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New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies

机译：旧视野的新视角：构建数学概念，基本的抽象过程和感官策略

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The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical approaches and abstraction-from-objects theoretical approaches. Acknowledging and building on research on knowing and learning processes in mathematics, this article presents a theoretical framework that provides a new perspective on the underlying abstraction processes and a new approach for interpreting individuals' ways of constructing concepts on the background of their strategies to make sense of a mathematical concept. The view taken here is that the abstraction-from-actions and abstraction-from-objects approaches (although different) are complementary (rather than opposing) frameworks. The article is concerned with the theoretical description of the framework rather than with its use in empirical investigations. This article addresses the need for more advanced theoretical work in research on mathematical learning and knowledge construction.
机译：本文的最初假设是，在认识和学习数学的研究中过分强调“从动作抽象”的理论方法。本文对学生构建数学概念的方法进行了批判性反思，以区分“从动作抽象”理论方法和“从对象抽象”理论方法。承认并基于对数学知识和学习过程的研究，本文提出了一个理论框架，该框架为潜在的抽象过程提供了新的视角，并提供了一种新的方法来解释个人在其有意义的策略背景下构建概念的方式数学概念。这里的观点是，从动作抽象和从对象抽象的方法（尽管有所不同）是互补的（而不是相对的）框架。本文关注的是该框架的理论描述，而不是其在实证研究中的使用。本文解决了在数学学习和知识构建研究中需要进行更高级的理论工作的需求。

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