Junior High School Mathematics Textbooks Function Content Processing Research

As modern mathematics development shows, function is the basic concept of describing movement and variation. Many concepts in mathematics are derived from function, commanded by function or based on function research. That is to say, the forming of the function concept itself indicates the significant transition of thoughtway in mathematics—from constant mathematics to variable mathematics. The application of function leads to radical change in mathematics, including objects, theory, method and structure. Based on these reasons, when it comes to secondary mathematics, function is important without doubt. It has been the ligament of secondary mathematics but one of the most difficult concepts as well. Therefore, how should students' function concept be developed? How can the textbook compilation help students form the function concept better? Based on the previous research results, the function content in the old edition of PEP textbook and Beishi textbook is regarded as the research object in this paper. The main research is as follows:1. Holistic comparative research on the compilation of function content in two textbooks. Two aspects in the two textbooks are compared, including "the arrangement of different chapters on function" and " the sequence of function, equation and inequality". The teaching content in the old PEP textbook is based on the logic of function knowledge and is compiled in the order of "number—formula—equation, inequality—function". Beishi textbook is learner-oriented on choosing function content. It orients to learners' cognitive situation and finally to the role of function in social life. Meanwhile, the main line of function constructs the knowledge system of connecting function, equation and inequality.2. Comparative research on specific problems of compiling function content in two textbooks. Two aspects in the two textbooks are compared, including "on function concept" and "on function image". It is found that, old PEP textbook focuses on abstract speculation of function concept and regards function as the math knowledge with the logical method, which emphasizes on the comprehension and grasp of function expressions. In addition, function image demands that students be able to draw function image and analyze the quality of function by using function image. However, in the process of building up, infiltrating and deepening the function concept, Beishi textbook emphasizes on lead-in through number forms in the real situation, description of various functions and connection of function, equation and inequality. It regards function image as one of the function concepts, attaching importance to analyzing the relations of functions by understanding and applying the function image and solving the problems in the real life.3. Characteristic analysis of Beishi Textbook. Dealing with the function concept, Beishi Textbook pays more attention to the law of students' cognitive development, their way of studying, teachers' way of teaching and cultural value of mathematics.It is the constantly-pursuing object for math teaching in the future to further penetratefunction ideology, strengthen the connection of function and relative subjects, even real life, andenhance the role of computer science in function studying.