Mapping the sources of mathematical controversy: A source-based typology of pre-service teachers’ reasoning on misleading media, procedures, and operations

Erry Hidayanto; Subanji; Rivan Gestiardi

doi:10.32674/ed2yma36

Authors

Erry Hidayanto Universitas Negeri Malang
Subanji Universitas Negeri Malang
Rivan Gestiardi Universitas Negeri Malang

DOI:

https://doi.org/10.32674/ed2yma36

Keywords:

cognitive conflict, diagnostic framework, mathematical reasoning, pre-service mathematics teachers, qualitative content analysis, student errors, teacher education

Abstract

Research on counterintuitive mathematics tasks describes levels of resolution but rarely distinguishes where a contradiction originates. This qualitative study examines a provisional typology of misleading media, procedures, and operations. Fifty Indonesian pre-service mathematics teachers in a university teacher education programme completed four tasks on percentage growth, fraction representation, algebraic cancellation, and root–exponent rules; 16 joined follow-up interviews. Responses were coded through three cycles. Participants showed different item-level patterns, and combining source and level produced a two-axis diagnostic matrix. Because media and operation were each represented by one task, source cannot be separated from item content or difficulty. The matrix is therefore a heuristic for further validation, not a tested intervention. It may help teacher educators organise analysis of student reasoning.

Author Biographies

Erry Hidayanto, Universitas Negeri Malang

ERRY HIDAYANTO is a faculty member of the Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Negeri Malang, Indonesia. His research interests include mathematical thinking and reasoning, mathematics teacher education, and the design of cognitively challenging tasks for pre-service mathematics teachers. He has long-standing experience teaching the Mathematical Thinking and Reasoning course (Berpikir dan Bernalar Matematis) and supervises undergraduate and graduate research in mathematics education. Email: erry.hidayanto.fmipa@um.ac.id
Subanji, Universitas Negeri Malang

SUBANJI is a senior faculty member of the Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Negeri Malang, Indonesia. His research focuses on mathematical reasoning, problem-solving processes, covariational reasoning, controversial reasoning of pre-service mathematics teachers, and the development of mathematics teacher education in Indonesia. He has authored numerous publications in national and international journals on mathematics learning processes and serves as a doctoral supervisor in the Postgraduate Program of Universitas Negeri Malang. Email: subanji.fmipa@um.ac.id
Rivan Gestiardi, Universitas Negeri Malang

RIVAN GESTIARDI is an independent researcher based in Wagir, Malang, Indonesia. He holds a doctoral degree from the Postgraduate Program of Universitas Negeri Malang and has published peer-reviewed articles on character education, technology readiness in learning, and quality management in elementary schools. His current research concerns pre-service teachers’ mathematical and pedagogical reasoning. Email: gestiardirr@gmail.com

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