|Number and Space are Inextricably Connected
Try this: close your eyes, and think of an open number line. You just need to picture a line, no intervals marked, just a certain amount of space. That line will have a length, although it is difficult to tell how long your mental image of this line is.
We know this line could stretch from some starting point, to infinity, or rather to some infinite length, which we cannot measure. We could mark an infinite number of points on this line, and actually, we could mark two different types of infinity on this line: counting numbers, and real numbers, which are demonstrably at a higher level on the “tower of infinity”.
But we are getting ahead of ourselves.
Close your eyes, and picture a line of length 10 units. Hold up your hands however long you think that line should be.
Now open them. Where are your hands?
Try the same exercise for 20. Where are your hands?
Here is an interesting tweet thread about some experiences I had working on number lines with grade ones. My colleague asked them to visualize 20.
Consider trying this with your students. Whether “shoulder width” is a preferred human length for number lines is an open question. Perhaps “body scale” is most relatble to us humans.
If you want to blow their minds, ask them to draw an open line of some length, mark 0 and one million as the ends. Where is 1000? Now do the same for one billion. Where is one million?
Space and number are mysteriously connected. As I understand the research, we know they are connected, there is no doubt, we just don’t really know how.
Work is being done in this area. See the pre-print in this tweet below, and consider reading it. Zach Hawes and Daniel Ansari are working on what happens in the brain to connect space and number. Basically, there is an emerging body of evidence that spatial reasoning and thinking about numbers are connected, as shown by fMRI mapping of the regions of the brain responsible for each.
Research continues, seeking to find this “missing link”. In the meantime, an open number line is a tool “with legs” in grade 1-12 education. (Typically, Kindergarten students aren’t quite ready to go past concrete counting objects, ten frames, and on to the number line).
Written by Matthew Oldridge (@MatthewOldridge)