Monday, June 11, 2007

Let's start with counting

In an overview of the history of mathematics, J. J. O'Connor and E. F. Robertson begin by saying that ”Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.” (MacTutor History of Mathematics, http://www-groups.dcs.st-and.ac.uk/~history/)

On the same note, I believe that the first brick in understanding mathematical cognition is counting. Fortunately (for me) there has been a great deal of research on this subject. There is a significant amount of evidence through studies done for at least the last 30 years (as far back as I looked) that show a recognition of numerosity and counting not only in people but also in a variety of animals – birds, rats, various monkeys/apes, etc. Granted the animals do not exhibit an ability to detect numerosity much above quantities of 3 – 5, but it’s there. This leads me to believe that a basic knowledge of counting is hard-wired into our brains. It’s an evolutionary trait handed down from our ancient ancestors.

There was a study reported on in SCIENCE in 1999 that sheds a little bit of light on how our brains are wired for counting. This is an illustration that appeared with the article.

DIAGRAM: Figuring out arithmetic. The principal brain regions involved in calculating exact and approximate mathematical problems. The left inferior frontal lobe is involved in verbally coded number facts that can be used in exact calculations. The intraparietal sulci of the left and right parietal lobes are implicated in estimations and approximate calculation, which are dependent on visuo-spatial representations of numbers. The intraparietal sulci are part of the circuit controlling finger movement and are likely to be crucial to finger counting, a near universal stage in learning arithmetic. (Butterworth, Brian. “A Head for Figures”. Science, 1999, 284(5416), p. 28-28-29)

subitize, v.
Psychol.
[f. L. subitus SUBITE a. + -IZE.]

intr. and trans. To apprehend immediately (the number contained in a small sample). Hence subitizing vbl. n.

1949 E. L. KAUFMAN et al. in Amer. Jrnl. Psychol. LXII. 520 A new term is needed for the discrimination of stimulus-numbers of 6 and below... The term proposed is subitize... We are indebted to Dr. Cornelia C. Coulter, the Department of Classical Languages and Literatures, Mount Holyoke College, for suggesting this term. Ibid., If no discontinuities had appeared in the results, no distinction between subitizing and estimating could have been drawn. 1971 Jrnl. Gen. Psychol. Jan. 121 The number of items in an array capable of being subitized. 1981 Nature 15 Oct. 569/2 Judgements of ‘small’ numerosities..are ordinarily attributed to subitizing.

Over the next couple of weeks, I'll review six relatively recent journal articles I've down loaded and also talk about some older studies that looked at counting in pre-verbal babies. The first article on tap is entitled "Analog Numerical Representations in Rhesus Monkeys: Evidence for Parallel Processing" - the study it reports on pretty much disputes the idea of subitizing.

Now aren't you just holding your collective breaths waiting for these?

9 comments:

vw bug said...

It keeps me thinking. I'll take whatever you pass this way.

MathCogIdiocy said...

Thinking is good. :-)

Anonymous said...

Lord have mercy, when does Numb3rs return to TV to keep you occupied *eyes crossing* LOL Sue

MathCogIdiocy said...

ROFLMAO!!!

Sometime in the fall...

Harvey said...

*inhales deeply*

MathCogIdiocy said...

LOL!

Anonymous said...

I stumbled upon your blog by accident but stayed and read a number of posts. Given your background and interests, you might enjoy this post at the Britannica Blog, "Why Math Geeks (Especially Immigrant Geeks) Rule": http://blogs.britannica.com/blog/main/2007/07/why-math-geeks-especially-immigrant-geeks-rule/

All the best.....

rahul said...

excellent work

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