<![CDATA[This study aims to explore pre-service elementary school teachers' conceptual understanding and problem-solving strategies in fundamental mathematics concepts, with a specific focus on arithmetic series and fractions with mixed-methods methodology. A total of 84 pre-service teachers completed a written test covering 10 basic mathematics concepts, and the scores were analyzed to identify the most difficult concepts. Based on these results, six participants representing the high, medium, and low score categories were interviewed to investigate their conceptual reasoning and to analyze their problem-solving strategies using Polya's steps. The findings reveal that arithmetic series and fractions were the most challenging concepts, as evidenced by low scores, recurring errors, and persistent misconceptions. Interview results, particularly through the lens of Polya's framework, show that high-performing participants tended to use structured procedural strategies but often failed at the looking-back stage. In contrast, low-performing participants relied on intuitive, misaligned strategies, indicating weaknesses across multiple Polya steps. Overall, this study highlights the critical need to strengthen pre-service teachers' conceptual understanding through instructional approaches that emphasize representation, reasoning, and the systematic application of problem-solving heuristics.]]>
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