International Group for the Psychology of Mathematics Education (PME)

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

Replicating the Derivative Knowledge Model: Evidence from Taiwanese High School Students

Pin-Chen Guo, Kai-Lin Yang, Kristin Litteck, Aiso Heinze

National Taiwan Normal Universsity

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 539–546ISSN 2790-36482026Scopus conference code 336559
⬇ Download PDF

Abstract

Using Sfard’s (1991) description of operational (process-oriented) and structural (object-oriented) knowledge, Litteck et al. (2024) empirically validated a derivative knowledge model with German students’ data. This study replicated their work with a Taiwanese sample (N = 373) to examine whether the model holds across educational systems. Operational items were found to be consistently more difficult than structural ones; however, the relative difficulty among structural sub-concepts differed from the German results. Model-comparisons showed that a three-factor model (ratio, limit, function) best represented the Taiwanese data, whereas Litteck et al. identified a two-dimensional structure (operational, structural). These results suggest that while the process-object distinction is robust, its internal organization may vary across contexts.

Keywords

DerivativeReplication StudyQuantitative StudyOperational-Structural KnowledgeInternational Comparison

Recommended citation

Guo, P., Yang, K., Litteck, K., & Heinze, A. (2026). Replicating the Derivative Knowledge Model: Evidence from Taiwanese High School Students. 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. 539–546). Psychology of Mathematics Education (PME). ISSN 2790-3648.
BibTeXRIS

← All PME 49 Research Reports