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PROBLEMS OF HIGHER EDUCATION IN CIVIL ENGINEERING

Reproduction of mathematical knowledge in the educational process from the viewpoint of humanistic philosophy of mathematics

Vestnik MGSU 9/2012
  • 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 .

Pages 259 - 263

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
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