Developmental Research on Measuring Instrument of Cognitive Patterns in Arithmetic/Mathematics Learning

1.认知模式的理论与访谈研究通过以往的研究，我们认识到认知模式对算术/数学的学习方法和数学问题解决的方式有着重要的影响，进而与算术/数学学习的成功与否密切相关。因此，我们设计了学习辅导来证实上述认知，并对学龄儿童和初中生进行了实践。研究结果表明：1.认知模式反映在学习策略中，如理解监控策略和自我控制策略。小学生数学学习策略的调查我们编制了由26个项目组成的反映认知模式的数学学习策略量表（LSM），并对小学九年级学生进行了测试。在26个项目中，高、低成就学生在18个项目上有显著性差异，说明认知方式与成就有关。其次，以数学的最小二乘模型为基础，构建了由25个项目组成的算术最小二乘模型，并对小学六年级学生进行了实验。在25个项目中有14个项目上，高、低成就学生之间存在显著性差异。算术LSM和数学LSM共有21项。通过对这些项目的分析，可以看出，六年级和九年级学生的学习策略或认知模式没有显着差异。如何改善小学生的认知模式，如何将认知模式与小学生学习策略的发展联系起来，还有待于进一步的研究。

1. THEORETICAL AND INTERVIEW RESEARCH ON COGNITIVE PATTERNSThrough the preceding researches, we have recognized that the cognitive patterns have an influence on the learning methods of arithmetic/mathematic and on the way of mathematical problem solving, and then they are greatly concerned with the success in arithmetic/mathematics learning. So, we designed the counseling of learning to confirm the above recognition, and practiced it to school children and junior high school students. As the result of it, it became clear that the cognitive patterns were reflected in the learning strategies such as the way of comprehension monitoring and self-controlling.2. THE INVESTIGATION OF LEARNING STRATEGIES OF ELEMENTARY AND JUNIOR HIGH SCHOOL PUPILSWe constructed the Learning Strategies Measure (LSM) of mathematics consisting of 26 items which reflected the cognitive patterns, and practiced it to the ninth-grade pupils. We got the significant differences between high and low achievement pupils on 18 items out of 26 items, and it became clear that the cognitive patterns were related to the achievement. It also became clear that there was no significant difference between boys and girls.Next, basing on LSM of mathematics, we constructed LSM of arithmetic consisting of 25 items, and practiced it to sixth-grade pupils. We also got the significant differences between high and low achievement pupils on 14 items out of 25 items. There are 21 common items to both LSM of arithmetic and LSM of mathematics. Through the analysis of these items, it became clear that there was no remarkable difference relative to the learning strategy or cognitive patterns of sixth-grade and ninth-grade pupils. I remains to be proved that how to improve the cognitive patterns of pupils and how to connect them with the development of learning strategies of pupils.