Exploring the linguistic complexity of third-grade numerical literacy

Abstract

Reading numbers aloud, a central aspect of numerical literacy, is a challenging skill to acquire, but the origins of this difficulty remain poorly understood. To investigate this matter, we examined the performance of 127 third- and fourth-grade children who read aloud, in Hebrew, numbers with 2-5 digits. We found several key observations. First, we observed a substantial variation among the 3rd graders-7% and 59% errors in the top and bottom deciles, respectively. Second, the task difficulty stemmed from syntactic processing: Most errors were distortions of the number's syntax, as opposed to digit substitutions or transpositions, and the main factor affecting a specific number's difficulty was not its magnitude, as is commonly assumed, but rather its syntactic structure. Third, number reading performance was not predicted by a school-like task that assessed syntactic-conceptual knowledge of the decimal system structure, but rather by knowledge of specific syntactic-verbal rules, suggesting that the syntactic-verbal knowledge is separate from the syntactic-conceptual knowledge. Last, there was a double dissociation between 4-digit numbers and 5-digit numbers, which in Hebrew have completely different syntactic structures: Half of the children showed a significant advantage in one number length compared to the other, with equal numbers of children preferring either length. This indicates that the different syntactic-verbal rules are learned relatively independently of each other, with little or no generalization from one rule to another. In light of these findings, we propose that schools should specifically teach number reading, with focus on specific syntactic-verbal rules.

Keywords: Conceptual versus procedural knowledge; Development of numerical skills; Number reading; Number syntax.

Fig. 1

Error rates for a 3rd-grade and b 4th-grade children in reading aloud numbers with 2–5 digits. The thin bars show each child’s error rates (gray = overall, colored = specific error types, classification detailed in section “Error classification”). The insets show the mean rate of errors of each type, and the effect of number length on the overall error rate. Error bars/shaded area show one standard error of the per-participant means

Fig. 2

Error rates of the a 3rd graders and b 4th graders in reading aloud numbers with different syntactic structures, grouped by the number of digits. a In the third grade, the highest error rates were in the numbers with irregular syntactic structures (2,xxx and 10,xxx). Numerically, these numbers were not larger but smaller than other numbers with the same number of digits, supporting the idea that the degree of difficulty was affected by syntactic irregularity more than by the number size. b In the 4th grade, the error rates in the ten thousand (10,xxx) structure became lower, indicating that by this age the children have already learned this specific structure

Fig. 3

The error rates of each 3rd grader in reading numbers with 4 digits versus 5 digits (excluding the children with fewer than 10 errors and the items with the irregular syntactic structures: 2,xxx and 10,xxx). Colored dots indicate the 35/68 children whose error rate in numbers of one length was significantly higher than in the other

Fig. 4

The syntactic error rate in number reading versus the error rates in a the digit-in-position task (e.g., “what is the hundred digit in 2,975?”; n = 95 children), which taps knowledge of the decimal system structure; and b the grammaticality decision task (“is ‘thirty-two’ grammatical?”, “is ‘fifty-sixty’ grammatical?”, etc.; n = 37 children), which taps knowledge of verbal-syntactic rules. Each dot represents one child. In a, minor horizontal jitter (< 1.5%) was added for visual clarity, and the correlation was computed without the 4 participants who were outliers in the digit-in-position task (red dots). Grammaticality decision was a good predictor of number reading, but the digit-in-position task was not