Abstract:

Central European mathematics teaching generally began in the middle of the 18th century by introducing compulsory school education in Austria, Hungary, and the Czech lands. The obviously applied praxis of teaching emerged from the previous history of education influenced mainly by John Amos Comenius in this region. Elementary education in reading, writing, and arithmetic was provided, but most secondary education was open only to those who could afford it. In the 18th and 19th centuries, the industrial revolution required at least some basic numeracy skills. Within the new public education systems, mathematics became a central part of the curriculum from an early age. By the time of World War 1, the major nations had given further attention to secondary education. During the twentieth century, mathematics education was established as an independent field of research.

The eternal problem of math education is to find the equilibrium between the required basic knowledge and time devoted to the creative investigation in group teaching with respect to all members of the group. From the second half of the 1950s, there were many attempts to make mathematics lessons more creative instead of the previously prevailing rote learning. The discussion on whether children should be taught to calculate by rehearsing (or memorising) arithmetic facts (such as learning the multiplication tables), or whether students should be taught to learn arithmetic and other math skills by discovering the principles, is still continuing. Principles of problem-solving based on reasonable guessing and finding patterns introduced by George Polya was followed by Zoltan Dienes´s six-stage theory of learning mathematics, stressing the importance of an approach to mathematics learning that uses games. The Bloom taxonomy first published in 1956, however, classified the educational learning objectives into levels from a traditional point of view. In geometry particularly, the Van Hiele model originated in 1957 described the stages of geometry learning. In the 1970s, Hans Freudenthal also called for urgent change in the teaching of mathematics in the primary and the secondary level. At the same time in Hungary, Tamás Varga introduced a new approach to elementary mathematics teaching based also on recognition of a uniform pattern in various games and mathematical models. The newest method in this line is the Hejny method or H-mat (named after Milan Hejný and his father Vít Hejný) first applied in the Czech Republic. The Hejny method is a scheme-oriented education concept that allows children to discover mathematics on their own and with pleasure. It builds on 40 years of experimental work and puts into practice historical notions that have been occurring throughout the history of mathematics. In the paper, we analyse and compare the mentioned concepts and give examples from the practice. The common denominator of all endeavours mentioned is the aptly expressive saying from G. Polya: "Teaching is giving opportunities to students to discover things by themselves".

Keywords:

Problem-solving, mathematics education.