Analysis of Mathematics Education Students' Reasoning in Determining the Truth Value of Quantification

Reasoning refers to the structured and logical process of drawing conclusions from given premises. Students of mathematics education, who are being prepared as future educators, are expected to possess strong logical reasoning skills in order to comprehend and convey more advanced mathematical concepts. This study aims to analyze the reasoning abilities of mathematics education students in determining the truth value of quantified statements. The central research question is: How do students' reasoning abilities relate to the accuracy of their problem-solving in the context of quantification? An explorative qualitative approach was employed to explore students' reasoning in evaluating the truth values of quantified statements. The study involved 13 students from the Mathematics Education Department at Universitas Muhammadiyah Ponorogo who were enrolled in the Mathematical Foundations course during the 2024/2025 academic year. Data collection instruments included a set of test questions and open-ended interview protocols. The analysis focused on indicators of mathematical reasoning, including: (1) identifying facts, patterns, properties, and relationships, (2) drawing logical conclusions, (3) making predictions and solving problems, and (4) constructing systematic and valid arguments. Following the written assessment, three students representing different levels of performance were selected for in-depth interviews. The findings revealed that while all three participants demonstrated potential in mathematical reasoning, each exhibited specific areas requiring further development. Subject N was proficient in deconstructing quantification problems and drawing logical conclusions, although further probing during the interview revealed gaps in deeper conceptual understanding. Subject A displayed semantic comprehension of quantification but lacked precision in applying formal logic and integrating numerical analysis. Subject F demonstrated a verbal understanding of truth value criteria and was capable of drawing conclusions, yet faced challenges with formal notation, particularly with singular quantifiers. Overall, the participants exhibited promising reasoning abilities but required reinforcement in interpreting formal notation, constructing valid arguments, and accurately applying logical structures. Misinterpretations of quantifier symbols and formal argument patterns were identified as common errors. Keywords: mathematical reasoning, truth valu, quantification.