Research studies have found that mathematics teachers face challenges when designing technology-integrated lessons to support mathematical inquiry with authentic problems. This suggests that teachers need to develop technological pedagogical knowledge (TPACK) or their professional knowledge for technology integration. Drawing upon the concept of…

Geometry is used in different ways in the teaching of linear algebra. In this paper, I offer a typology of these ways, which I call varieties, and address three central questions. The first question is, "What varieties of use of geometry in the teaching of linear algebra exist?" This question is addressed through an analysis of six…

The simple and compound interest formulas in isolation have limited usefulness for financial planning--until the concept of a regular payment is introduced. This article presents and discusses a simple investigation given to an advanced Year 10 mathematics class, with most students looking to study Mathematical Methods in Years 11 and 12. This…

Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and…

Teachers' self-efficacy has been measured a number of ways and linked to important outcomes including teacher satisfaction, goals for students, and student achievement. However, most of these existing measures are intentionally general in their design. Given the importance of context, researchers have begun to construct more domain-specific…

Eye tracking is getting increasingly popular in mathematics education research. Studies predominantly rely on the so-called eye-mind hypothesis (EMH), which posits that what persons fixate on closely relates to what they process. Given that the EMH was developed in reading research, we see the risk that implicit assumptions are tacitly adopted in…

This article examines collaborative mathematical tasks that entail sympathetic coordinated movements. We discuss the affective bonds that form when students participate in such tasks. Using Maxine Sheets-Johnstone's term "affectivity" to characterize the responsive nature of bodies, we analyse data from a teaching experiment where…

Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing…

Subitising, a quick apprehension of the numerosity of a small set of items, has been found to change from an individual's reliance on perceptual to conceptual processes. In this study, we utilised a constructivist teaching experiment methodology to investigate how the subitising activity of one preschool student, Amy, related to her construction…

Prior research showed that many secondary students fail to construct arguments that meet the standard of proof in mathematics. However, this research tended to use survey methods and only consider students presenting their perceived proofs in written form. The limited use of observation methods and the lack of consideration of students presenting…

According to the recent MAA National Study of College Calculus (Bressoud, Mesa, & Rasmussen, 2015) more than a third of US Calculus I students come in contact with undergraduate mathematics peer tutors (UMPTs) and mathematics tutoring has the ability to influence affect as well as academic learning, but, undergraduate mathematics tutoring is…

Extensive research has documented students' difficulty understanding and applying the Empirical Law of Large Numbers, the statistical principle that larger random samples result in more precise estimation. However, existing interventions appear to have had limited success, perhaps because they merely demonstrate the Empirical Law of Large Numbers…

What are the substantive differences between flipped and non-flipped instruction? This study examined the instruction of two teachers who have worked together within the same school using the same Algebra 1 curriculum for years. One teacher flipped his instruction (creating lecture videos assigned as homework), while the other teacher continued…

Based on an empirical study of policy enactment and mathematical enculturation in Swedish school-age educare, a conceptualization of mathematics as the assemblage of "activities" and "values" is proposed. Observations were analysed using policy enactment theory and the lens of mathematical activities. The result shows that…

Epistemological beliefs (EB) play a vital role in students' performance (Buehl & Alexander, 2001, 2006; Fives & Buehl, 2004; Lodewyk, 2007). The paper was designed to examine the relationship between students' EB about the Mathematics curriculum and their academic achievement (marks) at the secondary level. Eight hundred and ten…