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

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

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