On Students' Maths Skills Development Evaluation

Maths skills are important contents of maths teaching and learning. This thesis focused on different understanding and viewpoints between China and America, and Chinese students' maths skills development.In Chapter One and Chapter Two, we had a review about researches on maths skills and learning assessment. Based on the revision of Bloom's Taxonomy of educational objectives, we defined maths skills, which have two dimensions:In this framework, maths skills' content dimension include "fact", "method", and "strategy"; level dimension include "remember", "understand", "apply", "analyze", "evaluate", and "create".In Chapter Three, we chose Full-time compulsory education mathematics curriculum standard (experimental manuscript) which stands for Chinese curriculum standard and Principles and Standards for School Mathematics from NCTM which stands for American curriculum standard. Use the two dimension framework as a tool, we compared these two curriculum standards' difference in Number and Algebra, Space and Shape, Statistic and Probability, and drew the following conclusions:(1) About "Fact", NCTM's standard has higher proportion in "Understand", "Apply", "Analyze", and "Evaluate" than Chinese standard. About "Method", the two standards both emphasis on applying method. But Chinese standard stresses repeating and modeling, NCTM's standard stresses recognizing and organizing different methods. About "Strategy", Chinese standard emphasizes on applying, but NCTM's standard stressed "Analyze" level. A few demands for "Create" level also to be focused on "Strategy".(2) About "Number and Algebra", Chinese standard have higher proportion in "Remember" and "Understand" level, and lower proportion in other four. About "Space and Shape", Chinese standard stresses "Remember" and NCTM's standard stresses "Analyze". About "Statistic and Probability", the former stresses "Understand", the latter stresses "Apply".(3) In general, Chinese standard put more points on grasping maths skills' content, NCTM's standard cares about content using in practice context.In Chapter Four, we tested 8 grade students' maths skills, and drew the following conclusions:(1) Students have a good situation on "Remember" and "Understand", skills about "Apply" and "Analyze" are normal, skills about "Evaluate" and "Create" are to be developed.(2) Skills about "Apply" and "Analyze" have a high correlation with that about "Remember" and "Understand", and low correlation with that about "Evaluate" and "Create".(3) Maths skills in two dimensions can be segmented into three categories, which are Simply Operating, Virtually Grasping, and Creatively Appling.In Chapter Five, we analyzed some teaching cases, and found three factors which can promote students' development. The first is "Understanding", which can help students to grasp skills' nature. The second is "Appling", which can help students to relate to contents and practice. The third is "Exploring", which can help students to use contents creatively.In the last chapter, we suggested that teaching should focus on all categories of maths skills, and promote students to have balanced development.