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影响着算术/数学的学习方法和数学问题的解决方式，进而影响着算术/数学学习的成功与否。因此，我们设计了学习辅导来确认上述认识，并对在校儿童和初中生进行了实践。结果表明，认知模式反映在理解、监控和自我控制等学习策略中。中小学生学习策略的调查构建了由26个反映认知模式的项目组成的数学学习策略量表，并在九年级小学生中进行了实践。我们在26个项目中的18个项目上得到了成绩高低的学生之间的显著差异，很明显，认知模式与成绩有关。同样清楚的是，男孩和女孩之间没有显著差异。其次，在数学LSM的基础上，构建了包含25个题项的算术LSM，并对六年级小学生进行了实践。我们还发现，在25个项目中，高、低成绩学生在14个项目上存在显著差异。算术LSM和数学LSM共有21项。通过对这些项目的分析，我们发现六年级和九年级学生在学习策略和认知模式方面没有显著差异。如何改善学生的认知模式，如何将其与学生学习策略的发展联系起来，还有待证明。

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.