When children learn to count, they do so by rote. Understanding what the numbers really mean comes later. This is reflected in the way children draw a number line. In the beginning, they typically put more space between the smaller numbers, with the larger numbers all scrunched up at the end (a logarithmic number line). Eventually they progress to a number line where the numbers are evenly spaced (linear number line).
Now a series of experiments with preschoolers and second graders has revealed that the more linear the child's magnitude representations (as seen on the number line as well as in other tasks), the better the child was at remembering numbers (for example, from a story with some numbers included).
This was true for preschoolers for numbers from 1-20 and for elementary school children for numbers from 1-1000, and for four different number tasks measuring numerical-magnitude representations (categorization and number-line, measurement, and numerosity estimation). Other types of numerical knowledge—numeral identification and counting—were unrelated to remembering numbers.
(2010). Linear Numerical-Magnitude Representations Aid Children’s Memory for Numbers.
Psychological Science. 21(9), 1274 - 1281.