A Study Of Junior High School Mathematics Teachers' Understanding Of The Method Of "Plausible Reasoning"

Since the new curriculum reform,plausible reasoning has been included in the examination content in the mathematics of the senior high school entrance examination,so it has become more regarded,and become a main concern of mathematics education research.As a part of reasoning,plausible reasoning is a way of thinking and a main mathematical method,which plays a very important role in teaching.Plausible reasoning can inspire students' thinking development,cultivate students' innovative consciousness and creative thinking,which has been recognized by many front-line math teachers and education researchers.However,in teaching,junior high school math teachers said that they seldom heard the term "plausible reasoning" in junior high schools,and the role of plausible reasoning methods on students' learning and development is uncertain.In this paper,the author try to know the status of plausible reasoning test in the mathematics of the senior high school entrance examination in Guangdong Province and Guangxi.Beside,to know the junior high school math teachers' understanding of the meaning of plausible reasoning methods,and some factors' influence to understanding and application of plausible reasoning,for example,the teachers' teaching age,teachers' professional title,teachers' gender,teachers' district,and types of school etc.Firstly,in this study,the text analysis method was used to statistically analyze the reasonable reasoning test questions of the middle school entrance examination in Guangxi,Guangdong province in the past 11 years.Then,the author selects 89 junior high school math teachers from Guangdong and 68 mathematics teachers from Guangxi as objects.We use questionnaire survey and individual interview and we mainly use quantitative analysis,supplemented by qualitative analysis.At the same time,bivariate correlation is used to analyze whether there is a correlation among the three dimensions in the questionnaire,and multi-factor analysis of variance and estimated marginal mean graph are used to analyze the influence of teachers' personal background factors on the cognition of plausible reasoning.And the result shows that:Firstly,through the analysis of the test questions,it is found that(1)the nearly eleven-year high school examinations in Guangdong and Guangxi have involved the examination of plausible reasoning,but the number of plausible reasoning test questions in the two regions is on a downward trend and the examination intensity of reasonable reasoning in Guangxi is lower than that in Guangdong;(2)the plausible reasoning questions in the two regions are mainly made in the form of objective questions,and most of them are final questions;(3)plausible reasoning in Guangdong and Guangxi eleventh-year mathematics of the senior high school entrance examination infiltrated widely and varied,mainly with graphic growth and variation,but the types of test questions in Guangdong are more diverse than those in Guangxi;(4)the plausible reasoning test questions in Guangdong and Guangxi mainly use graphics and geometry,numbers and algebra as the carrier to examine inductive conjectures,but Guangxi is inclined to examine numbers and algebra,while Guangdong is evenly distributed in these two areas.Secondly,through the questionnaire survey,the results show that:(1)Through specific analysis,the average score of teachers' cognition on the meaning of plausible reasoning is low,which means that the teachers are ambiguous about the meaning and basic knowledge of plausible reasoning methods.And the scores on the importance of plausible reasoning are higher than plausible reasoning teaching behavior.And they are unbalanced development in three aspects.(2)Through correlation analysis,the three dimensions of the investigation: the cognitive component of plausible reasoning connotation is not correlated with the cognitive compononent of plausible reasoning importance,but the cognitive component of plausible reasoning importance is positively correlated with plausible reasoning teaching behavior.That is,teachers' cognition of the importance of plausible reasoning is related to their experience of plausible reasoning teaching.In addition,there is a positive correlation between teachers' cognition of the importance of plausible reasoning and their teaching age and the region where they work.And the penetration of plausible reasoning in teachers' teaching is positively related to their understanding of the training requirements of plausible reasoning in the "Compulsory Curriculum Standard".(3)Using multi-factor analysis of variance to test the statistic F,it is found that the school category has a significant impact on teachers' cognition of the importance of plausible reasoning,and educational background has a significant impact on teachers' cognition of the basic meaning of plausible reasoning.However,provinces,work area,gender,teaching age,and professional title had no significant impact on teachers' cognition of plausible reasoning methods.According to the contour map drawn by estimating the marginal mean,the change of factors will influence the three components,and there is discipline between them.At last,combined with the survey conclusions and the teacher's interviews,the following suggestions are put forward for the mathematics of the senior high school entrance examination on plausible reasoning propositions:(1)broaden the types of test questions and strengthen the penetration of plausible reasoning by answering questions;(2)enrich the background of the test questions,such as exploring the materials in life,and penetrating the content of mathematical culture;(3)add analogy content and broaden the scope of knowledge examination.At the same time,the following suggestions are put forward to improve teachers' understanding of plausible reasoning methods:(1)provide relevant training for pre-service teachers(normal students)and in-service teachers;(2)study the plausible reasoning in the "Mathematics Curriculum Standards for Compulsory Education";(3)strengthen teachers' comprehensive understanding of the importance of plausible reasoning,and guide them to mine plausible reasoning resources in textbooks.