Reasonable Inference And Mathematical Learning

The educational circle of our country is usually considered as "mathematical inference" which refers to the highly formalized and abstract deductive inference. It is just because our traditional mathematical teaching that emphasizes the rigour of inference, our using the way of "formalization" to improve the students' ability of deductive inference and emphasizing the rigour of deductive inference that divide the inference into two incompatible parts, ignoring the function of the reasonable inference and other non-formalized thought, (e.g. Intuition, association, attain enlightenment)This article is based on the relative research materials of reasonable inference with the theory of mathematical teaching and relative logical knowledge. It carefully analyzed the character of reasonable inference as well as defined and classified reasonable inference. Then it make a deep research into several modal structures of reasonable inference, conclusive inference, analogous inference, source inference, statistical inference, affirmative inference, possible basis, incompatible proposition, gradually weak inference, gradual affirmation and so on. Use the examples to study the relation between all kinds of modal structures and math studies, analyzing the effect on the math study which the reasonable inference have in several aspects of the formation of conception, assimilation, the mastery of theorem and the solution of problems.And these methods can enlighten students to make full use of reasonable inference structure in our teaching to comprehend and seek the truth and find the way or methods of the truth in the process of the formation of conception and in the final discussion process of summarizing the formula and the theory.