-
Boykova Daria Valeryevna -
Moscow State University (MSU);
Moscow State University of Civil Engineering
(MGSU)
postgraduate student, Department of Philosophy
and Methodology of Science
Assistant Lecturer, Moscow State University (MSU);
Moscow State University of Civil Engineering
(MGSU), Building 4, 27 Lomonosovskiy prospekt,
Moscow, 119991, Russian Federation;
26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
This e-mail address is being protected from spambots. You need JavaScript enabled to view it
.
Teaching mathematics may be equally interesting for teachers and philosophers of science.
Nonetheless, mathematical education was no popular topic for discussion for a very long time. The
main issue was the problem of fundamentals of mathematics. However, mathematical education
was no mere transfer of knowledge. Mathematical education is a reproduction of knowledge; moreover,
it is a way of existence of mathematical knowledge. In this connection, modern philosophy of
mathematics believes that humanism is a relevant area for thorough consideration. In this article,
we will talk about it with account for the book of American mathematician and philosopher Reuben
Hersh entitled "What's Mathematics, Really?".
One of the main ideas of the humanist philosophy of mathematics is that mathematics is a
social, cultural, and historical reality. Mathematics is what mathematicians do. It changes; therefore,
the criteria of its strictness change, too. Mathematical education is one of types of mathematical
practice. Valid philosophy of mathematics should be compatible with mathematical practice, so, the
study of mathematical education falls within the subject matter of the philosophy of science.
Reuben Hersh connects success of mathematical education with the notion of the nature
of mathematics. He compares three viewpoints concerning its nature: Platonism, formalism and
humanism, and their influence on the mathematical education. Platonism can justify a student who
isn't successful in mathematics: mathematical objects are just in the other world and this world
isn't available for everyone. Formalism isn't compatible with mathematical practice: mathematical
assertions are meaningless symbols. However, whenever one is teaching mathematics, mathematical
assertions have the same meanings as they do in the mathematical research. The goal of the
education is the understanding rather than formal correctness of sequences of symbols. Humanism
accepts informal and incomplete proofs. In addition, R. Hersh demonstrates that there are no formal
complete proofs in real mathematics. Mathematics doesn't need them. Students learn mathematics
by solving problems, making calculations. And it's not an easy version of mathematics, because in
scientific research mathematicians solve problems and make calculations, too. Whatever mathematicians
teach determines the rules of mathematics.
DOI: 10.22227/1997-0935.2012.9.259 - 263
References
- Hersh R. What’s Mathematics, Really? Oxford University Press, 1997, 368 p.
- Davis P.J., Hersh R. The Mathematical Experience. Cambridge, Birkhauser, 1981.
- Kitcher P. The Nature of Mathematical Knowledge. New York, Oxford University Press, 1983.
- Ernest P. The Philosophy of Mathematics Education. New York, Falmer, 1991.
- Asmus V.F. Problema intuitsii v filosofii i matematike [The Problem of Intuition in Philosophy and Mathematics]. Moscow, Mysl’ Publ., 1965, 312 p.
- Gil’bert D. Osnovaniya geometrii [Fundamentals of Geometry]. Petrograd, Seyatel’ E.V. Vysotskogo Publ., 1923.
- Veyl’ G. Matematicheskoe myshlenie [Mathematical Thinking]. Moscow, Nauka Publ., 1989, 400 p.
- Tselishchev V.V. Poiski novoy filosofii matematiki [The Search for a New Philosophy of Mathematics]. Filosofiya nauki [Philosophy of Science]. 2001, no. 3(11), pp. 135—148.
- Petrov Yu.P. Istoriya i filosofi ya nauki. Matematika, vychislitel’naya tekhnika, informatika [History and Philosophy of Science. Mathematics, Computer Facilities, Information Science]. St. Petersburg, BKhV-Peterburg Publ., 2005, 448 p.
- Uspenskiy V.A. Prosteyshie primery matematicheskikh dokazatel’stv [Simplest Examples of Mathematical Proofs]. Moscow, MTsNMO Publ., 2009, 56 p.
- Davies B. Whither Mathematics? Notices of the American Mathematical Society. December 2005, vol. 52, no. 11.
-
Pamyatusheva Viktoriya Viktorovna -
Moscow State Academy of Municipal Economy and Construction (MGAKHIS)
Candidate of Philosophical Sciences,
Associated Professor, Moscow State Academy of Municipal Economy and Construction (MGAKHIS), 30 Srednyaya Kalitnikovskaya St., Moscow, 109029, Russian Federation;
This e-mail address is being protected from spambots. You need JavaScript enabled to view it
.
The present-day Russian society is undergoing profound structural social and cultural transformations.
The existence of the Russian society and the relevance of problems of science and
education are playing a key role in the present-day social and economic environment. A high level
of skills acts as the main source of material prosperity and advancement of the Russian science
and culture.
This level is attainable through the involvement of universities and the professional education
that they provide, namely, professional training at universities. Undoubtedly, it is necessary to
improve the quality of teaching and science management at undergraduate and graduate levels.
In addition, there is a pressing need to develop and to implement a youth research policy and to
consider the problems of youth within its framework. Third, there is a need to decide on the postponement
of the army service for full-time students and postgraduates. Fourth, there is a need to
reconsider the remuneration.
The research work of graduate students in a specialized field of knowledge is based on the
foundation of general knowledge, including the philosophy of science. The study of philosophy and
philosophy of science facilitates the development of skills of young researchers and their heuristic
thinking. Researchers specializing in the philosophy of science should focus on the new areas in
their research and generate a new vision of their own problems to refocus the mode of thinking of a
young scientist. Currently, besides the growing complexity of the post-graduate research that serves
as the reason for (i) the growing need for its information support, (ii) its longer duration, and (iii)
the need for sophisticated process equipment required for experimental studies, profound changes
in the relationship between theoretical and applied knowledge and domination of the former are
underway. The centre of gravity is transferred into the sphere of the sciences of man and society.
Whoever believes that his or her objective is to to link their lives with the science of the XXI
century, whoever thinks about developing new technologies, increasing the production rate and
the economic well-being of our society as a whole, must, above all, understand that he or she is
dependent not only on the laws of the market, but on the will to live a life the main value of which is
a harmonious development of a personality, human rights, social stability, and education rather that
the profit generation.
DOI: 10.22227/1997-0935.2012.9.264 - 271
References
- Toynbee A.J. Issledovanie istorii [The Research of History]. Moscow, 2006, Oleg Abyshko Publ., 2006.
- Zakharov V.E. Chto i kak nado spasat’ v rossiyskoy nauke [What Is to Be Saved in the Russian Science and How It Should Be Done]. Nezavisimaya gazeta [Independent Newspaper]. Available at: http://www.ng.ru/science/2010-01-13/12_ran.html. Date of access: 03.07.12.
- Balabanov S.S., Bednyy B.I., Kozlov E.V., Maksimov G.A. Mnogomernaya tipologiya aspirantov [Multi-dimensional Typology of Postgraduates]. Sotsiologicheskiy zhurnal [Journal of Sociology]. 2003, no. 3, pp. 147—160.
- Rakitov A.I. Budushchee natsii: nauka, tekhnologiya, obrazovanie — reshayushchiy faktor blagosostoyaniya i sotsial’no-ekonomicheskogo razvitiya Rossii [The Future of the Nation: Science, Technology, Education as Decisive Factors of Prosperity, Social and Economic Development of Russia]. Available at: http://istina.inion.ru/html/rak1.html. Date of access: 03.07.2012.
- Rogov S.M. Rossiya dolzhna stat’ nauchnoy sverkhderzhavoy [Russia Is to Become a Scientific Superpower]. Vestnik Rossiyskoy akademii nauk [Bulletin of the Russian Academy of Sciences]. 2010, no. 7, pp. 579—590.
- Nalivayko N.V., Panarin V.I., Parshikov V.I. Global’nye i regional’nye tendentsii razvitiya otechestvennogo obrazovaniya (sotsial’no-filosofskiy analiz) [Global and Regional Trends in the Development of Education (Social and Philosophical Analysis)]. Novosibirsk, SO RAN Publ., 2010.
- Porus V.N. Filosofi ya nauki dlya aspirantov: experimentum crucis [The Philosophy of Science for Post-graduate Students: Experimentum Crucis]. Mysl’ Publ., 2008, no. 7, pp. 9—22.
- Zobov V.N. Filosofi ya nauki: problemy i perspektivy [Philosophy of Science: Problems and Prospects]. Filosofi ya i nauka: al’manakh po filosofi i obrazovaniya, evristike, metodologii i metodike prepodavaniya sotsial’no-gumanitarnykh distsiplin [Philosophy and Science: Collected Works in the Philosophy of Education, Heuristics, Methodology and Methods of Teaching Social and Humanitarian Disciplines]. St. Petersburg, SPGU Publ., 2006.
- Habermas J.H. Filosofiya kak «mestoblyustitel’» i «interpretator». Moral’noe soznanie i kommunikativnoe deystvie [Philosophy as a «Locum Tenens» and «Interpreter». Moral Consciousness and Communicative Action]. St. Petersburg, 2000, pp. 8—9.
- Mamzin A.S. Kak prepodavat’ filosofiyu nauki aspirantam spetsial’nykh fakul’tetov [How to Teach Philosophy of Science to Post-graduate Students of Specialized Departments]. Filosofiya i nauka: al’manakh po filosofii obrazovaniya, evristike, metodologii i metodike prepodavaniya sotsial’no-gumanitarnykh distsiplin [Philosophy and Science: Collected Works in the Philosophy of Education, Heuristics, Methodology and Methods of Teaching Social and Humanitarian Disciplines]. St. Petersburg, SPGU Publ., 2006.