<![CDATA[Purpose - This study examined whether inference constitutes a critical-thinking performance bottleneck when National Science Olympiad (OSN) students solve controversial geometry problems requiring them to adjudicate between competing mathematical claims. Methods - A sequential explanatory mixed-methods design was used with 25 OSN students from a senior high school in Cirebon, Indonesia. Students solved three controversial geometry problems and were assessed on five indicators: interpretation, analysis, synthesis, evaluation, and inference, using an analytic 0–4 rubric. Written-response data were analysed descriptively across the three problems and across high-, moderate-, and low-performance groups. Nine students were purposively interviewed to explain the quantitative performance pattern, and quantitative and qualitative evidence were integrated at the interpretation stage. Findings - Interpretation had the highest achievement (84.00%), whereas inference had the lowest (50.00%). Inference remained the lowest-performing indicator across all three problems and across the high (71.67%), moderate (47.55%), and low (27.78%) performance groups. At the individual level, inference was the sole lowest-scoring indicator for 17 of 25 students (68%). Interview and written-response evidence showed that some students could identify, compare, and verify mathematical information but did not consistently convert that evidence into an explicitly warranted conclusion. Novelty - The converging evidence supports interpreting inference as a critical-thinking performance bottleneck within this assessment context rather than as evidence of a general cognitive bottleneck. Significance - The findings provide implications for mathematics teachers and curriculum developers to integrate controversial mathematical problems into learning, assessment and explicitly strengthen students’ capacity to construct evidence-based and mathematically justified conclusions.]]>
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