Relations of different types of numerical magnitude representations to each other and to mathematics achievement.
We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both magnitude comparison and number line estimation tasks. After controlling for non-mathematical cognitive proficiency, both symbolic and non-symbolic numerical magnitude understandings were uniquely related to mathematics achievement, but the relation was much stronger for symbolic numbers. A meta-analysis of 19 published studies indicated that relations between non-symbolic numerical magnitude knowledge and mathematics achievement are present but tend to be weak, especially beyond 6 years of age.
Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Electronic address: lkf12@pitt.edu.
Lisa K
LK
Fazio
Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
Drew H
DH
Bailey
Department of Psychology, University of Oklahoma, Norman, OK 73019, USA.
Clarissa A
CA
Thompson
Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA; Siegler Center for Innovative Learning, Beijing Normal University, Beijing 100875, China.
Robert S
RS
Siegler
D000124:Achievement; D002648:Child; D032882:Comprehension; D003210:Concept Formation; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D008960:Models, Psychological; D013561:Symbolism
Approximate number system; Fractions; Magnitude comparison; Magnitude representations; Mathematics achievement; Number line estimation