The frequent misinterpretation of the nature of confidence intervals by students has been well documented. This article examines the problem as an aspect of the learning of mathematical definitions and considers the tension between parroting mathematically rigorous, but essentially uninternalized, statements on the one hand and expressing…

In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the…

This article investigates some of the specific features involved in accommodating the idea of actual infinity as it appears in set theory. It focuses on the conceptions of two individuals with sophisticated mathematics background, as manifested in their engagement with variations of a well-known paradox: the ping-pong ball conundrum. The APOS…

In this article we explore the mechanisms through which one group of preservice teachers engage in "Collective Property Noticing"--a phenomenon in which group members integrate individual contributions such that the group, as a unit, notices mathematical properties of their collective image. Drawing on improvisational theory to help to…

The complementary use of the theories of instrumental genesis and shifts of attention enabled me to obtain insights into students' understandings of the concepts of eigenvector and eigenvalue. My analysis suggests that the use of different dragging modalities can provide evidence of shifts in structure of a student's attention and…

Science education research has built a strong body of work on students' understandings but largely overlooked the nature of science knowledge itself. Legitimation Code Theory (LCT), a rapidly growing approach to education, offers a way of analyzing the organizing principles of knowledge practices and their effects on science education. This…

This article offers explanations as to why good candidates for mathematics or physics degrees might opt to study subjects other than STEM (science, technology, engineering, mathematics) subjects at university. Results come from analysis, informed by psychoanalytic theory and practice, of narrative-style interviews conducted with first-year…

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

This article presents a study done in an elementary mathematics methods course that focused on the transition of novice teachers' epistemological stances: former elementary student, university student, and teacher stances. In order to help them develop the teacher stance, we designed a three-phase activity, where two phases took place inside…

There is a chronic international shortage of mathematics and science teachers, particularly physicists. The study reported here examines why physicists become teachers and why they stay in teaching. Physicists from seven preservice teacher training cohorts from three English universities were invited to answer an online survey with follow-up…

This article addresses some of the curriculum implications of adopting a socioscientific issues (SSIs)-oriented approach to science education, including (a) the need to provide scientific knowledge on a need-to-know basis and adapted to the complexity, multidimensionality, and fluidity of real-world situations and the constraints of particular…

In this article, we obtain a genetic decomposition of students' progress in developing an understanding of the decimal 0.9 and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory that would be the first substantial change in…

What is the evidence that teachers who return to learn more mathematics are better teachers? Over more than a decade we have been involved in six different projects giving teachers the opportunity to reengage with mathematics. We have returned to them to ask the teachers about the long-term impact and to give us examples. The result extends…

Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

We propose that what teachers can say or write about their views of mathematics and about a range of pedagogic strategies and didactic tactics that they use is of minor importance compared to what comes to mind moment by moment when they are planning or leading a lesson. Beginning with a quote from a teacher that provoked a focus on the role and…