Johns Hopkins University who led the research, published online yesterday by the journal Nature. "It was very surprising."

It's not all that surprising to some of us, especially those of us who have a number disability. One of us (Fernette) has been woefully aware of her impaired math and estimation sense - still managed to pass out of math at Harvard by doing well enough on the AP Calculus exam, but today still counts on fingers, and is the fastest one in the family to reach for a calculator when the number crunching is really important. How did she survive advanced high school math? The old-fashioned way, driving rote memory systems, drill, drill, drill, and oh yes, counting on fingers to not make careless errors with subtraction.

In the study at left, Dehaene beautifully shows that there is more than one way to get at a math answer. If you don't have much in the way of spatial problem solving ability, you can use rote systems and grunt it out.

Strong spatial mathematicians often solve their problems intuitively, or in other words, they arrive at answers that are not easily described in verbal terms. Answers may seem to come to them instantaneously (definitely not the case for poor rote mathematicians). When questioned, many spatial math problem solvers say they "feel" math quantities or have some movement or kinesthetic imagery associated with numbers or quantity. Needless to say, this seems magical to people who have little or no sense of spatial quantity.

If you don't have number sense, rest assured it is possible to do quite a bit of mathematics by rote memory; it just isn't as quick or as effortless.

It would be interesting to see whether the latest data from this study may help customize early math instruction. Intensively driving rote systems is what many teachers and parents currently try to do, but we wonder perhaps training the spatial system (e.g. visually [e.g. computer display] or proprioceptively [weights?]) could ultimately culminate in effortless math?

References and Other Links
Individual differences in nonverbal number acuity correlate with maths achievement
Math in the News: photo
Eide Neurolearning Blog: Dyscalculia - Two Different Brain Pathways for Mathematics

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