Empirical Study On Errors Committed In Function Related Problem-solving By Senior One Students

In the overall processes of learning mathematics, students’mathematics learning errors, including errors in solving mathematical problems are inevitable to some extent. But from teacher’s perspective, we expect students to be able to grasp mathematical knowledge more successfully. Therefore, in-depth study of students’all kinds of errors in learning mathematics is very important. Error analysis and error correction are very important for mathematics instruction and mathematics education research.The concept of function is rich, profound, and widely used. It is one of the core topics in high school level mathematics. However, senior high school students are confronted a series of problems and have showed variety of errors in solving problems related to the topic of function. Therefore, an empirical study of problem solving errors in function learning by10th graders is needed, which has important theoretical and practical value.The study is based on high school mathematics textbook (compulsory one A version by PEP), and the three focuses are:(1) what types of errors are committed when senior one students solving mathematical problems related to function?(2) what are the main causes of these errors?(3) how could students correct these errors effectively?By reviewing researches on errors in mathematics learning (mathematical problem solving), the author selected appropriate research methods, elaborated the analytical frame work and chose the research tools, and so on. The main research methods used in this study are:literature analysis; interviews; task(paper) analysis; case studies and surveys, etc. These methods support and complement each other, so that we can successfully" overcome difficulties", and successfully complete the research tasks.The study analyzed students’errors in mathematics problem solving from the following perspectives:identifying problem-solving errors, analyzing error, correcting error, evaluating and improving correction program, which form the basic framework of the study. When analyzing errors students made in solving function-related questions, a specific analytical framework were used from four categories of errors: mathematical error, logic errors, strategic errors and careless errors. In addition,"error model" and error "reproduction rate" were also used in analyzing errors made by senior one students in this study. The textbook used by student participants is the compulsory one A version by PEP, which is the main teaching material analyzed in this study.The main research tools used in this study are:"Questionnaire on senior one students learning mathematics", and seven sets of "senior one math tests", which were specifically developed by the author. By the two research tools, a set of rich, vivid first-hand research data were collected, formed a solid "material base" for the research.Based on the existing researches, the author initially built the basic principles, the basic framework for error correcting, and the basic processes of correcting mathematical problem solving errors. The summary and reflection of individual counseling and classroom correction based on "problem-solving errors" were collected from the teaching practice.Through this study, the author has obtained the following conclusions:Firstly, more mathematical errors and careless errors have appeared in solving mathematical problems, rather than logic errors and strategic errors in addition, through in-depth analysis of series of the tests, it has been found that errors made by the10th graders have some "models" and "structures", which contributes to analyzing causes of errors, clarifying errors, and correcting errors.Secondly, based on the existing researches, the analysis of the seven tests in the study, as well as interviews with the students and the teachers, the author has drawn that the main causes of students’mathematical problem solving errors are: mathematics content factors, mathematics teaching factors and mathematics learning factors.Thirdly, individual counseling is an effective and important method for analyzing and correcting errors. Individual counseling is flexible, easy to be adjusted. Through individual counseling, the process of problem solving can be understood more deeply and more comprehensively. In addition, through individual counseling, we can understand the characteristics, habits, hobbies, ideological trends of the student’s, and individual counseling can also promote feelings between teachers and students, which all are benefit to study and correct students’errors.Fourthly, classroom correction based on "individual problem-solving errors" seems to be an efficient error correction method, as it is very convenient, and easy to be operated. Mathematics teaching, math homework, and math tests are important sources of collecting students’ mathematical problem solving errors. Modern technological tools can provide great convenience for collecting students’solving errors. Basic teaching material of classroom correction based on "individual problem-solving errors" is students’ problem-solving errors, All instructing activities focus on students’ problem-solving errors, the ultimate goal of which is to correct students’ errors more effectively and to eliminate students’ misconceptions more thoroughly...