| The ability to infer mathematical logic is crucial for mathematical learning and the growth and development of students.This article focuses on the critical period of students’ logical reasoning ability in eighth grade.Based on a literature review of logical reasoning ability,starting from the research background,the concept of mathematical logical reasoning ability in this study is defined.On the basis of Professor Yu Ping’s evaluation framework,a horizontal dimension is added,The research framework and evaluation criteria for this article were developed based on Professor Xu Binyan’s criteria for dividing the level of mathematical reasoning ability and the detailed rules for dividing the mathematics curriculum standards of ordinary high schools.Based on the framework and standards,the test paper and scoring rules for this study were adapted based on Teacher Yu Ping’s test paper,and a complete research tool for this article was obtained.With the help of research tools,this article selected eighth grade students from three junior high schools in three cities in Jiangsu Province to conduct a survey using the test papers developed.Based on the developed test framework and rating scale,the results of the test papers were collected,organized,and analyzed.Two frontline teachers were interviewed,and the following results were obtained:1.The overall mathematical logical reasoning ability of eighth grade students is at a moderate level,with the strongest simple reasoning ability and the weakest hypothetical reasoning ability;The internal statistical inference ability of the sample is the most stable,and the disjunctive inference ability fluctuates the most.2.There is no significant difference between students’ ability of deductive reasoning and plausible reasoning,and the difference between their mean values is not significant,but the stability of plausible reasoning ability within the sample is less than that of deductive reasoning ability.3.Students have achieved a moderate level of logical reasoning in solving problems with mathematical backgrounds that require mathematical knowledge,as well as in solving pure logical knowledge.The former has a slightly lower level than the latter,and the former has lower mean and stability than the latter.Therefore,the mastery of mathematical knowledge can affect the level of logical reasoning.4.The stability of students’ mathematical and logical reasoning abilities in the middle level is lower than that in the low and high level levels,and the number of students in the low level is much higher than that in the high level.5.From the perspective of gender,there is no significant difference overall,and both levels are at a moderate level of logical reasoning.The overall average score shows that boys are slightly higher than girls,but their internal stability is lower than girls.6.There is no significant difference in the level of logical reasoning between male and female students in both formal and content dimensions,but the stability of male students in both dimensions is slightly lower than that of female students.From a horizontal perspective,the proportion of male students in Level 2,Level 3,and Level 4 is relatively balanced,but female students tend to focus more on Level 2.7.From the perspective of regional differences,there are significant differences among the three cities.S city has reached level four,while Y city and Q city are both around level three,and the level of participants in Y city is relatively higher than that in Q city.There are significant differences in various dimensions between S city,Y city,and Q city,and both are due to Y city and Q city in terms of mean and stability.There is no significant difference between Y city and Q city in pure logical knowledge dimension except for content dimension.All other dimensions have significant differences,and overall,Y city has a higher mean than Q city but less internal stability than Q.By combining the research conclusions of the test paper with the results of teacher interviews,it was found that eighth grade students have issues such as excessive reliance on intuitive thinking,weak mathematical foundation,weak logical reasoning integrity,and low degree of conservative and divergent thinking.Teachers also have issues with how to balance teaching tasks and cultivate students’ logical reasoning ability.Based on the main issues of both,the following suggestions are proposed.In terms of teachers,first of all,teachers must attach importance to the cultivation of students’ mathematical and logical reasoning abilities.In the classroom,they must consciously keep the dual foundation teaching and ability cultivation on par;Secondly,in the process of cultivating students’ mathematical logical reasoning ability,teachers should consider their physical and mental characteristics during adolescence,adopt appropriate methods to stimulate students’ interest,and guide them to learn to think independently and be diligent in thinking independently;Finally,teachers should fully understand the physical and mental condition and knowledge level of each student,teach according to their aptitude,and take targeted measures to improve their reasoning skills.In terms of students,first of all,teachers encourage students to think diligently and not overly rely on intuition;Secondly,teachers should lead students to consolidate their knowledge foundation;Finally,teachers should encourage students to think from multiple perspectives and help them break away from conservative thinking tendencies. |
