Single-digit and two-digit Arabic numerals address the same semantic number line

Many theories about human number representation stress the importance of a central semantic representation that includes the magnitude information of small integer numbers, and that is conceived as an abstract, compressed number line. However, thus far there has been little or no direct evidence that units and teens are represented on the same number line. In two masked priming experiments, we show that single-digit and two-digit Arabic numerals are equally well primed by an Arabic numeral with the same number of digits as by an equally distant Arabic numeral with a different number of digits (e.g. the priming effect of 7 on the target 9 is the same as the priming effect of Il on the target 9). The finding was obtained both with a number naming task and with a parity judgement task. This is in line with the hypothesis that units and teens are part of a continuous number line

The approximate number system cannot be the leading factor in the acquisition of the first symbolic numbers

When learning the meaning of symbolic numbers, children learn the numbers up to 4 sequen-tially. A prominent account of this learning process proposes that the increasing sensitivity of the preverbal approximate number system (ANS) allows for reliable discrimination of increasingly large neighboring numbers, which, consequently, leads to the sequential acquisition of the first symbolic numbers. In this work, a more complete quantitative description of this account is provided. This description is based on the mathematical model of the ANS and on additional relevant parameter values reported in the literature. The quantitative description demonstrates that, in the time period during which children learn the meaning of the first number words, the improvement of ANS sensitivity cannot provide the assumed changes in the discriminability of these numbers. The present result challenges the role of the ANS as a leading factor in the acquisition of the first symbolic numbers

Automatic number priming effects in adults with and without mathematical learning disabilities

This study examined automatic number processing in adults with mathematical learning disabilities (MLDs). The performance of adults with MLD during an automatic symbolic and non-symbolic priming task was compared to gender-, age-, and IQ-matched controls. No difference in the priming distance effect was found between the adults with and without MLD, suggesting that adults with MLD have an intact magnitude representation. Moreover, the adults with MLD did not have problems in processing the numerical symbols 1-9, suggesting that this basic deficit which is experienced by children with MLD is resolved by adulthood

Can You Trust Your Number Sense: Distinct Processing of Numbers and Quantities in Elementary School Children

Theories of number development have traditionally argued that the acquisition and discrimination of symbolic numbers (i.e., number words and digits) are grounded in and are continuously supported by the Approximate Number System (ANS)—an evolutionarily ancient system for number. In the current study, we challenge this claim by investigating whether the ANS continues to support the symbolic number processing throughout development. To this end, we tested 87 first- (Age M = 6.54 years, SD = 0.58), third- (Age M = 8.55 years, SD = 0.60) and fifth-graders (Age M = 10.63 years, SD = 0.67) on four audio-visual comparison tasks (1) Number words–Digits, (2) Tones–Dots,(3) Number words–Dots, (4) Tones–Digits, while varying the Number Range (Small and Large), and the Numerical Ratio (Easy, Medium,and Hard). Results showed that larger and faster developmental growth in the performance was observed in the Number Words–Digits task, while the tasks containing at least one non-symbolic quantity showed smaller and slower developmental change. In addition, the Ratio effect (i.e., the signature of ANS being addressed) was present in the Tones–Dots, Tones–Digits, and Number Words–Dots tasks, but was absent in the Number Words–Digits task. These findings suggest that it is unlikely that the ANS continuously underlines the acquisition and the discrimination of the symbolic numbers. Rather, our results indicate that non-symbolic quantities and symbolic numbers follow qualitatively distinct developmental paths, and argue that the latter ones are processed in a semantic network which starts to emerge from an early age