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<p>The relationship between the graph of a derivative and its antiderivative is an important aspect of calculus and has applications across many disciplines. In this study, a constructivist grounded theory approach was used to analyze the problem-solving and problem-posing processes of 20 undergraduates as they engaged with nine derivative tasks, aiming to develop a model of students’ graphical reasoning about derivative-antiderivative relationships. In the initial coding, 133 codes were identified and categorized into eight main categories during the focused coding phase. During the theoretical coding phase, four approaches were identified: <i>calculation</i>, <i>approximation</i>, <i>shape guessing</i>, and <i>numerical</i>, plus a combination of approximation and calculation. The proposed model is supported by the literature, particularly by static and emergent shape thinking, and can be used to enhance the quality of teaching and learning of the derivative, as well as serve as a lens to explore students’ understanding of this topic.</p>

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A grounded theory model of students’ graphical reasoning on derivative-antiderivative relationships

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月8日

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  • Saeid Haghjoo,
  • Farzad Radmehr,
  • Ebrahim Reyhani,
  • Abolfazl Rafiepour

摘要

The relationship between the graph of a derivative and its antiderivative is an important aspect of calculus and has applications across many disciplines. In this study, a constructivist grounded theory approach was used to analyze the problem-solving and problem-posing processes of 20 undergraduates as they engaged with nine derivative tasks, aiming to develop a model of students’ graphical reasoning about derivative-antiderivative relationships. In the initial coding, 133 codes were identified and categorized into eight main categories during the focused coding phase. During the theoretical coding phase, four approaches were identified: calculation, approximation, shape guessing, and numerical, plus a combination of approximation and calculation. The proposed model is supported by the literature, particularly by static and emergent shape thinking, and can be used to enhance the quality of teaching and learning of the derivative, as well as serve as a lens to explore students’ understanding of this topic.