Scale and the Evolutionarily Based Approximate Number System: An Exploratory Study

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Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.