Investigation And Research On Non-logical Thinking Of Mathematics In Middle Schools In Ethnic Regions

Mathematics is a discipline with strict logic and systematic formalization.Overemphasizing the cultivation of logical thinking will cause students in a stereotyped thinking pattern.Science and invention in mathematics are not only related on the rules of logical thinking,while non-logical thinking is the source of innovative thinking.The keys of mathematics education should pay attention to the cultivation of non-logical thinking and logical thinking.There is a cross-cultural phenomenon in mathematics education in ethnic areas,meanwhile the conception of education lags behind.How to improve the innovative awareness of middle school students in ethnic areas has become a problem that local educators must focus.This study concentrated on the current situation of students' non-logical thinking in Mathematics,and puts forward suggestions to cultivate students' non-logical thinking to promote the development of students' innovative thinking in ethnic areas.This study mainly used literature review method to analyze the connotation and characteristics of illogical thinking,clarify the basic relationship between illogical thinking,innovative thinking and logical thinking,and modify the questionnaire of middle school students' mathematical illogical thinking in ethnic areas.This paper used questionnaire to know the current situation of middle school students' mathematical illogical thinking in Shui nationality area,and to explore whether there are Significant differences between middle school and high school students' illogical thinking.The interview method was used to grasp the understanding of the first-line teachers in the Shui nationality area on the illogical thinking and whether the teaching method of the teachers in the minority area is conducive to the cultivation of the students' illogical thinking.Based on the research of many scholars on illogical thinking,four dimensions of illogical thinking(divergent thinking,associative thinking,intuitive thinking,inspiration thinking)are determined.886 middle school students from two junior high schools and two senior high schools in Shui nationalityarea were investigated.After collected questionnaires and analysis through mean test,correlation analysis,factor analysis and principal component analysis,the following conclusions were obtained:(1)Through the independent sample t-test and one-way ANOVA homogeneity test of gender,grade and different schools,the Sig value is less than 0.05,which showed that there were Significant differences in students' illogical thinking level among different gender,grade and school in Shui nationality area.(2)Through the comparative analysis of the average value of non-logical thinking of middle school students from Grade 8 to Senior 3,the results showed that:with the increase of grade,the level of students' non-logical thinking is lower;for the comparative analysis of the average value of student' innovative thinking,it is also with the increase of grade,the students' mathematical innovation ability is lower.It showed that the more knowledge and experience the middle school students have,the more serious their thinking pattern will be.(3)Through the correlation analysis of illogical thinking and innovative thinking,Pearson correlation coefficient is 0.712,Sig = 0.000 > 0.01,it indicated that the correlation between illogical thinking and innovative thinking is Significant;the Pearson correlation coefficient is 0.357,between 0.30 ? 0.50,which indicated that illogical thinking and mathematical performance were positively correlated,Sig =0.000.(4)Through multiple comparative analysis of students' illogical thinking among different grades in Shui nationality area,the results were as follows: there were Significant differences in illogical thinking between Grade 8 and Grade 9 to Senior 3;there are Significant differences in illogical thinking between Grade 9 and Senior 3;there are Significant differences in illogical thinking between Senior 1 and Senior 2,and there are Significant differences in illogical thinking between Senior 1 and Senior3.(5)Through interviews with teachers and students in Shui nationality area,it showed that the education conception of local teachers is relatively backward.,which influenced by the teaching progress and the pressure of entering school,the teachingmode is not conducive to the cultivation of students' illogical thinking,and the teaching process of teachers and students is not harmonious is the reason that classroom atmosphere are not active.According to the research conclusion and the characteristics of non-logical thinking,the current situation of non-logical thinking of middle school students in Shui nationality areas,three suggestions are as follows: changing teachers' traditional teaching conceptions,changing students' traditional learning methods,establishing new differences,basing on the classroom,and breaking through students' thinking patterns.