http://hdl.handle.net/11716/57 2026-10-07T06:48:47Z http://hdl.handle.net/11716/14359 Wybrane uwagi na temat roli zadań matematycznych w procesie nauczania-uczenia się matematyki Major, Joanna; Olik-Pawlik, Bożena; Ratusiński, Tadeusz; Zaręba, Lidia The paper presents the comments relating to the role of tasks in the process of teaching and learning of mathematics in the context of education of students studying to become teachers. In the considerations part, reference was made to the fragments of undergraduate and postgraduate works, made at seminars of didactics of mathematics. 2016-01-01T00:00:00Z http://hdl.handle.net/11716/14357 O pewnej implikacji Górowski, Jan; Łomnicki, Adam The purpose of this paper is to show how the process of proving a theorem in different ways or proving generalized versions of the theorem, after learning one its proofs, influences the development of the skills of proving theorems and analysing proofs by the students of mathematics. To illustrate this process we use an elementary theorem about numbers and its generalizations, giving fourteen proofs. Proving theorems we use methods and facts which are available to high school students. 2016-01-01T00:00:00Z http://hdl.handle.net/11716/14356 Propozycja wyzwalania twórczości matematycznej studentów przy pomocy pewnej nierówności funkcyjnej Fidyk, Edyta; Siudut, Stanisław T. Szostok and Sz. Wąsowicz in (Szostok, Wąsowicz, 2011) studied the following functional inequality: $\vert F \left( y \right)-F\left( x \right)-\left( y-x \right)f\left(\frac{x+y}{2} \right)\vert \le \varepsilon$ stemming from the Lagrange mean value theorem. They proved that the functon $f$ is affine, provided $f,F:\mathbb{R}\to \mathbb{R}$ satisfy the above inequality for all $x,y\in \mathbb{R}$. The aim of our paper is to extend the results of (Szostok, Wąsowicz, 2011) to more general situations (for example, we change $\mathbb{R}$ to $\mathbb{C}$ or $ \mathbb{H})$. 2016-01-01T00:00:00Z http://hdl.handle.net/11716/14354 Twórcza aktywność matematyczna uczniów związana z rozwiązywaniem pewnych zadań na zastosowanie wzorów Viète’a Chronowski, Antoni; Powązka, Zbigniew In this article we propose ways of developing the active and creative attitude of students towards solving mathematical problems. The tasks were sourced from various mathematical competitions for secondary school students, such as the so-called Mathematical Olympiad, and require the use of Vieta’s formulas for third-degree polynomials. These problems inspire students to conduct their own elementary research work and foster their creative attitude towards mathematics. This article is dedicated mainly to students who are pre-service mathematics teachers, but may also be of use to in-service teachers. 2016-01-01T00:00:00Z