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.

Scale, proportion, and quantity constitute a “crosscutting concept” in science education – a concept that pervades science and can help students connect their knowledge across topics and disciplines. An understanding of wide ranges of size is a prerequisite for the learning of scale. Students must have a good understanding of size and scale if they are to leverage them to connect their science understanding. In this study, we examine two qualitatively different types of knowledge that may underlie the understanding of size and scale: the evolutionarily-based approximate number sense, and the culturally-based understanding of measurement units. We explore how closely these two types of knowledge are related to size and scale knowledge useful for secondary science classrooms. This study has implications for instruction: evolutionarily-based abilities are biologically primary, are acquired universally, and are motivating, whereas culturally-based abilities are biologically secondary, and depend on instruction, practice, and external motivation. Different educational approaches might be better suited to biologically primary and secondary abilities. The results of an empirical study with 36 seventh grade students are reported.