Online Resources
Submitted by Heather09 on Mon, 07/30/2007 - 3:18pm.
I've been spending the past few months researching the cognitive and neural underpinnings of mathematics, as well as their implications for math education. What follows is a brief list of some of the more accessible articles I have found:
- http://en.wikipedia.org/wiki/Cognitive_science_of_mathematics
- http://en.wikipedia.org/wiki/Numerical_cognition
These are short, non-technical Wikipedia articles on the cognitive science of math and on numerical cognition. They both serve as a good introduction.
Lab website dealing with arithmetic and the brain. Includes neuronal modeling of the brain areas involved and examples of how individuals in other cultures count and do math (see http://www2.cnrs.fr/en/319.htm for press release).
Lab website from the same researchers on developmental dyscalculia, a difficulty in learning mathematics perhaps due to abnormalities in the parts of the brain responsible for numbers and calculation. Also has a software program designed to help children with this condition.
A review from the above lab website.
An excellent paper on the possible existence of a biological, domain-specific area for number representation in the brain. Gathers evidence on number cognition in animals and babies, parallels between them, evidence from brain lesion patients and neuroimaging.
Written by a professor who studied the counting system of Pirahã tribe in Brazil, this piece asks whether or not those who grow up with only two or three words to represent numbers can come to distinguish between four, five, six and so on.
This is a synthesis of many experiments dealing with non-verbal numerical cognition. The hypothesis proposed is that nature provided us with real numbers and we have extrapolated integers; arithmetic processing is based on real numbers (magnitudes).
This article sums up findings from a study involving aphasics and their ability to calculate. The overall implication is that math functions in the brain are not dependent on language, since lesions to language centers in the brain do not impair mathematical ability.
English-speakers and Chinese-speakers may process numbers differently, even when using only Arabic numerals, due to cultral differences in mode of language learning. Could this be used to help failing math students?
The same area of the brain, the intraparietal sulcus, is activated in 4-year-olds as in adults during arithmetic tasks. In other words, the same neural circuit is responsible for mathematical functions throughout life, from basic math skills to advanced ones.
Describes two studies published in the January 2007 issue of Neuron. The researchers claim that their findings shed light on how the brain processes abstract quantities and how symbols representing numerosities of real objects are constructed and interpreted.
This is a online copy of Levi L. Conant's 1896 book entitled The Number Concept: Its Origin and Development. At its heart it's a study of numerical systems from an anthropological and psychological perspective, being the first systematic attempt to compare North American numerical systems. Not for the easily offended, the author unconsciously belittled Native American culture but it is an interesting read for those who enjoy the historical aspects of scientific research.
Research dealing with children and their mathematical abilities:
According to researchers at Duke University, babies appear to possess an abstract sense of numbers before they are even able to speak.
Children may have an innate sense of numbers that allows them to roughly add and subtract before they are formally taught how to do so.
Closely related to the previous one, the study cited here suggests that children who do poorly in math classes simply don't grasp the symbolism involved in the learning process. That is, they are able to do simple math when it is not presented in a verbal or written format because of an innate sense of numbers.
Infants as young as six months old may be able to detect arithmetical errors.
Research specifically concerning numerical cognition in animals:
A general overview of some of the evidence amassed thus far that animals have a concept of numbers.
A short argument that our mathematical abilities are evolutionarily derived.
Lab website concerning primates.
- http://www.dukenews.duke.edu/2005/06/BrannonCurrBio.html
- http://www.duke.edu/web/mind/level2/faculty/liz/Jordanetal2005.pdfBoth
Both of these pertain to a study which indicates that number representation in monkeys is abstract, as monkeys appear to understand numerosities across senses. The second link is to the actual experimental write-up, the first is a summary.
There may be similar neural mechanisms at work in humans and other primates when they think numerically. Because of the similarities found between humans and other primates in this domain it seems that numerical thinking is not dependent on language, since non-human primates do not have a language comparable to ours.
A published article by the same researcher on animal numerical ability.
Perhaps birds and other animals think logarithmically when dealing with time.
----
If anyone is interested in some in-depth reading, consider one of these books:
What Counts: How Every Brain is Hardwired for Math by Brian Butterworth
The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by George Lakoff and Rafael Núñez
Post new comment