Varieties of Number-Line Estimation: Systematic Review, Models, and Data

• Published in: Developmental review Vol. 74; p. 101161
• Main Authors: Qin, Jike, Kim, Dan, Opfer, John E.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2024
• Subjects: Cognitive development; Mathematical cognition; Number-line estimation; Psychophysical function; Mathematical cognition; Cognitive development; Psychophysical function; Number-line estimation
• ISSN: 0273-2297
• DOI: 10.1016/j.dr.2024.101161

•There is a debate on the best psychophysical function for number-line estimation.•Competing accounts emerge from distinct variants of estimation tasks.•We find that the logarithmic-to-linear shift theory best accounts for existing and novel variants of the task.•Logarithmic-to-linear shift theory uniquely predicts mathematical proficiency. The psychophysical function that best fits human data from number-line estimation is the subject of a lively, on-going debate with important theoretical and practical implications. We comprehensively reviewed articles which tested competing psychophysical functions and found systematic variablility in task design. To test whether one function could account for data across diverse tasks, we examined 158 children’s and adults’ estimates using two 2 × 2 designs, crossing symbol (symbolic, non-symbolic) and boundedness (bounded, unbounded) on free number-line tasks (Experiment 1) and crossing the same factors on anchored tasks (Experiment 2). This yielded eight varieties of number-line estimation: four old varieties for testing replicability and four new varieties for testing generalizability. Across the eight varieties, 88.84 % of participants provided estimates better fit by a mixed log-linear model than competing models, with weights of the logarithmic component (λ) decreasing with age in each task. Unlike parameters of competing models, λ on any given task significantly predicted λ on the other 7 tasks, as well as predicting arithmetic skills. Results suggest that representations of numerical magnitude play the largest part in number-line estimation, and the “logarithmic-to-linear shift” provides the most accurate and generalizable description of how number-line estimation develops. (196 words)