The paper is the result of extensive research carried out among Czech students and focuses on a conception of infinity. The questionnaire survey was taken by 861 students ranging from grades 7 to 13. The aim of the research was to describe the development of students' conceptions of infinity. These conceptions are built on the intuitive phenomenon…

This article reports on a study of Kuwaiti college students' knowledge about the concept of functions. It also shows the connections these students make between different representations of functions. The results indicated that most students (96%) were unable to provide a definition of a function and only a third could provide examples of a…

Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes 'for each input there is one…

Literature suggests that students need to be exposed to cognitively demanding tasks (CDT). In this qualitative study, we examined in-service secondary school teachers' challenges in understanding (e.g. recognizing, solving, and designing) and implementing cognitively demanding tasks in mathematics classrooms. Purposive sampling consisted of eleven…

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their…

We examine what kind of concept definitions of area a group of Finnish primary and lower secondary student teachers (N = 82) use, and how the quality of the definitions is associated with the participants' success in seven exercises involving area. We are especially interested in how the understanding of the two-dimensionality of area appears in…

This study explored first-semester calculus students' understanding of tangent lines as well as how students used tangent lines within the context of Newton's method. Task-based interviews were conducted with twelve first-semester calculus students who were asked to verbally describe a tangent line, sketch tangent lines for multiple curves, and…

Mathematical learning and teaching are increasingly seen as a multimodal experience involved in cultural and social semiotic registers and means, and as such social-cultural semiotic analysis is expected to shed light on learning and teaching processes occurring in the mathematics classroom. In this research, three social-cultural semiotic…

The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers' construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics…

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…

In this article, we demonstrate that prospective teachers' content knowledge related to defining mathematical concepts is dependent on content area. We use the example of generation (a research tool we developed in a previous study) to investigate prospective teachers' knowledge. We asked prospective secondary mathematics teachers to provide…

We investigate the conceptual and procedural knowledge in integration of a group of students who has successfully completed a one-year calculus course. The participants are asked five questions and their responses are analysed in detail. We observed that the students do not have satisfactory conceptual understanding of integration. Moreover, it is…