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Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective

机译：战略构建过程中的概念和程序知识：复杂的知识系统视角

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摘要

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated for decades. Recently, there has been mounting empirical evidence that conceptual and procedural knowledge can develop by mutual bootstrapping in a bidirectional and iterative fashion (e.g., Rittle-Johnson & Schneider, 2014). However, the very constructs of conceptual and procedural knowledge (especially procedural knowledge) have been critiqued for inconsistency in definition and lack of operationalization (Star, 2007). The analysis in this article addresses this critique by modeling the diverse forms of conceptual and procedural knowledge needed to implement a strategy as a complex knowledge system: a strategy system. Furthermore, the strategy system model is used to elaborate processes of mutual bootstrapping between conceptual and procedural knowledge at a moment-by-moment time scale. The strategy system model builds upon the Knowledge in Pieces epistemological perspective (diSessa, 1993), and coordination class theory in particular (diSessa & Wagner, 2005). Both the theoretical notion of a strategy system and the bidirectional model of mutual bootstrapping between conceptual and procedural knowledge are illustrated using data from a case study of a pre-algebra student who iteratively refined a procedure for solving algebra word problems. The strategy system model highlights the complexity of both strategies and concepts and offers a window into what can be learned by students during strategy construction processes.
机译：本文阐述了研究新颖策略的新方向，该策略使研究人员能够在解决数学问题期间模拟学生可观察到的战略动作的概念基础。数十年来，关于概念性知识和过程性知识之间关系的性质一直存在争议。最近，越来越多的经验证据表明，概念和程序知识可以通过双向引导和迭代方式的相互引导来发展（例如Rittle-Johnson＆Schneider，2014）。然而，由于定义不一致和缺乏可操作性，人们对概念和程序知识（特别是程序知识）的构造提出了批评（Star，2007）。本文中的分析通过对将战略作为复杂的知识系统（战略系统）实施所需的概念和程序知识的多种形式进行建模，从而解决了这种批评。此外，策略系统模型用于详细说明概念和程序知识之间在瞬间之间相互引导的过程。战略系统模型建立在“知识在碎片”的认识论观点（diSessa，1993），尤其是协调阶级理论（diSessa＆Wagner，2005）的基础上。策略系统的理论概念和概念知识与程序知识之间的双向相互引导的双向模型都使用来自代数前学生的案例研究的数据进行了说明，该案例迭代地完善了解决代数词问题的过程。策略系统模型突出了策略和概念的复杂性，并为了解学生在策略构建过程中可以学到的知识提供了一个窗口。

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  • 来源
    《Cognition and instruction》 |2018年第3期|247-278|共32页
  • 作者

    Levin Mariana;

  • 作者单位

    Western Michigan Univ, Dept Math, 1903 W Michigan Ave, Kalamazoo, MI 49008 USA;

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  • 正文语种 eng
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