International Group for the Psychology of Mathematics Education (PME)

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

From Half of a Half to a Third on the Number Line: Interpreting and Responding to Fraction Thinking

Zelha Tunc Pekkan, Beyda Yilmaz

University of Agder

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 1499–1506ISSN 2790-36482026Scopus conference code 336559
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Abstract

Fractions are challenging, requiring teachers to interpret and respond effectively to students’ reasoning. This study examines how 12 experienced teachers (ET) and 10 pre-service teachers (PST) interpret and respond to problematic situations involving fractional knowledge on number lines. Using professional noticing as a framework, we analyzed two dimensions: interpreting and responding. Fraction sub-constructs and units coordination guided analysis. Participants viewed fraction-related video clips and answered open-ended questions probing noticing skills. Findings show ET more often demonstrated advanced interpretations and responses involving units coordination, while PST relied on quotient subconstruct. Results underscore the need for targeted teacher education on content-specific noticing.

Keywords

fractionsnumber lineteachers' noticing

Recommended citation

Tunc Pekkan, Z., & Yilmaz, B. (2026). From Half of a Half to a Third on the Number Line: Interpreting and Responding to Fraction Thinking. 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. 1499–1506). Psychology of Mathematics Education (PME). ISSN 2790-3648.
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