Tracing teachers’ engagement in counterintuitive mathematics from intuition to reasoning, calculation, and peer discussion

Baimukhanov A. Sony S.D. Kоchshanova G. Smagulov Y. Balta N. Cézar R.F.
April 2026 Bastas

European Journal of Science and Mathematics Education
2026 #14 Issue 2 251 - 269 pp.

This study examines mathematics teachers’ engagement with counterintuitive problems through a structured four-stage process: intuitive responses, reasoning, calculation, and peer discussion. Using convenience sampling method, 60 mathematics teachers from Kazakhstan’s Zhetysu Region were selected for the study. Data were collected using an adapted set of four counterintuitive mathematics tasks. Results revealed that initial intuitive responses frequently led to systematic errors. Reasoning explanations were often only partially correct, indicating that intuitive responses were grounded in incomplete conceptual models. Formal calculations improved accuracy across most tasks, though the average speed problem remained especially resistant to resolution. Peer discussion proved to be the most effective intervention, leading to substantial gains in correctness, particularly for the most counterintuitive tasks. Comparative analysis across the four stages revealed distinct learning trajectories, with collaborative reasoning consistently yielding the largest improvements. Regression analysis demonstrated a moderate positive relationship between reasoning quality and solution accuracy. These findings show the pedagogical value of counterintuitive problems for improving reasoning, conceptual understanding, and collaborative learning in mathematics education. Copyright

counterintuitive problems , mathematics education , peer discussion , problem-solving , reasoning , teacher learning

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Faculty of Physics and Mathematics, Zhetysu University named after I. Zhansugurov, Taldykorgan, Kazakhstan
School of Mathematics and Statistics, Northwest Missouri State University, Maryville, MO, United States
Department of Basic Sciences, Yessenov University, Aktau, Kazakhstan
SDU University, Almaty, Kazakhstan
University of Castilla-La Mancha, Ciudad Real, Spain

Faculty of Physics and Mathematics
School of Mathematics and Statistics
Department of Basic Sciences
SDU University
University of Castilla-La Mancha

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026