The Development And Teaching Research Of Junior High School Students' Logical Reasoning And Intuitive Imagination Ability

Key competency embodies the necessary of lifelong development and social development,the cultivation of students’ key competency is a task entrusted to education by the age.For a long time,the ability of logic reasoning and intuitive visualization have been the goal of mathematical education,now proposed as key competency,not only the continue of traditional,but also contains new meanings.Focusing on the ability of logic reasoning and intuitive visualization of junior high school students,a series of researches have been earried out,which belong to two threads.A main thread is the revealing of regularities of the development of two abilities,the correlation between two abilities,and a teaching experiment which studied the effect of visual method in the learning of modus ponens.The branch is exploring of the value of the two abilities,their effects on mathematics performance and the solving of open-ended problems were studied.The specific research questions are as follows:1.What are the regularities of junior high school students’ development of logic reasoning ability?2.What are the regularities of junior high school students’ development of intuitive visualization ability?3.What is the correlation between the ability of logic reasoning and intuitive visualization?4.Do the two abilities have effect on mathematics performance and the solving of open-ended problems?How are the effects?5.Does visual lethod in the learning of modus ponens promote understanding and transfer?Such researches rely on the assessment of two abilities.Basing on review of journals and theoretical thinking,the fralnework of assessment of logic reasoning and intuitive visualization have been constructed,and according to the frameworks,two tests:"Test of Logic Reasoning ability of Junior High School Students" and "Test of intuitive visualization ability of Junior High School Students" have been designed.After item analysis,exploratory factor analysis and reliability analysis,the tests are good in construct validity and reliability.Samples are more than 4000 students from 8 provinces.Teaching experiment is designed according to the result of assessment,the core is the visualize of modus ponens.Research results are as follows:1.The development of logic reasoning ability runs through the whole junior high school period,the growth of modus ponens is the most;Performance of key school students are better than students from normal schools,but the diversity reduces after two years;Ability of logic reasoning of junior high school students are effect by the understanding of relationship of mathematical concepts,as well as the form of reasoning.2.The development of intuitive visualization ability appears between grade 8 and grade 9,which ean be found in every dimensions of the ability.At the same time,the diversity between students from different areas increases.Junior high school students are lack in both the ability and inclination of visualizing.3.Correlation between logic reasoning ability and intuitive visualization ability is high in junior high school students.On the one hand,the process of logic reasoning rely on spatial factor;on the other hand,spatial manipulation contains using of rules.4.The two abilities both have middle level correlation with mathematics performance and the solving of open-ended problems,and significantly influence mathematics performance and the solving of open-ended problems.The effect of visualizing and deduction are direct.5.The effect of visual method is available only for those who have high ability of intuitive visualization,the visual understanding of modus ponens can promote the transfer to other form of reasoning and situation.6.For the development of logic reasoning and intuitive visualization ability,suggestions can be made from two perspectives.One is for the design of mathematics curriculum and textbooks:the content of curriculum and textbooks should be arranged according to the regularities of junior high school students’ development of logic reasoning and intuitive visualization ability;logic reasoning should be involved in different areas.The other is for teacher and teaching:rethink the value of inductive reasoning,emphasize the plausibility of inductive and analogy reasoning;respect difference between students,emphasize the importance of visualizing fundamentally;deepen understanding of mathematics,explore the necessary of ability in learning knowledge;using different form of propositions to construct relations between concepts.