The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

The use of dynamic geometry software (DGS) is becoming increasingly familiar among teachers, but letting students conduct inquiries using computers is still not a welcome idea. In addition to logistics and discipline concerns, many teachers believe that mathematics at the lower secondary level can be learned efficiently through practice alone.…

The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

Individuals and societies that can use mathematics effectively in this period of rapid changes will have a voice on increasing the opportunities and potentials which can shape their future. This has brought affective characteristics, such as self-efficacy, that affect mathematics achievement into focus of the research. Teacher efficacy refers to…

This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in…

We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…

The purpose of this study is to define teacher views about the difficulties in learning and teaching middle school statistics subjects. To serve this aim, a number of interviews were conducted with 10 middle school maths teachers in 2011-2012 school year in the province of Trabzon. Of the qualitative descriptive research methods, the…

Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students' conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically…

Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…

In this study, the effect on the achievement and attitudes of prospective teachers is examined. With this aim ahead, achievement test, attitude scale for statistics and interviews were used as data collection tools. The achievement test comprises 8 problems based on statistical data, and the attitude scale comprises 13 Likert-type items. The study…

We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same…

Visualization is mostly despised although it complements and--sometimes--guides the analytical process. This study mainly investigates teachers' preferences concerning the use of the visualization method and determines the extent to which they encourage their students to make use of it within the problem-solving process. This study was conducted…

In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order…