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Poster #83 - Staggering Individual Differences in Preschoolers’ Multi-digit Number Knowledge

Fri, March 22, 2:30 to 3:45pm, Baltimore Convention Center, Floor: Level 1, Exhibit Hall B

Integrative Statement

Mastery of the symbolic number system is foundational to success in mathematics. However, it has long been documented that school-aged children err at learning the place-value concept of multi-digit numbers. Recent studies have suggested surprisingly early knowledge of multi-digit numbers in some preschool children. However, it remains unclear whether all children have this knowledge and how individual factors, such as gender and SES, are related to the mastery of this knowledge. Using a representative sample of over 500 children, we provide the first comprehensive test of children’s early knowledge of multi-digit numbers.

Five-hundred and eighteen preschoolers (3- to 5-years-old, approximately half males and half females) participated in the study. In the Which-N task (10 trials), children were shown two written multi-digit numbers side-by-side (“241” and “412”), and were asked to point to one by name (e.g., “Which is two-hundred and forty-one?). In the Which-More task (10 trials), children were shown two written multi-digit numbers (“591” and “159”), and were asked to point to one that signifies the larger magnitude (no number name was provided). Each child was presented with a subset of items from a pool of items that include multi-digit numbers with transpositions (350 vs. 305), with one-digit difference (12 vs 22), with adding a zero (201 vs. 21) or with a combination of these features (807 vs. 78, both transposing and adding a zero). This allowed us to include a comprehensive sample of multi-digit numbers; thus, the interpretation of children’s performance was not constrained to specific numbers.

A general linear regression showed a significant age-related growth in both the Which-N task (b = .38, SE = .06, p < .0001) and the Which-More task (b = .22, SE = .05, p < .001). However, there were large individual differences in the performance of these tasks. As shown in Fig. 1, about 20% of 3-year-olds had already achieved mastery level of this knowledge (defined at 75% accuracy). In contrast, over 40% of 5-year-olds still struggled at these tasks. We next examined possible individual differences that may be associated with this early knowledge. Not surprisingly, SES is related to children’s understanding of how multi-digit numbers are used to represent magnitude (r = .18, p = .06). However, in contrast to previous studies demonstrating gender difference in mathematics and number learning, we found no significant gender difference in early multi-digit number knowledge (Fig. 2).

The emergence of early multi-digit number knowledge in some young children is surprising given previous studies documenting the difficulties in the school learning of this concept. The implication is that some preschoolers are discovering and building implicit knowledge of the place value principles of multi-digit numbers on their own. However, the large individual difference in this early knowledge is staggering, and will almost certainly affect the individual children’s readiness of place value learning in school and later math achievement in general. The quality of the early learning environment for children from different backgrounds may be the key contributor to the large early gap in multi-digit number knowledge.

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