The Application Status And Infiltration Research Of The Thought Of Combining Of Number And Shape In High School Mathematics

With the development of society and the renewal of educational concepts,the teaching of mathematical thinking and methods is increasingly being valued by people.The thought of combining numbers and shapes is an important mathematical idea,which plays an important role in mathematics education.Therefore,it is very necessary to study the application and penetration of the thought of combining numbers and shapes,so I combined my own teaching experience to carry out the investigation and research on this topic.First of all,based on previous research combined with the mathematical problems encountered by the author in teaching,literature research methods and case analysis methods are used in this article.And it summarizes the related concepts of the thoughts of combining numbers and shape.In addition,the textbooks and exam questions are also sorted out.And the author found that the application of the combination of number and shape thought is very widespread,and it is deeply examined in the college entrance examination,which produces high requirements for students' abilities.Secondly,this article studies the educational and teaching theory of the combination of number and shape.According to the viewpoint of constructivism,in teaching,teachers should create situations to inspire students to construct new knowledge based on previous knowledge.According to the theory of representation,teachers should pay attention to the multiple representations of mathematical objects and cultivate students'representation conversion ability.In addition,the teaching of the combination of number and shape must follow the teaching principles.Under the premise of student participation,the abstract into the concrete,step by step,systematically and repeatedly infiltrate the thought of combining number and shape.Subsequently,in this paper,the author uses the test paper survey method to investigate the students' understanding and application of the thought of combining numbers and shapes.The results of the survey found that:students' understanding of the combination of number and shape is relatively one-sided;students have different levels of awareness and ability to use the combination of number and shape in different knowledge points;students' ability to solve shapes with numbers is better than that with shapes to assist numbers,and their ability to take balanced account of numbers and shapes is poor;the overall application ability of the third-year students is better than that of the second-year students;the interview method is used to understand the conditions when students are answering and thinking,to summarize the problems that students have encountered in answering the questions.Through interviews with teachers,it is found that the teachers' emphasis on the thought of combining numbers and shapes is generally in exercises or review classes,and less in new classes.Young teachers will use information technology to assist in the teaching of combining numbers and shapes.Based on the results of the survey,in this article,the author deeply explores the penetration strategy of the thought of combining of number and shape,and puts forward several suggestions:? Make full use of teaching materials;?Use information technology to assist teaching;? Pay attention to the multiple representations of mathematical objects;?Penetration approach:experience the thought in the process of knowledge forming,activating the thought in problem-solving,summarizing it in topic review,and internalizing it in practice consolidation;?Cultivate students' habit of summarizing and reflecting;?Improve teachers' individual mathematics literacy.Finally,this article provides specific teaching examples.