认知与发展心理学研究室知识库

本研究的土要日的在于揭示儿童解决加减文字题的基本心理过程。要达到这一目的，需要了解有哪些因素影响儿童解答问题(解题成绩和正确列式方式)以及这种影响是如何发生的。过去的研究在方法上和理论解释上均存在一些不足。本研究假设基本心理过程包括语言理解、语义推理和语义关系向数学运算映射三个阶段。根据这一假设，对儿童解答加减文字题的行为作出一些预测。经验性研究分为6个部分，通过克服过去研究方法上的某些不足来检验预测，主要要求小学儿童在学习加减文字题之前或之后通过纸笔方式解答不同类型的加减文字题，实验结果从三个角度分析:影响问题难度的因素、，错误类型及其成因和影响正确列式方式(是a-f-b还是b-I-a)的因素。研究结果与假设是一致的。与先前研究相比，新的发现主要有以下儿个方面:一些语言因素(例如主语一致性)对问题难度没有显著影响作用、在一些情况下不能根据语言理解成绩预测或解释解答问题的成绩、一些数学知识因素(例如运算类型和数量大小)对问题难度没有显著影响作用、情境表征复杂性显著影响儿童解答问题的成绩、错误的列式方式可以归结为一些容易和简单的表征类型、正确列式方式受集合在集合关系中的位置和问题熟悉性的影响。本研究的主要结论是:语言理解和数学知识在一定程度上影响儿童解答加减文字题，但是不能认为解决加减文字题的过程就是理解语言的过程或者应用数学知识的过程;语言理解模型和数学知识应用模型具有局限性;解答加减文字题的基本，集合关系推理和将客体集合关系映射为数学运算三个阶段。心理过程大致分为理解语言、客体根据上面的结果和结论，在本文的讨论部分提出解答加减文字题的表征构造模型。本研究可以丰富人们对数学认知和儿童认知发展的认识，也可以为相关内容的教学实践提供心理学基础。

The main goal of present study was to disclose the basic mental processes underlying children's solving addition and subtraction word problems. To reach the goal, it's necessary to disclose what types of external and internal factors influence children's performance (achievement and the surface of correct formula) and how the influences happen during children's solving word problems. There were some deficits in method and theoretical explanation used in previous research. Present study hypothesized basically that there should be three stages involving in children's performance: language understanding, semantic referencing, and mapping semantic relation of objects onto mathematical operations. Some predictions were derived from the fundamental hypothesis. The empirical research tried to overcome some problems found in the methods used in previous research and systematically explored children's performance. The children in primary school were asked to solve typical addition and subtraction word problems by paper and pencil before or after they formally accepted the instniction on these word problems. The results would be analyzed from three dimensions: factors that influenced problem difficulty, solution error types and the underlying causes, and factors that influenced the surface of correct formula(a-f-b or b-1^a). The empirical research was branched of3' into G parts. The results were consistent with predictions. The new findings were as following: (1)some linguistic factors didn't contribute to problem difficulty; (2)children's performance on word problem solving couldn't be explained according to their performance on language understanding; (3)some mathematical knowledge didn't contribute to problem difficulty; (4)the situation complexity could bring substantial influence on children's performance; (5)the incorrect formulas could be traced back to some easy and simple representations; and (6)the surface of correct formula was systematically related with the position of object set in set relation and children's familiarity level to word problems. The main conclusions derived from empirical research were that the basic mental processes of solving addition and subtraction word problems couldn't be considered as the processes of understanding language or applying mathematical knowledge but the processes involving language understanding,referencing and mapping activities. Present study can bring more knowledge about human's mathematical cognition and children's cognitive development, meanwhile, provide some psychological principles for instructional practice.