What You Missed: A Mathy Roundup

Aug 22 2010 Published by under Links Best Served Cold

While Melody was enjoying Portland following the Cognitive Science conference, Jason took you on a mathematical tour of the mind and brain. This week we did a series on numerical cognition and developmental dyscalculia.

If you're just getting started now, might we suggest checking them out in order:

1. The Developmental Origins of Numerical Cognition

Unlike basic number abilities, calculation ability represents an extremely complex cognitive process, and requires explicit instruction. The loss of the ability to perform calculation tasks resulting from neuropathology is known as acalculia or acquired dyscalculia, which is an acquired disturbance in computational ability. The developmental defect in the acquisition of numerical abilities, on the other hand, is usually referred to as developmental dyscalculia, or simply dyscalculia.

2. What is Dyscalculia? How Does It Develop?

A more recent definition according to the DSM-IV-R is offered as well, which defines developmental dyscalculia as a learning disability in mathematics, the diagnosis of which is established when arithmetic performance is substantially below that expected for age, intelligence, and education.

3. Developmental Dyscalculia Explained: Strategy, Memory, Attention

Experimental studies of developmental dyscalculia and math disability in children have focused primarily on skill development in arithmetic, which can be divided into two sections: counting knowledge, and strategy and memory development.

4. Numbers on the Brain: Neurobiology of Mathematics

Depending on task demands, we speculate that this core quantity system, analogous to an internal “number line,” can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

For an evolutionary perspective, there were two companion pieces this week at The Thoughtful Animal:

5. What Are The Origins of Large Number Representation?

Surely, humans have something unique that allows us to do things like multivariate regression and construct geometric proofs, however, but let's start at the beginning. I will hopefully convince you that there is an evolutionarily-ancient non-verbal representational system that computes the number of individuals in a set. That knowledge system is available to human adults and infants (even in cultures that don't have a count list), as well as to monkeys, rats, pigeons, and so forth.

6. The Origins of Small Number Representation

Small numbers do not need to be counted or estimated; instead, they are subitized. Upon seeing a scene with a small number of objects you have a sudden, immediate sense of how many objects there are. This happens in parallel rather than serial- you do not need to count the items individually. Therefore, judgments made about displays of 1, 2, 3, or 4 items are rapid, accurate, and confident. As the number of items in the scene increases, judgments are increasingly less accurate and made with less confidence.

And if you haven't had quite enough child development this week, here are a few more links to whet your appetite:

From the Washington Post: Working Mothers Not Necessarily Harmful to Child Development

Should kids be walking to school instead of driving?

Childhood memories of dad might help men effectively cope with stress later in life.

Does Parenting Rewire Dads? A fascinating article in Scientific American by Brian Mossop

Parents' mental health suffers when children struggle. No surprise there, really.

Are today's superheroes sending the wrong message to boys?

For today's dose of kids are cruel: Kids who squint are less likely to be invited to peers' birthday parties.

From the New York Times: What Is It About 20-Somethings? Is "emerging adulthood" a new developmental stage? And a response in Slate.

Signing off from the city of angels,

Melody & Jason

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