High School Students' Research On Cognitive Process Of Mathematical Procedural Knowledge

Mathematics procedural knowledge is an important part of high school mathematics learning,it not only can affect the student's academic record,but also have certain influence on students' learning beliefs,learning enthusiasm and other various aspects.The reality is that many high school students can't understand mathematics procedural knowledge,therefore,it is very important to study the understanding process of high school mathematics procedural knowledge.The current researches on mathematical understanding mostly focus on the content, level,characteristics,functions,investigation and so on.there is almost no research on the psychological process of understanding procedural knowledge.On the basis of previous studies,combining with the current learning situation of high school mathematics procedural knowledge,I study the cognitive psychological process of understanding mathematics procedural knowledge of the high school in-depth,and put forward some corresponding teaching requirements and teaching suggestions based on the research.This paper mainly used the literature analysis,interview method,oral report method and other research methods.The order of this paper is:first,read a large number of literature related to the understanding of mathematics,review and summarize the mathematical understanding of the existing research at home and abroad;Second,read a lot of relevant literature of the procedural knowledge and mathematics cognitive understanding,analyze related theory;Third,establish the interview outline of teachers,and preliminarily determine the factors that influence the understanding of high school mathematics procedural knowledge through the interview;Fourth,develop interview outline of students,and eventually determine the influencing factors of the understanding of high school mathematics procedural knowledge through the interview;Fifth,undertake interviews to the students to determine what is the key factors influencing the understanding of high school mathematics procedural knowledge;Sixth, undertake interviews to the students,on the basis of the key factors influencing the understanding of high school mathematics procedural knowledge,sum up the cognitive understanding process,characteristics and model of high school mathematics procedural knowledge;Seventh,according to the above research results and conclusions, put forward the corresponding teaching requirements and teaching advice.In this paper,the main conclusions that we get are:First,there are mainly six factors influencing the high school students' understanding of mathematics procedural knowledge,they are the connection between the old and new knowledge,the related history,certificate,applications,principles and scope of application of mathematics procedural knowledge;Second, the key factors influencing the understanding of high school mathematics procedural knowledge is the connection between old and new knowledge;Third,the cognitive understanding process of high school mathematics procedural knowledge has some characteristics like initiative,continuity,sequentiality,delay,inertia,and quickness;Fourth,the cognitive understanding process of high school mathematics procedural knowledge is mainly the continuous improvement of the production system in cognitive structure of students.Specific processes are as follows:When students meet new mathematics procedural knowledge,they will search related propositional network in cognitive structure actively,and form the production after certain operations.By screening and combining these productions,simple production system take shape.If students are satisfied with the simple production system,then they will be in a state of false understanding.If students are not satisfied with the current state,they will continue to search propositional network in cognitive structure actively,and finally filter and combine productions into a complete production system to achieve real understanding.Finally,based on the above research results and conclusions,I put forward the following teaching requirements:first,improve teachers' knowledge reserves;Second,make specific mathematics teaching plan according to the specific procedural knowledge;Third,understand the high school students' cognitive level of mathematics procedural knowledge,pay attention to students' psychological mechanism; Fourth,realize the teacher's leading role and play the role correctly and effectively;Fifth,pay attention to students' dominant position;Sixth,pay attention to the excitation of students' learning motivation and learning enthusiasm.Teaching suggestions are as follows:first,don't give the template of solving problem,guide students to understand mathematics procedural knowledge;second, guide students to reflect, promote the understanding and acquisition of procedural knowledge; Third, communicate with students actively,evaluate students' learning situation in time;Fourth, formulate appropriate teaching situation and teaching content;Fifth,guide students to strengthen the connection between old and new knowledge, promote students to get systematic knowledge;Sixth, since the students' understanding level of mathematics procedural knowledge is different, teach students in accordance to their aptitude;Seventh,teach related principle,application and related history and other related knowledge of mathematics procedural knowledge more;Eighth,use appropriate materials to promote students to transform from false understanding to the real understanding.