Junior High School Students To Understand The Reason Of Difficulty Of Quadratic Function Of The Actual Problems And Countermeasures

Quadratic functions are important and difficult for Junior high school students as well as thebasis for senior high school students. Solving practical problems by virtue of the knowledge ofquadratic functions is one of the hot issues of entrance examination for secondary school. Inrecent years, the comprehensive problems on quadratic functions were often regarded as thecrucial one of test paper for the entrance examination of secondary school. Understanding andmastering of quadratic functions’ image and properties is learning focus for junior high schoolstudents. They are required to draw quadratic functions’ image and observe implicit informationfrom it. Meanwhile, they are also required to investigate properties of image and solvepractical problems by virtue of the image of quadratic functions. The students find it verydifficult to solve practical problems involved in quadratic functions. The main reason isincomprehension not only on the concept of quadratic function but also the meaning of practicalproblems. The present paper investigates the reason why students find it hard to understandpractical issues involved in quadratic functions.At first, it is stated that why present paper investigates such problem. Meanwhile, researchstatus on practical issues involved in quadratic functions is summarized. By comparing andanalyzing the references, the related research on this topic mainly focused on the following threeaspects. One is the standing on functions. Another is how to solve and the method、strategy tosolve practical issues. The other is the study on solving practical issues involved in quadraticfunctions. However, there is no paper concerned with the study on junior high school students’understanding difficulty for practical problems involved in quadratic functions. The purpose ofpresent paper is to fill this gap. The cause of difficulties and corresponding countermeasures forjunior high school students to understand the practical problem involved in quadratic functionsare investigated.Secondly, we state all kinds of understanding theories and what are the understandingdifficulties. Then we obtained that the understanding is to obtain new knowledge by virtue of theknown one, to construct their relationship, and to unite it to be a part of individual cognitive structure. The key of understanding is construct the relationship between the new and the knownknowledge, the relationship between the new concept and its subordinate concept, therelationship between the new concept and its relevant concept. The understanding difficulty isthat the student could not correctly master or not completely obtain the new knowledge by theknown one and subjective effort and then the thinking bias or thinking fragment occur during theprocess of knowing the nature and the law.Thirdly, we studied the difficulties of understanding practical issues involved in quadraticfunctions and why these problems emerge by using investigation methods such as questionnaires,interviews, questionnaires, tests, and so forth. The results showed that the main reasons why thejunior high school students found it difficult to understand the actual problems of quadraticfunctions are as follows:1. The difficulties from mastering and understanding well the keywords and sentences;2. The difficulties from being unfamiliar with technical terms;3. The difficulties from obtaining some information by graphs;4. The difficulties from analyzing quantitative relation;5. The difficulties from constructing appropriate rectangular plane coordinate system;6. The difficulties from the relationship between the data in questions and coordinates ofpoint in graph of functions;7. The difficulties from analyzing the changes of all kinds of quantities.The reasons why the above difficulties emerge are as follows:1. shortage of reading ability, not developing good reading habits;2. not learn basic definitions and concepts well;3. lack of life experience;4. the low ability on symbolic-graphic combination;5. not mastering and understanding well for the basic knowledge on quadratic functions;6. not developing good habits of summarizing and introspection, the objective is only tosolve questions.Finally, some teaching countermeasures corresponding to difficulties mentioned above areput forward, which come from three aspects such as emphasizing formation procedure offundamental knowledge and concepts, habit formation and ability training, and emotional attitude training of students.1. strengthening students’ ability understanding and mastering the basis of the quadraticfunction;2. emphasizing formation procedure of concept;3. enhancing reading ability of the students and developing good habit of reading;4. developing habits of summarizing and introspection;5. training student’s ability of symbolic-graphic combination;6. stimulating students’ study interest and heightening their self-confidence.