Integrating The History Of Mathematics Into The Teaching Of The Derivative:an Action Research

As a tool of studying the properties of a function, the derivative is an important part of senior high school mathematicss. The concept of derivative is often neglected because much attention is paid to its application and the concept of infinite is omitted. Due to the pseudo concept of derivative, the students’ comprehension of the properties of the derivative is deficient.In recent years, HPM is a popular topic in mathematics education and more and more relevant papers appear, of which most focus on theoretical analysis and only a few on teaching practice. None of the files are on integrating the history of mathematics into the teaching of the derivative, which is a gap in HPM research.In view of the situation of the teaching of the derivative and that of the HPM research, the author carried out an action research on integrating the history of mathematics into the teaching of the derivative, conducted to the students of liberal arts in an elite class and in an ordinary class in a key high school. The research consisted of two stages. The first stage was to integrate the history of mathematics into the teaching of the concept of the derivative, and the second one was to integrate the history of mathematics into the teaching of the application of the derivative. Three lessons were designed and given in the first stage and two lessons were designed and given in the second one. Two interviews and three questionnaire surveys were conducted in the process of the research. The first interview was designed to know about the current situation of the derivative teaching and was conducted to13mathematical teachers in a key high school. The second one was designed to know about the teaching effect and was conducted to8students who participated the action research.By analyzing the process of the action research and the interview and the survey materials, the following conclusions are arrived at:(1) Senior high school mathematics teachers usually help students to understand derivative concept by physical models and Geometer’s Sketchpad program, and to improve their ability to apply the derivative by designing specific problems. Most teachers acknowledge the value of mathematical history, but few of them use mathematical history in their classroom teaching.(2) Students have many representations of the concept of derivative, but lack organic construction. In the application of derivative, students’instrumental understanding is good but their relational understanding is poor. Participatants in this action research are better than those who didn’t participated the research in the concept and application of the derivative.(3) The cognitive value of the mode of integrating the history of mathematic into teaching lies in the instructional function of the history of mathematics which includes those of instructional element and historical element. The former is that history of mathematics is used to fulfill the teaching task and achieve instructional goal. The latter is that history of mathematics concentrates the genesis and development of concepts and contains the ancient thought, and is also an irreplaceable element for students to understanding concepts and mathematical thoughts.(4) The mode of integrating the history of mathematic into teaching is welcome by the students because of its immediacy and relish. History of mathematics improves students’confidence and persistence.(5) The teaching research of HPM makes teachers acquire a deeper understanding about mathematical concept, and contributes to teaching designs and practice. Furthermore, it helps teachers to promote professional development and research ability.Based upon the research conclusions, the following teaching suggestions are proposed at the end of the thesis.(1) For students’better understanding, more attention should paid to the teaching of the concept of derivative. The mode of integrating the history of mathematics into teaching helps students to understand the concept of the derivative.(2) The process of integrating the history of mathematic into teaching includes determining the objectives of teaching, selecting and dealing with historical materials, selecting the mode of teaching and classroom practising. Five problems should be paid attention to. The teaching goal should be set before selecting materials. The historical materials directly used or adapted should accord with students’ cognitive ability and help promote classroom teaching. They should form a whole and all parts should be joined. The suitable mode of integrating the history of mathematic into teaching should be selected.(3) The instructional researches of HPM for longer cycle and wider field have important significance to teaching and research.