An Investigation On Grade 8 Students' Level Of Plausible Reasoning

Reasoning Ability is one of the ten core concepts listed in Curriculum Standards for Mathematics of Compulsory Education(2011 version).Reasoning generally consists of deductive reasoning and plausible reasoning.Innovation comes from questioning and discovery,and plausible reasoning is considered as a major discovery method.Thus the study of both its connotation and assessment framework possesses theoretical value.Meanwhile,eighth grade is the “critical period” to develop students' reasoning ability.And “Graphics and Geometry” are the “key parts”.Therefore,what level of plausible reasoning have the eighth-grade students reached in “Graphics and Geometry”?Or have they realized the expectation of curriculum standard in this field? This exploration owns positively practical meaning.This paper adopted the mixed research methods of mainly qualitative analysis and supplemented by quantitative analysis.Based on combining literature concerning the connotation of plausible reasoning,the study constructs an evaluation framework of the plausible reasoning ability from three dimensions,including the main forms of plausible reasoning,the main contents of “Graphics and Geometry” and the plausible reasoning ability level.Restricted by the research time,this study only investigated on some eighth grade students in one Middle School of Suzhou which the author interned.Through the investigation,this paper drew conclusions as follows:(1)The eighth grade students basically possess the plausible reasoning ability,and overall be in the second level.Most of them have the plausible reasoning consciousness,also can use the reasoning in the process of solving the problems.However,to get perfectly logical and reasonable results,they must do more.(2)The eighth grade students have significant individual differences in the plausible reasoning of “Graphics and Geometry”.The development of plausible reasoning ability is positively related to the students' class level and the performance of mathematics,and has little correlation with gender.(3)The eighth grade students show imbalanced performance in the plausible reasoning of “Graphics and Geometry”.The students do better in “the Character of the Graph” and “the Graph and Coordinates” compared to “the Change of the Graph”.The analogical reasoning ability is obviously better than inductive reasoning ability.Accordingly,this paper suggested that less normal but more flexible mathematics problems should be emphasized in the exercise of “Graphics and Geometry”.It is necessary to integrate conjecture into reasoning.We can develop students' reasoning ability by coordinating the balance between the plausible reasoning and deductive reasoning.