International Group for the Psychology of Mathematics Education (PME)

Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1

High Schoolers' Spontaneous Use of Cross-notation Knowledge of Rational Numbers

Jake McMullen, Jon Star

University of Turku

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 1011–1018ISSN 2790-36482026Scopus conference code 336559
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Abstract

Many students face difficulties in acquiring the skills needed for such adaptive expertise with rational numbers, a key aim of education systems worldwide. This study investigates the possibility that cross-notation knowledge, understanding the relationships between different notations of rational numbers, should be considered a feature of adaptive expertise with rational numbers. 447 high school students completed measures of adaptive expertise, including the Arithmetic Sentence Production Task. Results indicate that students who employed cross-notation solutions on this task performed well on other measures of adaptive expertise. These findings underscore the importance of cross-notation knowledge for adaptive expertise with rational numbers.

Keywords

rational number knowledgeadaptive expertisestrategic flexibility

Recommended citation

McMullen, J., & Star, J. (2026). High Schoolers' Spontaneous Use of Cross-notation Knowledge of Rational Numbers. In Krzywacki H., Hähkiöniemi M., Haataja E., Hannula M.S., Hästö P. (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education, Volume 1 (pp. 1011–1018). Psychology of Mathematics Education (PME). ISSN 2790-3648.
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