Changes in Problem Representation as a Mechanism of Knowledge Change

理解发展的关键之一是了解儿童的知识如何随着时间的推移而变化。因此，发展研究的一个重要挑战是明确知识变化的机制。本研究的重点是在数学知识的发展变化的一个潜在的机制：即，儿童如何表示的问题的变化。我将问题表征定义为对问题的特定特征的内部、心理副本的创建。我认为，表征是一个重要的联系儿童的知识之间的数学概念和他们的知识解决数学问题的策略。这项拟议中的研究在学习数学等价概念的儿童中测试了这一说法，数学等价概念是一个等式的两边代表相同的数量。儿童对这一概念的知识是用3+4+5=_+5的公式来测试的。建议的研究解决两个主要问题的变化问题表征的知识变化的机制。首先，问题表征的变化如何影响儿童的知识？拟议的研究测试的假设，即儿童的问题表征的变化可能会导致他们的理解的问题解决策略的变化，并在他们的知识的相关概念的变化。第二，是什么使表征发生变化？拟议的研究探讨了三种类型的因素，可能有助于改变的表征：（a）在概念知识的增益，（B）学习新的解决问题的策略，（c）获得经验的问题域。本研究将揭示表征在数学学习中的重要性，以及导致和影响表征变化的因素。我的总体目标是构建一个明确的理论模型，说明问题表征的变化如何作为认知变化的机制。

One of the keys to understanding development is understanding how children's knowledge changes over time. Thus, an important challenge for developmental research is to specify the mechanisms of knowledge change. This research focuses on one potential mechanism of change in the development of mathematical knowledge: namely, changes in how children represent problems. I define problem representation as the creation of an internal, mental copy of particular features of a problem. I argue that representation is an important link between children's knowledge about mathematical concepts and their knowledge about strategies for solving mathematical problems. The proposed research tests this claim among children learning the concept of mathematical equivalence, which is the notion that the two sides of an equation represent the same quantity. Children's knowledge of this concept is tested using equations of the form 3+4+5=_+5. The proposed studies address two main questions about changes in problem representation as a mechanism of knowledge change. First, how do changes in problem representation influence children's knowledge? The proposed studies test the hypothesis that changes in children's problem representations can lead to changes in their understanding of problem-solving strategies, and to changes in their knowledge of related concepts. Second, what makes representations change? The proposed studies explore three types of factors that may contribute to changes in representation: (a) gains in conceptual knowledge, (b) learning new problem-solving strategies, and (c) gaining experience within a problem domain. This research will shed light on the importance of representation in mathematical learning, and on factors that lead to and influence representation change. My overarching goal is to construct a well-specified theoretical model of how changes in problem representation function as a mechanism of cognitive change.