The Theoretical Construction Of "History Of Mathematics-Inquiry" Teaching Model And Researching On Its Implementation Strategies

Since the International Study Group on the Relations between History and Pedagogy of Mathematics was founded over thirty years ago, the research of theories and implementation of HPM has developed rapidly. But when looking at the current situation of HPM, we will discover that comparing to the rich HPM theory, the research of implementing in classroom is very less systematic and stays at individual cases in which certain teachers apply certain historical contains in classroom. And whether individual cases of applying mathematical history can be extended to other teachers, schools or other levels is a moot point. Those are urgent problems to be solved in HPM research. On the other hand, our mathematics education or even the whole education is more and more incommensurate the need of the social and economic development in China, and is widely scolded by specialists and the persons concerned. The lost of the learners'creative ability has became an important problem which affecting the future development of our country. Our educating and teaching methods must be reformed in the angle of enhancing the learners'creative ability. So the inquiry teaching is advocated very strongly. Because the historical-genetic principle is the theoretical base of both HPM theory and inquiry teaching, we integrate them to solve the problems above concerned. The main results we have obtained in this paper are as follows:(1)In order to solve the problems in HPM practice system, we should start our research with the HPM theory itself at first. By further collecting and analyzing the concern literatures of HPM at home and abroad, we find that the cause of problem in the HPM practical research is that the HPM theory is rather miscellaneous and unsystematic. Hence, we anatomize the representative theories of HPM to this day by classification. In which the key is that we specifically separate "the way of using history in mathematics education" from "the arguments for using history" and reclassify them. In this way, we build a theoretical platform for teaching practice of HPM. Thus almost all the teachers who want to apply history of mathematics to mathematics teaching practice can find the corresponding application model through their specific teaching goals by this platform, and then implement it.(2)Through the above platform, in combination with the current situation of applying the history of mathematics to education in our country, and integrating the inquiry teaching that is vigorously promoted at present, this paper constructs the "History of Mathematics-Inquiry" teaching model by utilizing the worksheets, which are aimed at changing the learners'passive study and nurturing their creative ability. The content of the mode is as follows:Firstly, according to some key feathers of concept formation in its history, teacher analyzes and explores the potential barriers of students in the process of studying this concept. Secondly, teacher deconstructs the concept, and reconstructs it sequentially by the historical development process of this concept and the learners' cognition developing laws, then reorganizes the teaching process of the concept. Lastly, by the guiding function of the worksheets and the teacher's guide, let the learners go through the inquiry activities that mathematicians have experienced in the critical periods of the concept formation, and achieve the self-construction of the mathematical knowledge.(3)The paper provides the relative implementing strategies of the given model, and especially puts forward the relative strategies of enhancing the teacher's history of mathematics attainment, which plays an important role in implementing this teaching model. Owing to the given model and its implementing strategies, there is a performance model on the application in teaching of the HPM theory, which has established regular process and can be generally followed. It is very convenient for the general teachers to follow it repeatedly, and then to revise and perfect it. On the other side, the model solves the existing application problems both of HPM and inquiry teaching respectively, and achieves 1+1>2 integrated effect.(4)This paper constructs the evaluating system of the given model, and takes teaching experiments for the model. Experiments illustrate that this model is clearly superior to the traditional one in enhancing the students'performance and nonintellectual factors.In brief, based on the HPM theory and the built theory platform from it, integrating inquiry teaching, this paper constructs the "history-inquiry" teaching model and puts forward its relative implementing strategies.