Study On The Theory And Practice Of Inductive Reasoning In Primary Mathematics Curriculum

Inductive reasoning is an important cognitive activity and the basic thinking form in primary school. Pupils form mathematical concepts, obtain mathematical rules, construct knowledge system, and solve problems by inductive reasoning. Therefore, inductive reasoning is an important part of primary school mathematics to improve students’ mathematical quality, especially creative consciousness. Adding inductive reasoning into obligation education, especially primary mathematics education is an important measure of mathematics education and curriculum reform. However, the understanding to basic teaching aims and requirements of inductive reasoning on stage of primary school is still superficial, which result in the unclear and disorder of the curriculum design and teaching. This situation is inconsistent with the demands of curriculum reform, and disadvantageous to the implementation of quality education of primary school, which urgently need be solved by theory and practice.Based on the current primary mathematics curriculum our country elementary school mathematics course actual ,this study investigated mathematics inductive reasoning of primary mathematics from theory and practice of elementary school level comprehensively. Firstly, the concept of inductive reasoning is defined as“based on experience and concept, the deduction of probable relation between conditions and conclusions according to some rules”though the methods of literature literature review.The theory of inductive reasoning suitable for primary mathematics is discussedSecondly, in order to explore inductive reasoning curriculum and teaching of primary mathematics thoroughly, the 52 primary school teacher were surveyed and some teachers of them were tested and interviews , materials related to inductive reasoning in two sets of textbook on the version of Beijing Normal University and PEP were compareda sample of about 650 pupils in five primary schools of different levels was selected to test their reasoning abilityFinally, the basic idea ,gradual stages and valuable Suggestions of curriculum and teaching of inductive reasoning were put forward. Studies show:1. The theory of inductive reasoning suitable for primary mathematics need be further studied .The concept of inductive reasoning should be defined as“based on experience and concept, the deduction of probable relation between conditions and conclusions according to some rules”. The inductive reasoning suitable for primary mathematics can be classified into to two types, enumerative induction and scientific induction. At the stage of primary school, the learning of inductive reasoning can be classified into instinctive level, enumerate inductive reasoning level and scientific inductive reasoning level.2. Now the design and implementation of induction content in primary mathematics have some shortage. As far as the content design of inductive reasoning is concerned, the model of inductive reasoning is“concrete examples-general rule- test”from first-grade to sixth grade, which easily makes pupils develop think set and cognitive illusion, which is not consistent with the requirements of mathematics curriculum standards. Moreover, the arrangement of the inductive reasoning subjects is not systematic and hierarchy. As far as the teaching of inductive reasoning is concerned, the primary school teachers’understanding of inductive reasoning is insufficient, for example, lacking of the understanding of the importance of inductive reasoning, and the externalization of their thinking process of inductive reasoning. As far as the pupils’mathematics competence,their mathematical reasoning, abstractness and representation competence are insufficient, namely, lacking of consciousness of inductive reasoning, lacking of appropriate basic model of inductive reasoning“observing examples-obtaining guess-looking for proof/justification/raising counterexample”; lacking of the easiest deduction , abstractness and mathematical thinking,; unable to express their thinking process clearly, and represent the rules they found using mathematical language logically.3. Curriculum design and teaching of inductive reasoning at the stage of primary school should be improvedThe learning of inductive reasoning should be a cognitive activity across the primary mathematics. Based on pupils’psychological characteristics and the three level of inductive reasoning, the curriculum of inductive reasoning for primary mathematics can be classified into four stages, namely, the preparation of inductive reasoning-first grade curriculum, the primary stage of inductive reasoning–second and third grade curriculum, the improving stage of inductive reasoning-fourth and fifth grade curriculum .Pre-deductive reasoning stage–sixth grade curriculum. We should recognize the development of inductive reasoning is a gradual and successively constructive process, and integrating induction and deduction contribute to the students to find conclusions and test conclusions, and develop high level mathematical inductive reasoning ability A suitable model is put forward for the teaching of inductive reasoning,Which is composed of three steps: examining problem---trying and guessing---generalization of result...