title: Who can escape the natural number bias in rational number tasks? A study involving students and experts.
abstract: Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth-grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.
authors.affiliation: Center for Instructional Psychology and Technology, University of Leuven, Belgium.|TUM School of Education, Technical University of Munich, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Obersteiner
authors.affiliation: Center for Instructional Psychology and Technology, University of Leuven, Belgium.
authors.forename: Jo Van
authors.initials: JV
authors.lastname: Hoof
authors.affiliation: Center for Instructional Psychology and Technology, University of Leuven, Belgium.
authors.forename: Lieven
authors.initials: L
authors.lastname: Verschaffel
authors.affiliation: Center for Instructional Psychology and Technology, University of Leuven, Belgium.
authors.forename: Wim Van
authors.initials: WV
authors.lastname: Dooren
mesh_terms: D000293:Adolescent; D005260:Female; D006801:Humans; D019545:Intuition; D019359:Knowledge; D007858:Learning; D016015:Logistic Models; D008297:Male; D008433:Mathematics; D011930:Reaction Time; D013334:Students
keywords: algebraic inequalities; effect of arithmetic operations; rational numbers; whole number bias