In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a…

Decades of research have documented young students' misinterpretations of the equal sign and the impediments these present for children's mathematical development. Much less is known about individual differences in adults' knowledge of the equal sign. We assessed 182 college students from developmental math courses and present analyses from a…

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

This study reports the results of a study examining how easily students are able to transfer frequency solutions to conditional probability problems to novel situations. University students studied either a problem solved using the traditional Bayes formula format or using a natural frequency (tree diagram) format. In addition, the example problem…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of…

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…

This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore…

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…

The aim of the research presented in this paper is to contribute to our knowledge about problem solving in mathematics. My purpose in this paper is to compare, from this point of view, two very different institutions in the French tertiary education system, with the intention to interpret the chronic inequality of performance in problem solving…

Presents perspectives from students and teachers about project work in mathematics. Presents a theoretical framework consisting of problem-centered studies, interdisciplinarity, participant-directed studies, and the exemplarity principle. Contrasts theoretical conceptions with practice. (MKR)