From “Brain Mysteries” 5-2-2012:
Tape measures. Rulers. Graphs. The gas gauge in your car, and the icon on your favorite digital device showing battery power. The number line and its cousins – notations that map numbers onto space and often represent magnitude – are everywhere. Most adults in industrialized societies are so fluent at using the concept, we hardly think about it. We don’t stop to wonder: Is it “natural”? Is it cultural?
Now, challenging a mainstream scholarly position that the number-line concept is innate, a study suggests it is learned.
Another example of the vastly under appreciated role of learning in how our minds develop. What’s not learned?
Read: Study finds twist to the story of the number line (5/2/2012)
I believe it is both innate and taught. “”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,” said Nunez.
“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,” added former graduate student Cooperrider. “When confronted with radically different ways of construing experience, we can no longer take for granted our own. Ultimately, no way is more or less ‘natural’ than the Yupno way.”
http://www.brainmysteries.com/research/Study_finds_twist_to_the_story_of_the_number_line.asp
Example – true story
One night, walking down to the store with my youngest child who was 3 1/2 at the time, she pointed to a star, the brightest star in the sky, and spoke. Back then, my child barely talk, let alone said more than ten words in a conversation, and rarely ever initiated a conversation.
“Look Mommy, there’s heaven, and the number line goes through heaven.” I did not think too much of it, and I put it down to nursery school, but when we arrived home, she wanted to explained further. She grabbed a book, that had the star constellations and planets information and turned to the page where Earth is shown with the star constellations. She pointed to Earth, and told me that Earth is zero, and pointed to a star constellation that she believe is heaven, and said that is where the numbers ended.
By age 5, different place, different view of constellations, but I believed the same star, my 5 year expands her description of the number line. All positive numbers goes through heaven and all negative numbers are returned to Earth. Since Earth is the number zero, zero represents all the positive and negative numbers. She sees the number line as a circular line, instead of a straight line, that goes on forever.
I thought at the time, she should not have any problems with math at school. Was I wrong, the math curriculum being taught today, does not abide by such radical concepts as zero being one composed of negative and positive numbers but still represents nothing. Zilch. Nada. By the end of grade 1, my youngest child could no longer do the simple addition and subtraction done with such ease when she was smaller, and she was hopelessly confused. In her dyslexic mind, the number line was three dimensional that could be manipulated. In the classroom, math was flat and two-dimensional.
By grade 6, home tutoring and re-teaching at home, determined to turned my child into a child that is adept with numbers – I started with the number line. I only had 4 weeks before the unit test, to undo the damage by the fuzzy illogical math curriculum and math instruction. I had my work cut out for me. In the process, we spent a great deal of time on the number zero and the number line itself. It was one of those aha moments I had, remembering my child’s early concept of heaven and the number line. I told her to look at the straight line on the paper as a compressed circle that has also been stretched to where it is no longer a circle but a straight line. From the point, it was easy and math became easy for my child, and the first unit test came back with a 82.
Rather funny, my dyslexic child would relate very well with the natives of Papua New Guinea, but not in the 21st century elementary school math class. “Most adults in industrialized societies are so fluent at using the concept, we hardly think about it. We don’t stop to wonder: Is it “natural”? Is it cultural?”
It could be both. In the industrialized societies they are only fluent in the first and second dimensional thinking, but the cultural aspect won;t allow people to venture out into the third and fourth dimensions.