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<p>Understanding functions is a cornerstone of mathematics education, yet students’ conceptions of functions often remain fragmented—especially when tasks require coordinating formal definitions with graphical, symbolic, and contextual representations. This study investigated Greek upper-secondary students’ understanding of functions across Grades 10–12 using a quantitative, curriculum-referenced design. A 10-item questionnaire assessed key strands of function knowledge (definition/uniqueness, domain, graph–rule connections, variable roles, and contextual interpretation). Participants were 185 students from three public schools in Greece (school-access sample; intact-class administration). Descriptive and inferential analyses revealed persistent conceptual difficulties across grades. The most prevalent misconceptions involved identifying functions from graphs (62% incorrect), distinguishing dependent from independent variables (55% incorrect), and determining domain/range (48% incorrect). Although performance improved modestly from Grade 10 to Grade 12, misconception rates remained substantial, indicating incomplete conceptual consolidation despite repeated curricular exposure. Representation-based analyses showed a significant effect of representational format, F(2, 182) = 8.45, <i>p</i> = .0004, η² = 0.09, with higher performance on the contextual items than on the algebraic and graphical items; this pattern reflects relative success on the instrument’s context tasks (interpreting change from a real-data graph) rather than uniformly strong functional modelling. Interpreted through the Concept Image/Definition perspective and APOS theory, the findings suggest uneven representational coordination and a “high-resistance” misconception profile that persists across consecutive grades. Beyond documenting misconceptions in one national setting, the study contributes developmental–comparative evidence identifying which difficulties remain robust under increased formalization, offering targeted implications for instruction that foregrounds definition-based reasoning, domain justification, and coordinated work across representations.</p>

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Exploring high school students’ misconceptions of functions: A cross-grade comparative study

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Georgios Polydoros

摘要

Understanding functions is a cornerstone of mathematics education, yet students’ conceptions of functions often remain fragmented—especially when tasks require coordinating formal definitions with graphical, symbolic, and contextual representations. This study investigated Greek upper-secondary students’ understanding of functions across Grades 10–12 using a quantitative, curriculum-referenced design. A 10-item questionnaire assessed key strands of function knowledge (definition/uniqueness, domain, graph–rule connections, variable roles, and contextual interpretation). Participants were 185 students from three public schools in Greece (school-access sample; intact-class administration). Descriptive and inferential analyses revealed persistent conceptual difficulties across grades. The most prevalent misconceptions involved identifying functions from graphs (62% incorrect), distinguishing dependent from independent variables (55% incorrect), and determining domain/range (48% incorrect). Although performance improved modestly from Grade 10 to Grade 12, misconception rates remained substantial, indicating incomplete conceptual consolidation despite repeated curricular exposure. Representation-based analyses showed a significant effect of representational format, F(2, 182) = 8.45, p = .0004, η² = 0.09, with higher performance on the contextual items than on the algebraic and graphical items; this pattern reflects relative success on the instrument’s context tasks (interpreting change from a real-data graph) rather than uniformly strong functional modelling. Interpreted through the Concept Image/Definition perspective and APOS theory, the findings suggest uneven representational coordination and a “high-resistance” misconception profile that persists across consecutive grades. Beyond documenting misconceptions in one national setting, the study contributes developmental–comparative evidence identifying which difficulties remain robust under increased formalization, offering targeted implications for instruction that foregrounds definition-based reasoning, domain justification, and coordinated work across representations.