Research Of Plausible Reasoning In Mathematics Curriculum And Its Teaching

According to the common viewpoint of mathematics thinking and method, there are two reasoning in mathematics, on is argument reasoning, used to prove mathematics question, the other is plausible reasoning, used to discover mathematics question or to find the way of solving it. We pay more and more attention to plausible reasoning and its effect and meaning in mathematical education today. Developing plausible reasoning ability is already written in new mathematics curriculum standard. As a result, we should specially do some research about plausible reasoning in theory and demonstration.In this article, we first define the concept of plausible reasoning, and introduce some main methods of it: observing, experimenting, concluding and analogy. Second, we introduce plausible reasoning teaching and some didactics about it: mathematics education thought under Constructivism, Freudenthal's thought of Reinvention, and Piaget's research about development of children's reasoning level. And we also expound the inspire of them in plausible reasoning teaching. Then we analyze plausible reasoning in mathematical curriculum standard and its teaching in each study stage and each teaching material. Based on this, we investigate the actuality of plausible reasoning teaching in part of Yunnan, and get some main conclusion: teachers have paid attention to plausible reasoning ,but actually they haven't take it as keystone; at the same time, they think BJNU-edition textbook is contribute to plausible reasoning teaching.Then we do some research about plausible reasoning in demonstration. We first conceive the classroom teaching model of plausible reasoning teaching, and analyze some cases. Based on these analyze about cases and the results of questionnaire, we advanced proposal like these: pay attention to the validity of situation (including characteristic of opening, compendious, and phases); notice the avidity of cooperative learning; regard the exploring in the progress of getting knowledge.At last, we consider: the key of plausible reasoning teaching is to change the way of classroom teaching and learning fitly; it is necessary to avoid the deluge of explore; don't ignore the wrong reasoning in plausible reasoning teaching.