Construction Of A Preliminary Theoretical Study Of 'mathematics Learning

The paper wants to outline the learning theory of mathematics with the constructivism mainly through studying the correlated documents and data.First, the thesis briefly synthesizes and comments the constructivism and its learning theory The theory about the cognition development of children and the social-cultural theory are the basis of constructivism. There are mainly six different directions which are radical constructivism, social constructivism, soial-cultural cognition, information-processing constructivism, social construction and cybernetics. From different angles they deeply study the constructive cognition. We introduce the learning theory of constructivism. These opinions are synthetic from different constructivisms.One of their nucleus is the full respection and the deeply digging to the protagonist status of students.We must criticize and analyze constructivism by materialist dialectics because it is affected by many kinds of philosophy Otherwise we will easily go to the oppositivism and idealism.Because mathematics philosophy is largely the core of the philosophy of mathematics education, we briefly consider the essence of mathematics combined with the constructivism Ernest creates the social constructive philosophy of mathematics Going with the theory of mathematics pattern, we point out the development of mathematics is a constructive process of quantification pattern Its accuracy should be identified by the mathematics community Concepts, formulas, theorems and methods are all patterns The study of current philosophy reveals the definite philosophy of mathematics has turned into empirical and quasi-empirical philosophy The philosophy determines there are not only observing and proof, but understanding, analyzing, guessing, cooperation and communication in the learning community in the progress of mathematics development. Hence we raise the essence of constructive learning of mathematics is that subjects deeply construct quantification pattern by high-leveled thinking The result is continually expanding and precision of quantification patterns, and the consummating of cognition structure Based on the analysis about the learning essence, the essay probes the main characteristic of constructive mathematics learning:lthinking highly of the capacity of mathematical abstract The direct objects of mathematics is the products of abstract thinking, thereof we should ask students to be good at collecting a certain percentage about the features of things from quantitative angle By virtue of the importance of reflective abstraction, we should lead students to have abstraction and introspection about their own activities.2overall participance of intelligence It includes the using of capacity of observing, thinking and imagining which is the full play of recognition energy It is necessary for students to construct deeply quantification pattern Only when students are involved in the current duty, can they accomplish the construction of pattern.3powerful environmental support The constructivism emphasizes the importance of communication and cooperation to the pattern construction The environmental support includes not only the operation of multi-media software and network technology, but also the communication in the learning community especially between teachers and students The era asks mathematics education shoulder the task of developing the creativity of students The theory of investing creativity thinks creativity is the products of six elements (intelligence, knowledge, ^thinking styles, personality, motivation, environment)and mutual action among them So we think it is sure that constructive learning should promote the students creativity. Learning principlesreflect the features and laws of learning. We raise theoretically some principles:!reinvention principle. It is first advanced by Freudental. The essence of constructive mathematics learning is a process of pattern reinvention We should reinvent the meaning of quantification pattern in the mind through abstracting instead of only int...