Is pure left-to-right the best number line?
The team found that the eye movements could be used to predict the size of the next number before it was spoken. If a volunteer looked left and downwards, he would typically chose a number that was smaller than the previous number, and if he looked up and to the right, he chose a number that was larger . . . What’s more, the extent to which he looked in a particular direction correlated with the extent to which the number was larger or smaller than the last.
— New Scientist, Mind over matter? How your body does your thinking
Given that 10% of people see sequences as their own personal spacial arrangement, and even normal people appear to have some internal number line (see the quote above) how should that influence our teaching?
This is the standard representation of the number line:
However, according to studies like the one above, and also studies of synesthesia, it is quite common to include an up-down component:
[From Galton’s Visualized Numerals.]
While I’ve never heard it used before, I theorize it might be best when teaching students to intuitively handle the number line to present a tilted format: