This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students' reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world…

Expert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students' reasoning in topology is…

In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within…

We report on a teaching experiment with pre-service teachers (PSTs) intended to support their understanding of the validity of mathematical arguments, and their ability to formulate mathematical arguments by conducting case analysis. PSTs used Toulmin's framework (1958/2003) and engaged in collective argumentation while solving crypto-arithmetic…

Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, 'If H … , then C … ', where 'H' is a hypothesis and 'C' is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested a…

The aim of this study was to characterize and discuss ways of reasoning that prospective high school mathematics teachers develop and exhibit in a problem-solving scenario that involves the coordinated use of digital technologies. A conceptual framework that includes Virtual Learning Spaces (VLS) and Resources, Activities, Support and Evaluation…

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond…