This article focuses on exploring students' understanding of the concept of function concerning three main aspects: secondary students' ability to (1) define the concept of function and present examples of functions, (2) solve tasks which asked them to recognize and interpret the concept of function presented in different forms of representation,…

The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…

The study aimed to investigate students' conceptions on the notion of absolute value and their abilities in applying the specific notion in routine and non-routine situations. A questionnaire was constructed and administered to 17-year-old students. Data were analysed using the hierarchical clustering of variables and the implicative method, while…

Cognitive development of any concept is related with affective development. The present study investigates students' beliefs about the use of different types of representation in understanding the concept of fractions and their self-efficacy beliefs about their ability to transfer information between different types of representation, in relation…

In this study, we attempt to put in question students' spontaneous and uncritical application of the simple and neat mathematical formula of linearity. This is impelled with the help of a written test involving geometrical problems, which is based on an original experimental setting. In this setting, grade 9 and 10 students were instructed first…

The present study explores pupils' constructed definitions of the concept of function in relation to their abilities in dealing with tasks of functions involving different forms of representations and problem solving tasks. A major concern is also to examine the interrelations between these three ways of thinking about or dealing with the concept…

One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & Goldin, 2003). In this study the term representation is interpreted as the tool used for representing mathematical ideas such…