Katedra matematiky - Katolícka univerzita v Ružomberku

Catholic University in RužomberokScientific Issues, Teaching Mathematics II: Innovation, New Trends, Research, Ružomberok 2010EXAMPLES OF INTRODUCING CHOSEN CONCEPTSOF MATHEMATICAL ANALYSISZbigniew PowązkaUniwersytet Pedagogiczny, Instytut Matematykiul. Podchor¸ażych 2, 30-084 Krakówe-mail: powazka@up.krakow.plAbstract. In this paper we present examples of introducing basic concepts ofmathematical analysis. We especially accent didactical operations wchich havebeen used to facilitate understanding of those concepts to students.1. IntroductionDuring studying mathematical analysis it is essential to understand andcorrect use of concepts such as limit of a sequence, limit of a function,differentiability and integrality of function. These concepts are not easyand they cause many difficulties for students. There is a lot of teachingprocedures which are being used to vanquish these difficulties. One of themis so-called functional method of teaching mathematics.The foundation of this method of teaching mathematics on different levelsof education was elaborate by Z. Krygowska (1977, s. 81 - 129) who basedon results of researches of psychologist J. Piaget. According to H. Siwek(2005): conception of functional method is fundamental strategy of didacticallyproper teaching process - learning of mathematics, but it can be alsoeasily interpreted as basic strategy of discovering and creating mathematicsby students.Using this method of teaching gives an opportunity to form differentelements of mathematical activity. We can assume that building up theseactivities by learners is one of important goals of mathematics teaching(Krygowska 1986).We can distinguish three levels while developing concepts with use ofthis method:- level of concrete activities,- level of concrete - imaginative activities,- level of abstract activities.