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Monday, May 21, 2012

Number Line... Real or Invented

(via Wikimedia Commons)


Study concludes that the number line is not, as usually presumed, hard-wired within human intuition, but rather culturally learned and reinforced:

http://www.sciencedaily.com/releases/2012/04/120425192742.htm

full, original PLoS article here:

http://tinyurl.com/7dcucue
 
(interestingly, this all relates back to the sort of material covered in the David Berlinski book I reviewed last week)

Some quotes from the Science Daily piece:
"Influential scholars have advanced the thesis that many of the building blocks of mathematics are 'hard-wired' in the human mind through millions of years of evolution. And a number of different sources of evidence do suggest that humans naturally associate numbers with space"…
"Our study shows, for the first time, that the number-line concept is not a 'universal intuition' but a particular cultural tool that requires training and education to master. Also, we document that precise number concepts can exist independently of linear or other metric-driven spatial representations."

"Mathematics all over the world -- from Europe to Asia to the Americas -- is largely taught dogmatically, as objective fact, black and white, right/wrong, but our work shows that there are meaningful human ideas in math, ingenious solutions and designs that have been mediated by writing and notational devices, like the number line… Mathematics is neither hardwired, nor 'out there.'"

"These findings suggest that how we think about abstract concepts is even more flexible than previously thought and is profoundly affected by language, culture and environment."
"Our familiar notions on 'fundamental' concepts such as time and number are so deeply ingrained that they feel natural to us, as though they couldn't be any other way."

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