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Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education Yuxin Zheng Nanjing University

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Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education Yuxin Zheng Nanjing University Humanistic Mathematics Network Journal Issue 9 Article 9 2-1-1994 Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education Yuxin Zheng Nanjing University Follow this and additional works at: http://scholarship.claremont.edu/hmnj Part of the Logic and Foundations of Mathematics Commons, Mathematics Commons, Scholarship of Teaching and Learning Commons, and the Science and Mathematics Education Commons Recommended Citation Zheng, Yuxin (1994) "Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education," Humanistic Mathematics Network Journal: Iss. 9, Article 9. Available at: http://scholarship.claremont.edu/hmnj/vol1/iss9/9 This Article is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted for inclusion in Humanistic Mathematics Network Journal by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Philosophy of Mathematics, Mathematics Education and Philosophy of Mathematics Education Zheng Yuxin (Y. Zheng) Department of Philosophy Nanling University. China (P. R. C.) As a philosopher of mathematics. I have been the great infl uence of the philosophy of thinking about, or rather, worried about the mathematics on mathematics education. The third follow ing qu esti on: is there any important section discusses the problem of how to develop rel ation ship between the philosophy of the subject 'philosophy of mathematics education , mathematics and actual mathematical activities which in fact can be regarded as an impetus from (including mathematical research, teaching and mathematics education to the further development learning)? Or, does the philosophy of mathematics of philosophy of mathematics and philosophy in have any important infl uence on act ual general. mathematicalactivities? I think the answeris 'yes'; and I have also tried to do some things in this direction by working in the field of methodology of 1. New Developments of Mathematics Education While the advancement of hum an Mathematics education in the USA is now society, is the most importan t undergoing a new reform movement, to which Eyerybody CouOls, published by the National external impetu s, it is the Research Council in 1990, gives the following theoretical studies of mathematics description: education during the past decade "Over the next cwo decades, the nation's schools, which have laid the necessary colleges, and universities will undergo major transitions in mathematics programs-s-transitions foundation for the new reform that will involvefundamental changes in curricular movement. content, in modes of instruction, in teacher education, in profe ssional development , in methods of assessment, and in public attitudes," mathematics (cf. Y. Zheng, 1985, 1991a, 1991b). (p.87) But it is only a personal opinion and has limited influence, so when I came to the USA as a visiting While the advancement of human society, i.e. the scholar in 1991, this problem was still deeply transition from the industrial age to the infonnation rooted in my mind. However, what I have learnt age, is the most important external impetus, it is the in the field of mathematics education in the USA is theoretical studies of mathematics education during really a great pleasure for me, as it does show the past decade which have laid the necessary clearly that there is a close relationship between the foundation for the new reform movement. In this philosophy of mathematics, mathematics education sec tion, we ma ke a brief survey of the ncw and mathematics as well: it is modem research in theoretical studies. They are chiefly: the emphasis the philosophy of mathematics which offers the on probl em so lving , the psychology of necessary ideological foundation for the new mathema tical learning, and the social-cultural reform movement of mathematics education in the approach to mathematics education. USA, and then, in this way, the philosophy of mathematics can exert a great influence on the (1). The emphasis on problem solving future ofmathematics, ' Problem Solving' was the main slogan for The first and second parts of this paper will use the mathem atics education during the eighties. modem development of mathematics education in "Problem solving must be the focus of school the USA as a background to make an analysis of mathematics" (NCTM, 1980, p. 2); and by 32 HMN Journal #9 'problem solving'. it means ' to use a variety of behavior' but penetrate into the inner infonnation mathematical knowledge and methods effectively to processing of the mind, including the storage. solve nonroutine problems. including both actual retriev al , representation , development of problems and those originated from mathematics knowledge and so on. Also.the so-called itself. 'constructivist view' can be regarded as a main conclusion of cognitive psychology: as far as Putting forward the idea of focusing on problem mathematics learning is concerned. it asserts that solving is a giant step for mathematics education. the learning of mathematics is not a passive because the idea represents a great shift in the reception but a process of construction based on conception of mathematics education, i.e., the idea previous experience and knowledge. itself is a direct negation of the traditional conception of mathematics education, especially, If the idea "focusing on problem-solving" is a the teaching method based on 'transmission of direct negation of the traditional concept of information' and the trend of 'separating learning mathematics education, then the cognitive studies from application'. To explicate, the key points of of mathematics learning, especially the 'focusing on problem solving' are as follows: constructivist view of mathematics learning. have First. students should learn mathematics by the offered further arguments for this fundamental activities of solving problems. That is, "'knowing' transition from the microscopic view. And just for mathematics is 'doing' mathematics ....instruction should persistently emphasize 'doing' rather than 'knowing that' ... (NCfM, 1989, p. 7) Second. by we should take as a background the solving problems, especially those having actual whole culture of human society in meaning. students can learn to value mathematics, and become more confident in their own the study of mathematics education. mathematical abili ty. Third, the final aim of This is to say, mathematics mathematics education should be to improve education should represent clearly students' ability of problem solving, especially the features of the time. help them leam to think mathematically. Generally speaking, the idea that problem solving this reason, the constructivist view on mathematics must be the focus of school mathematics is now leaming has recently attracted great attentionsin the widely accepted; and as this idea is directly field of mathematics education. For example. as opposit e to the traditi onal conception of R. Davis, C. Maher and N. Noddings say in mathematics education, it is said that ' solving Constructivist Views on the Teachin& and Leamine nonroutine problems is the central theme of the of Mathematics: current reform movement in school mathematics.' (T. Romberg, 1991, p. 9) 'The idea of "constructivismt-s-hardly mentioned a few years ago-nowadays attracts a lot ofattention (2). The emphasis on th e psychology of in the world of mathematics education. A great mathematical learning many people now think and write about it. andthe people who do so do not agree with one another The study of the psychology of mathematical ..Still, beneath the theoretical argumentation. there learning is itself a result of the further development is a substantial agreement about the nature 0/ of psychology: it has been beyond the level of learners, the nature 0/ mathematics. and the general study and penetrated into special fields. appropriate form of pedagogy." (R. Davis, C. Furthermore, where modern studies of the Maher and N. Noddings / 99/, p. / 87) psychology of mathematics learning are concerned, we should pay more attention to the cognitive (3). The soclat-cultural approach to science approach to mathematics education and"the mathematics education constructivist view of mathematics learning". The first implication of the social-cultural study of To explicate. the basic position of cognitive mathematics is that we should take as a background psychology is that the study of psychology should the whole culture of human society in the study of not (as behaviorists suggest) be limited to 'visible HMN Journal #9 33 F mathematics education. This is to say. of some conception of mathematics and mathematics education should represent clearly the mathematics education, and the latter are in fact features of the time.In fact, it is exactly the most manifestations of the social nature of mathematics important feature of the new reform movement of education. Secondly, as far as students are mathematics education in the USA: it is the concerned. the importance ofconception lies in the transition from the industrial society to the fact that mathematics learning is a process in which information society which offers the most not only mathematical knowledge is constructed important impetus to the movement, and the final but also some conception, belief and attitude of aim of the movement is to create the kind of mathematics are formed, and the latter in tum will mathematics education that not only meets the
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