Several studies have explored students' understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students' understanding of the Fundamental Theorem of Calculus (FTC). In addition, students' metacognitive experiences and skills whilst solving FTC questions have not…

In "Maths for Business", a mathematics module for non-mathematics specialists, students are given the choice of completing the module content via short online videos, live lectures or a combination of both. In this study, we identify students' specific usage patterns with both of these resources and discuss their reasons for the…

Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide…

First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more…

This article describes the beliefs and their transformations of members of a cohort of early-childhood, elementary and middle-level pre-service teachers (PSTs) as they professionally develop. A typological analysis of both quantitative and qualitative data collected between August 2011 and May 2013 was utilized to categorize how 40 PSTs' beliefs…

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant…

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers'…

Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as…

Similar to countries such as the Netherlands and the United Kingdom, secondary schools in Ireland can decide how to allocate instruction time between curriculum subjects. Although there are national guidelines available from the Department of Education and Skills (DES), the majority of schools make their own decisions about how much time they…

The purpose of this study is to determine the effect of GeoGebra software on pre-service mathematics teachers' attitudes towards proof and proving and to determine pre-service teachers' pre- and post-views regarding proof. The study lasted nine weeks and the participants of the study consisted of 24 pre-service mathematics teachers. The study used…

In this study, instructors of undergraduate mathematics from post-secondary institutions in Newfoundland were surveyed (N = 13) and interviewed (N = 8) about their use of, experiences with, and views on, technologically assisted teaching. It was found that the majority of them regularly use technologies for organizational and communication…

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination--the final examination for students in…

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities,…

Learning to write formal mathematical proofs presents a major challenge to undergraduates. Students who have succeeded in algorithm-intensive courses such as calculus often find the abstract logic and nonprocedural nature of proof writing to be technically difficult, ambiguous and "filled" with potential errors and misconceptions. This…