The Impact Of Mathematical Knowledge Representation On Students' Understanding

Mathematical concepts and theorem are not only important components of students' mathematical knowledge but also the basic content of maths teaching in primary and secondary schools. In our teaching practice we find that, for learning the different topics, students have differences in their interests and abilities. Some students are good at algebraic operation but away from geometry. Others are just so-so in algebra, but they love Euclidean geometry. Is such an ability difference of maths learning common in the students? The main problems that this thesis focuses on is what should be paid attention to in teaching to fit this kind of difference and promote the students' understanding of mathematics.The aim of this thesis is mainly to study that different ways of knowledge representation impact on students' understanding. At the beginning of this research, we try to identify the students with biased learning styles follow the classification method of Kelujieciji in the former Soviet Union. A few of students are classified as algebra-type, geometry-type, partial-algebra, and partial-geometry. They will be further studied in later Teaching Intervention. Then teaching experiments show rich knowledge representation affects on students' understanding. To remove unconcerned variable disturbance, the design of the experiments adopts taking-turns method. To make sure of the impact of teaching strategy on understanding of the students in vocational secondary schools, this research uses Skemp's classification ways of understanding for reference and we also design some tests respectively for two teaching contents. After the students are taught, we test and analyze their understanding levels and have interviews with the selected students to know the concrete impact of knowledge representation on students' learning maths.It is found that only 1 student among the 72 subjects is labeled as algebra-type student and another 1 student is labeled not surely as geometry-type student. About 22% of the students in Junior 1, vocational secondary schools, are labeled as partial-algebra students or partial-geometry students. Most of the subjects did not behave so differently to the learning of algebra and geometry. Classroom teaching in two presentation ways of algebra and geometry has a positive effect on students' understanding than that of either of them purely. So we suggest that mathematics teachers should provide varieties of ways of knowledge representation to meet the study demand of students in different thinking types, promote knowledge understanding and improve teaching efficiency in class.