Not long after encountering the possibility that number lines have a privileged place in math learning, I read H. Wu's revelatory definition of a fraction as a point on the number line:
The following is a new approach to the teaching of fractions. It is not new in the sense of introducing new concepts; the subject is too old for that. Rather, it is new in the way the various skills and concepts are introduced and woven together. Whereas it is traditional to ask you to believe that the concept of a fraction is so profound that you have to be willing to accept multiple meanings for it at the outset, we merely ask you to accept one clear-cut deﬁnition of a fraction (as a point on the number line), and use reasoning to deduce as logical consequences all other meanings of this concept.I've been relying heavily on number lines for self teaching and reteaching for several years now.
On the Teaching of Fractions (pdf file)
David Geary's new longitudinal study seems to add further evidence that number lines are important:
The researchers also found that first-graders who understood the number line and how to place numbers on the line and who knew some basic facts showed faster growth in math skills than their counterparts during the next five years.
MU Psychology Study Finds Key Early Skills for Later Math Learning
Long-term study shows students must know about numbers at beginning of first grade
July 11, 2011