A historical survey on the place and role of tasks in mathematics teaching. (English)

Kiryakova, Virginia (ed.), Complex analysis and applications ’13. Proceedings of the international conference, CAA ’13, Sofia, Bulgaria, October 31 ‒ November 2, 2013. Dedicated to the 100th anniversary of Academician Ljubomir Iliev. Sofia: Bulgarian Academy od Sciences, Institute of Mathematics and Informatics (ISBN 978-954-8986-38-0). 93-99 (2013).

Summary: Mathematical tasks are a main tool to achieve educational, practical and instructional aims of mathematics teaching. In order to achieve long-term, as well as comprehensive adoption of the prescribed material, it is necessary to solve a significant number of tasks. Trying to emphasize the significance of mathematical tasks, it is sufficient to ask ourselves the following question: “Is mathematics teaching possible with our mathematical tasks?” In the beginning we will try to point out the role of mathematical tasks through history. Mathematical tasks were the basic tool for strengthening mathematical knowledge in pre-Greek period. However, over time, tasks were replaced first by theorems and than by concepts. Therefore, historically there is a certain dynamics between the set of theorems and set of tasks. Does this mean that with the change of the position of tasks through history their significance has been lost too?