Self-concept is an important noncognitive predictor of learning success and academic achievement, but mechanisms behind these effects are mostly unknown (Marsh, 2006). We analyzed the influence of mathematical self-concept on university students' eye movements in reading mathematical PISA items in a mathematical and a problem-solving context. In a…

Interest in understanding mathematics teaching and learning phenomena, and to develop new and effective methodologies to teach Differential Calculus and Linear Algebra led me to look for ways to dialogue between APOS Theory and other mathematics education theories. This enterprise has facilitated a better understanding of them. Bridges between…

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. I contribute to these efforts by expanding the constructs in Cobb and Yackel's (1996) interpretive framework that allow for coordinating social and individual perspectives. This expansion involves four…

This position paper discusses the role of open access research data within mathematics education, a relatively new initiative across the wider research community. International and national policy documents are explored and examples from both the scientific and social science paradigms of mathematical sciences and mathematics education…

The ubiquity of mobile devices demands the exploitation of their potentials in distance and face-to-face teaching, as well for complementing textbooks in printed or electronic format. There is a strong need to develop innovative resources that open up new dimensions of learning and teaching through interactive and platform-independent content.…

This research project involved teaching linear algebra to second year undergraduates. Using Tall's three worlds of mathematical thinking as a theoretical framework, students were taught fundamental linear algebra concepts using each of the embodied, symbolic and formal dimensions. By varying the order in which these approaches were used in each…

Measures of centre (the mean, median and mode) are fundamental to the discipline of statistics. Yet previous research shows that students may not have a thorough conceptual understanding of these measures, even though these statistics are easy to calculate. This study describes the findings of a study of pre-service teachers' ideas of measure of…

This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…

Problems teaching probability in Tonga (in the South Pacific) led to the question how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to find the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan…

The purpose of this study is to develop design principles for crafting tasks that will encourage conjecturing and proving in the context of elementary number theory at the undergraduate level. From the analyses of the written work of 46 prospective mathematics teachers on a task designed according to these principles, we think that there is…

Instructors are a chief input into the higher education production process, yet we know very little about their role in promoting student success. This is in contrast to elementary and secondary schooling, for which ample evidence suggests teacher quality is an important determinant of student achievement. Whether colleges could improve student…

Counting problems have applications in probability and computer science, and they provide rich contexts for problem solving. Such problems are accessible to students, but subtleties can arise that make them surprisingly difficult to solve. In this paper, students' work on the Groups of Students problem is presented, and an important issue related…

Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn. I describe a design research project in which we integrated formative assessment strategies into lesson materials that focus on developing students' conceptual understanding and their capacity to…

This study focuses on the development of four tertiary introductory statistics students' informal inferential reasoning while engaging in data driven repeated sampling and resampling activities. Through the use of hands-on manipulatives and simulations with technology, the participants constructed empirical sampling distributions in order to…

We describe an attempt by a former mathematics teacher to read an undergraduate mathematics proof aided by discussions with a mathematician using the language of mathematical problem solving. The literature on successful approaches to reading mathematics is scarce at the secondary and undergraduate levels. Shepherd, Selden and Selden (2012)…