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

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.