SGER: Encoding and Strategy Use in Children's Problem Solving

这个项目涉及儿童的概念发展，重点是儿童发展新的解决问题策略的过程。当孩子们解决问题时，他们“编码”——也就是说，提取和心理表征——关于问题的感知规律。该项目的核心理论前提是，当儿童需要构建新策略时，他们会使用这种编码知识。这个理论框架可以预测孩子们什么时候会产生新的策略，以及他们会产生什么样的策略。提出的实验研究了儿童学习数学等价概念时的问题编码和策略变化，数学等价概念是指等式的两边（例如，6 + 4 = 10）代表相同的数量。对这一概念的理解将以3 + 4 + 5 = ？+ 5;孩子们被要求提供缺失的数字（在本例中为7）。研究1检验了两个假设：(a)反馈和指导导致问题编码的变化；(b)对问题特征进行编码的孩子在应用他们当前的策略时不会用到这些特征，他们特别有可能创造新的策略。研究2探讨了另外两个假设：(a)儿童编码的改变会导致他们构建新的策略；儿童产生的新策略类型将取决于他们编码的具体问题特征。除了测试这些实质性假设外，该研究还将开发一套新的方法工具来评估儿童的问题编码。将开发两种新的行为措施：(a)对问题识别测试的表现进行评估(例如，你之前看到了哪个问题？，选项包括3 + 4 + 5 = ？， 3 + 4 + 5 + 5 = ？等);(b)评估在问题解释过程中产生的自发手势（例如，以特定顺序指向问题中的数字）。这些研究将探讨这两种测量之间的关系，以及每种测量与策略使用和策略生成之间的关系。该项目的结果将有助于理解认知发展，也应该为改进数学问题解决的教学提供基础。

This project concerns conceptual development in childhood, focusing on the processes whereby children develop new problem-solving strategies. When children solve problems, they `encode` - that is, extract and mentally represent -- perceptual regularities about the problems. The central theoretical premise of this project is that children use this encoded knowledge when they need to construct new strategies. This theoretical framework leads to predictions about when children will generate new strategies, and about the types of strategies they will generate. The proposed experiments examine problem encoding and strategy change in children learning the concept of mathematical equivalence, which is the notion that the two sides of an equation (e.g., 6 + 4 = 10) represent the same quantity. Understanding of this concept will be probed with problems of the form 3 + 4 + 5 = ? + 5; children are asked to supply the missing number (in this case, 7). Study 1 tests two hypotheses: (a) that feedback and instruction lead to changes in problem encoding; and (b) that children who encode problem features they do not use in applying their current strategies are especially likely to create new strategies. Study 2 explores two additional hypotheses: (a) that modifications in children's encoding will lead them to construct new strategies; an (b) that the types of new strategies children generate will depend on the specific problem features they encode. In addition to testing these substantive hypotheses the research will develop a set of new methodological tools for assessing children's problem encoding. Two novel behavioral measures will be developed: (a) assessments of performance on problem recognition tests (e.g., Which problem did you see earlier?, with choices including 3 + 4 + 5 = ?, 3 + 4 + 5 + 5 = ?, etc.); and (b) assessments of spontaneous hand gestures produced during problem explanations (e.g., pointing in a particular sequence to the numbers in the problem). The studies will explore the relationship between these two measures, and how each relates to strategy use and strategy generation. The results of the project will contribute to understanding of cognitive development, and should also provide a basis for improving instruction in mathematical problem-solving.