Research On The Application Of Reverse Thinking In Middle School Mathematics Teaching Under The New Curriculum Standard

Under the background of the new curriculum standard,new requirements have been put forward for the teaching and learning of thinking in mathematics teaching.It is clear that the key to the implementation of liberal education in mathematics teaching is to develop students' thinking ability,this is also the core of mathematics subject quality education.In the activities of mathematics teaching and learning in senior high schools,the reverse thinking should be introduced properly and the students should be guided to apply it.In the teaching consciously and systematically infiltrate the training of reverse thinking,can change the mind set of students,to improve the sensitivity,creativity and profundity of students' thinking.It makes students understand mathematical concepts,principles,formulas and theorems more deeply,and can grasp and apply them accurately.Based on this realistic background,this paper makes a clear definition of the contrary thinking,take the reverse thinking related concept and the Theory Foundation as the theory support,pointing out the necessity of reverse thinking in the middle school stage,the application of converse thinking in middle school mathematics teaching is demonstrated.The research on the application of reverse thinking in middle school mathematics mainly includes two aspects.First,the application of reverse thinking in the knowledge modules of solid geometry,function,trigonometric function and probability and Statistics is studied,The application of reverse thinking in the field of function mainly includes reverse thinking in the domain of function definition,monotonicity parity of function;the inverse function and comprehensive application are mainly used to prove parallel and vertical relations in solid geometry;reverse thinking in trigonometric function module is mainly used in theorem definition,image transformation and domain of definition;The application of reverse thinking in probability and statistics mainly includes the application in probability model and theapplication in permutation and combination,each knowledge module enumerates several examples,the importance and necessity of reverse thinking in every point of knowledge are pointed out by examples.Second,Studying the application of reverse thinking in middle school mathematics teaching strategy,mainly studying the teaching strategy of anti-case method,the teaching strategy of complement method and the teaching strategy of carrying out the result and exploring the cause,the counter-example teaching strategy is mainly embodied in the application of Reductio Ad Absurdum,the complement teaching strategy mainly studies its application in Algebra and geometry,and the counter-example teaching strategy mainly studies its application in the classroom and the construction method,through the study of these teaching strategies,the practicability and universality of reverse thinking in middle school teaching methods are illustrated.Through the questionnaire investigation,it is shown that the current situation of the application of reverse thinking in middle school teaching,the students' understanding of the concept and method of reverse thinking is not in place at this stage,and the application of reverse thinking in practice is not enough,the method and theory of reverse thinking is very limited in teaching,which makes the applied research of reverse thinking more meaningful in middle school mathematics teaching.Finally,through the example and the data research reverse thinking in the middle school mathematics teaching application effect,the experiment takes one of own three classes as the experimental group,during the second semester of senior high school,the other two classes were used as the control group to carry out routine teaching.The average scores,passing rate and standard deviation of the three monthly examinations,mid-term and final examinations were compared,compared with the two control bar,the results of students in the experimental class were improved.SPSS19.0 was used to analyze the significant difference.Applying the analytic hierarchy process(AHP)to analyze the examination results in different levels and categories,it is concluded that the application effect of reverse thinking of excellent students and good students is remarkable,and that middle students also have relatively remarkable effect,it provides more convincing force for the importance of reverse thinking in middle school mathematics.