Analysing Students' Higer-Order Thinking Ability Formation Processes in Mathematics Education and Developing Structured Mathematics Curriculum

1. 分析学生高阶思维能力的形成过程与课堂实践(1)调查统计解释能力：分析学生的统计问题解决过程。阐明了问题构建在这一过程中的重要作用。(2)研究养殖面积问题：对养殖面积问题提出了三个认识层次。（应用程序公式-使用组合等式-改变高阶概念）。各水平之间存在显著差异，说明数学知识绩效的重要性。(3)常规-非常规问题的解题能力：考察非常规问题的算法思维能力。非常规题成绩与标准数学成绩相关性较低，得分较低。该结果可应用于基于模型构建能力的数学culcula设计。(1)欣赏数学的课程开发：我们开发了欣赏数学的代数入门课程，并在初中课堂上进行了实践。该实践原则能够应用高阶图式指导，能够更充分地诊断学生的理解特征。(2)辅助数学归纳学习的电子文本开发：我们利用Mathematica软件实现了辅助高中数学归纳学习的电子文本。

1. Analysing students' higher-order thinking ability formation processes and classroom practices(1)Investigates statistical interpretation ability : We analyzed students' statistical problem solving processes. Its clarifyed that problem construction plays important role in the process.(2)Investigates culculating area problem : We developed three recognition levels about area problems. (Procedural formula applyed - Combinational Equality Using - Higher-order concept changing). There is significant differences in each levels, and this results suggests importance of mathematical knowledge performance.(3)Problem solving ability about routine - non routine problem : We investigated algorithmic thinking ability with non routine problem. Non-routine problem performance is low correlated with standard mathematics performance, and quite low score. This results can apply designing mathematics cullicula based on model construction ability.2. Mathematics cullicula development for higher-order thinking ability and database development(1)Curricula development to appreciate mathematics : We developed introductory algebra curricula to appreciate mathematics, and practiced in junior high school classroom. This practice principles are able to apply higher order schema instruction, and able to diagnose more adequately students' understanding characteristics.(2)Development of Electrical Text to assist inductive leraning of mathematics : We implement the Electrical Text to assist inductive learning of mathematics in high school with Mathematica.