Constructivism And Mathematical Education

A new round of mathematics curriculum reform is being deployed all-around. In the reform, mathematics curriculum absorbs reasonable parts of every educational theory; the educational thought of constructivism is one of important content. Study on thought of constructivism is very significance to guidance of mathematical teaching in secondary school. The main psychological tool is called"reflexive abstraction"by Piaget in knowledge structure, which is structure core mechanism. The reflective thinking of mathematical teaching and learning in my thesis is"reflexive abstraction". My thesis is based on the short introduction the research about thought and theory of leaning of constructivism, and elaborately analyzes the view of knowledge, the view of curriculum, the view of students, the view of teaching, and the view of mathematics about constructivism to guidance function for the theory of mathematical teaching of primary and secondary school, reflective thinking to the function of mathematical teaching and learning, the basic qualities of teachers'reflective thinking ability, the students'reflective awareness and ability. Through appropriate case analysis, ulterior analyzes my standpoint. My thesis contains four parts, as follow:1. I analyze several kind basic theory of constructivism, and summarize basic structure theory of Piaget and L.Vygotsky and new development of constructivism, for example, radical constructivism and societal constructivism. In the guidance significance aspect of idiographic teaching, I summarize the view of knowledge, the view of curriculum, the view of students, the view of teaching, and the view of mathematics about constructivism. Especially, in the aspect of mathematics education, the view of mathematics curriculum has important significance for guidance mathematical teaching. Therefore, I analyze mathematical structure cognition and children's mathematical learning which connects with structure knowledge in constructivism, too.2. I analyze the connection of content, characteristic, mathematical reflective thinking ability and other mathematical ability of reflective thinking and mathematical reflective thinking, reflective thinking has important significance in students'learning and mathematical knowledge structure. Consequently, I put forward the viewpoint that it's necessary to cultivate reflective awareness of students.3. I analyze the level, process and cultivating of teachers'teaching reflective, the aim of that is the key of teaching reform is teachers, the quality of teachers determine that mathematics education is succeed or fail. If you want to cultivate the reflective awareness and reflective thinking ability of students, the teachers must have favorable reflective awareness and reflective thinking ability, namely, teachers'reflective thinking is the example and precondition of students'reflective thinking. So today mathematics education needs mathematics teachers who have reflective thinking, which is first of all. My thesis enumerates some strategies to cultivate mathematics teachers'reflective thinking ability.4. I enumerate some approaches to cultivate the students'reflective awareness and reflective thinking ability in classroom and after school.In a word, I believe that teaching and learning are mutual effect, and the teachers'reflective and students'reflective are supplementary to each other.In addition, attached with the thesis are two appendixes:⑴A recorded interview with Zhang Dian Zhou, a famous mathematics educationalist Zhang Dianzhou in China.⑵Table of title of papers in Journal of Mathematics Education and Journal of Mathematics and some titles of thesis which connects with my thesis.