Algebra word problems are problems that require translating statements in ordinary language to equations in algebraic language, as George Polya (1957) once succinctly, but accurately, put it. As devices for enhancing the learning of algebra and abstract mathematics more generally, they have been a target of much interest to educators and cognitive scientists for years (for example, Nathan et al., 1992; Schwarz et al., 2000), especially since such problems have consistently shown themselves to be difficult to grasp and solve by students. Grasping the underlying conceptual structure encoded by the verbal story and translating it into algebraic structure poses a clear challenge, involving the interaction between language and mathematics. AI tools for solving such problems have been intensively developed (Zhang et al., 2019; Faldu et al., 2021; Liu et al., 2022), which extend into other areas, including critical cultural analysis (Neuman et al., 2022). The key aspect of such tools is that they allow for a veritable “dialogue” between human and machine, that is much like a Socratic dialogue, a form of argumentative dialogue between individuals and computers (in this case), based on asking and answering questions.

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AI and Mathematical Understanding: ChatGPT Goes to School

  • Marcel Danesi,
  • Yair Neuman

摘要

Algebra word problems are problems that require translating statements in ordinary language to equations in algebraic language, as George Polya (1957) once succinctly, but accurately, put it. As devices for enhancing the learning of algebra and abstract mathematics more generally, they have been a target of much interest to educators and cognitive scientists for years (for example, Nathan et al., 1992; Schwarz et al., 2000), especially since such problems have consistently shown themselves to be difficult to grasp and solve by students. Grasping the underlying conceptual structure encoded by the verbal story and translating it into algebraic structure poses a clear challenge, involving the interaction between language and mathematics. AI tools for solving such problems have been intensively developed (Zhang et al., 2019; Faldu et al., 2021; Liu et al., 2022), which extend into other areas, including critical cultural analysis (Neuman et al., 2022). The key aspect of such tools is that they allow for a veritable “dialogue” between human and machine, that is much like a Socratic dialogue, a form of argumentative dialogue between individuals and computers (in this case), based on asking and answering questions.