<p>Prior empirical research points to the criticality of logical implications in students’ transitions to proof-based mathematics. Research indicates that students who do not yet treat implications as objects (whole entities that can be transformed) often experience significant difficulties with proofs. To date, however, no in-depth analyses have been provided demonstrating the reasoning of students who treat implications as objects. Such an analysis would contribute important insights into students’ conceptions and reasoning about implications and inform how to support students’ construction of implications as objects. This article makes two contributions to the research literature. First, we contribute a conceptual analysis of one undergraduate student who participated in task-based clinical interviews focused on his logical reasoning. Specifically, we investigate how this student coordinated mental actions to form implications as objects, how he acted on implications as whole entities, and what epistemological obstacles remained for him. Second, we contribute a methodological toolkit for conducting conceptual analysis, framed around mental actions and their coordination to form mathematical objects.</p>

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What does it mean to treat logical implications as objects? The case of Zeke

  • Joseph Antonides,
  • Anderson Norton,
  • Rachel Arnold

摘要

Prior empirical research points to the criticality of logical implications in students’ transitions to proof-based mathematics. Research indicates that students who do not yet treat implications as objects (whole entities that can be transformed) often experience significant difficulties with proofs. To date, however, no in-depth analyses have been provided demonstrating the reasoning of students who treat implications as objects. Such an analysis would contribute important insights into students’ conceptions and reasoning about implications and inform how to support students’ construction of implications as objects. This article makes two contributions to the research literature. First, we contribute a conceptual analysis of one undergraduate student who participated in task-based clinical interviews focused on his logical reasoning. Specifically, we investigate how this student coordinated mental actions to form implications as objects, how he acted on implications as whole entities, and what epistemological obstacles remained for him. Second, we contribute a methodological toolkit for conducting conceptual analysis, framed around mental actions and their coordination to form mathematical objects.