The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

Researchers believe that the way that students talk, specifically the language that they use, can offer a window into their reasoning processes. Yet the connection between what students are saying and what they are actually thinking can be ambiguous. We present the results of an exploratory interview study with 10 participants, designed to…

This paper focuses on an inferential view on introducing new concepts in mathematics classrooms. A theoretical framework is presented which helps to analyse and reflect on the processes of teaching and learning mathematical concepts. The framework is based on the philosophies by Ludwig Wittgenstein and Robert Brandom. Wittgenstein's language-game…

A growing body of research has examined the experiential grounding of scientific thought and the role of experiential intuitive knowledge in science learning. Meanwhile, research in cognitive linguistics has identified many "conceptual metaphors" (CMs), metaphorical mappings between abstract concepts and experiential source domains,…

This article critically reviews the extant literature on scientific creativity and metaphorical thinking. Metaphorical thinking is based on a conceptual transfer of relationships or mapping, from a well-known source domain to a poorly known target domain, which could result in creative outcomes in sciences. Creativity leads to products that are…

This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

This study aims to investigate the effects of metaphors and pairing activity on programming performance of students with different self-regulated-learning (SRL) level. A total of 84 computing students were involved in this seven-week study, and they were randomly assigned either to a group that received a combination of metaphor and pair…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

Bodily manipulations, such as juggling, suggest a well-synchronized physical interaction as if the person were a physics expert. The juggler uses "knowledge" that is rooted in bodily experience, to interact with the environment. Such enacted bodily knowledge is powerful, efficient, predictive, and relates to sensory perception of the dynamics of…

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed…

This monograph proposes a theoretical basis for advocating a program of disciplinary arts education as an integral part of general education from kindergarten through grade 12. The theme of the essay is the role that images play in everyday experience and the formation of the educated mind. Images are sensory patterns or patterns produced by the…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…