Sep 10 2010

How’s Your Number Line?

As you might imagine, I am fascinated by how the mind works. It is, arguably, the most important thing to each of us – our own brain. We are our brains. It is our universal tool, the one tool to rule them all. And so understanding the strengths and weaknesses, the quirks and foibles of the human brain in general, and our own brains in particular, should be of paramount interest.

One aspect of brain function that is very interesting is how we model abstract concepts in our brain, like numbers. We often assign physical properties to abstract concepts, perhaps as a handle so that we can better think about them. For example, with numbers we tend to picture them spaced out along a line, with linear distance being proportional to number value. We put numbers into a physical space. An extreme example of this in number synesthesia – some people actually feel that numbers have a shape, color, or texture. In some cases they use these properties of numbers to help them do calculations in their heads.

A recent psychological study looked at the number line of children. Young children just learning numbers tend to have a logarithmic number line, with low numbers spaced out and higher number increasingly squished together. But as children mature their number line tends to become more linear, with spacing being proportional to value. The recent study asked children to place various numbers on a line where they belong, to see what their mental number lines look like. They then gave them a mental task that required remembering numbers. What they found was that the more linear the child’s number line, the better they performed on number memory tasks.

This result suggests that our mental map of numbers is important to our ability to think about numbers, and perhaps manipulate them in our minds. It also shows that this ability is variable. That much is not a surprise – the ability to perform mental calculations varies widely among people. There are those who are mathematically challenged and those who are gifted. While education certainly plays a huge role in our mathematical abilities, raw talent is clearly also important – like with music and many other mental abilities. Perhaps facility with numbers is closely tied to our ability to think of numbers as having a physical property, as this study suggests.

An interesting follow up question is – can this ability be taught, or is it a consequence of genetically determined hard-wiring. Perhaps this research may eventually point the way to teaching strategies that encourage children to develop their number lines and other mental maps as a way of enhancing their ability to deal with numbers.

This is an appealing idea – using our knowledge of how the brain works to craft optimal teaching programs. However – if history is any guide, preliminary knowledge about brain function can lead to teaching fads that are not themselves evidence-based, and common sense approaches can get displaced by fanciful and ultimately pseudoscientific teaching programs. Like any other area of science, translating it into specific applications needs to be done carefully and itself based upon evidence. It is not a trivial thing to extrapolate from basic science to real work application.

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