This study aims to examine the relation between spatial ability and creativity in Geometry. Data was collected from 94 ninth graders. Three spatial abilities were investigated: spatial visualization, spatial relations and closure flexibility. As for students' creativity, it was examined through a multiple solution problem in Geometry focusing on…

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…

In a previous article of the same journal, we have discussed the interrelations of students' beliefs and self-efficacy beliefs for the use of representations and their respective cognitive performance on the learning of fraction addition. In the present paper, we confirm a similar structure of cognitive and affective factors on using…

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

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…

Representations are used extensively in mathematics and translation ability is highly correlated with success in mathematics education. The authors investigate the translation ability of university students as far as the concept of function is concerned. The research focuses on the relationship between success in, solving direct translation tasks…

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…

The main objective of this study is to investigate the role of four different modes of representation in mathematical problem solving (MPS), and more specifically to develop a model, which provides information about the effects of these representations in the solution procedures of one-step problems of additive structures. Data were collected from…

This study investigated the role of different modes of representation, i.e., verbal description, decorative pictures, informational pictures and number line, in solving additive change problems. Data were collected from 1447 students in Grades 1, 2, and 3. Structural equations modelling affirmed the existence of four first-order…

This paper explores the role of diagrams in a specific problem solving process. Two types of tests were administered to 194, 12 year old students, each of which consisted of six non-routine problems that could be solved with the use of a diagram. In Test A students were asked to respond to the problems in any way they wished whereas in Test B…

Presents an analysis of written solutions to geometry exercises in the last year of Greek Lyceum which showed relatively low performance on vector methods. Justifies pupils' false preconceptions with regard to the concept of vectors, and the strong influence of classical geometry teaching in the previous years. (Author/ASK)

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…