Place value, which underlies the meanings of multi-digits, encompasses the principle of position and base-10 rules. To understand “65,” one needs to know that the digits “6” and “5” occupy different positions and thus represent ordered values of different magnitudes (the principle of position), and that the value of each position is determined by base-10 rules (e.g., the rightmost position is 10^0, followed by 10^1, 10^2, etc.). Without the principle of position, children cannot construct meanings for multi-digits. Previous studies show that children do not know the exact value of digit positions until early elementary school years, but less is known about the acquisition of positional knowledge for multi-digits. To study when and how children construct a relationship between position and value, this study explored when children begin to know that the leftmost digit represents the largest value, and whether such knowledge relates to learning number names. Four to 7-year-olds from primarily Caucasian, middle-class families were asked to compare different pairs of multi-digits. Some comparisons (e.g., 12 vs. 21) required knowledge of positional property, and some did not (e.g., 35 vs. 36). We found that as a group, 6-year-olds could recruit positional knowledge to compare multi-digits. We also found that children who knew the number names of both of the multi-digits in a comparison pair were above chance on multi-digit comparison. Our results shed light on the developmental steps towards acquiring place-value notation, and highlight a role of learning number names for learning positional property of the place-value notation.
Cracking the code of place value: The relationship between place and value takes years to master