The Application Research Of Polya Theory In The Teaching Of Conic Exercises

Exercise classes are an important part of mathematics teaching.Exercise teaching not only helps students to further master relevant knowledge,but also trains students' mathematical thinking methods and mathematical thinking skills,thereby further improving students' mathematical literacy.The conic curve is both an important point and a difficult point in high school mathematics learning.The related problems of the conic curve in the teaching of high school exercise classes are representative.This article selects the chapter of the conic curve,and tries to apply Polya's "How to Solve the Problem Table" to the teaching of the conic curve exercise class.Considering that the exercises in the conic curve exercise class are highly comprehensive and difficult,if the Polya theory is introduced for the first time in the exercise class,the students will be under greater pressure when mastering,and the effect will also be affected.Therefore,the author wants to use the Polya theory as a guide in the example presentations of the new lectures,lay a good cognitive foundation for the teaching of the exercise class,and make a good foundation.In order to apply theory to guide teaching practice in a targeted manner,the research questions of this article are as follows:(1)What types of problems do students have in solving problems before they start learning conic curves?(2)After learning the conic curve,what mistakes do students often make when solving the problem of conic curve?(3)How to apply Polya theory in the teaching of conic curve exercises to guide and improve students' existing problems?This paper mainly selects 78 students in the second grade of a high school in Songjiang District of Shanghai as the test object through the test paper survey method.The overall situation of the selected students in the class is relatively medium,which can represent the overall situation of the high school students in the area to a certain extent.Exercises are tested on the test subjects before and after learning the conic curve,and then the SOLO classification evaluation method is used to divide the cognitive level of the test object.The research conclusions of this article are as follows:(1)The main problems that students have in solving problems before learning the conic curve are the use of basic concepts,the lack of ideas for solving problems,the rigorous answering process and the lack of innovation awareness.(2)In addition to the above-mentioned problems,students also have other common problems: weak calculation ability,psychological exclusion,etc.(3)Aiming at the problem of students' use of basic concepts,in the exercise class teaching,you can sort and summarize the topic information through the list grid in the "understanding topic" link,and select useful basic concepts to apply;aiming at the problems that students lack in solving problems and unclear ideas,the process of thinking about problems can be strengthened in the process of "drawing up plans",this is also an innovation in this article;for students whose questions are not rigorous,you can standardize the students' answering process in the "execution plan";for the problem of students 'lack of innovation consciousness,through reflection and critical teaching in the "review" link,gradually cultivate students' divergent and innovative consciousness;for the problem of students' weak calculation ability,teachers can demonstrate the calculation process during "execution plan" to help students build confidence.