Students who actively engage in metacognitive thinking and self-regulation and are self-motivating appear to be more successful than those who take a more passive role in learning. This causal comparative research study explored whether increasing metacognitive awareness through participating in metacognitive surveys outside of class improved…

Entering a conversation where the framing question begins with the term "whither" draws into specific relief the importance of examining how that term is used--that is, its meaning or connotation. One might interpret "whither" interrogatively or relatively, with either interpretation being correct in the syntax of a question, such as "Whither…

The mathematical language and its tools are complementary to the formalism in chemistry, in particular at an advanced level. It is thus crucial, for its understanding, that students acquire a solid knowledge in Calculus and that they know how to apply it. The frequent occurrence of indeterminate forms in multiple areas, particularly in Physical…

The story is often told of the calculation by G.I. Taylor of the yield of the first ever atomic bomb exploded in New Mexico in 1945. It has indeed become a staple of the classroom whenever dimensional analysis is taught. However, while it is true that Taylor succeeded in calculating this figure at a time when it was still classified, most versions…

The body of literature on a Writing-to-Learn (WTL) approach in math courses offers up a variety of assignment types from which to choose. However, few of these articles provide empirical evidence on the ways these writing assignments contribute to students' learning. This mixed-methods study, conducted at the University of New Mexico, a…

The purpose of this study was to address Advanced Placement (AP)® policy-related questions from administrators at the University System of Georgia (USG) using current AP Exam records and student course performance at four institutions. Specifically, comparisons of sequent or subsequent course grades were made between AP and non-AP students. This…

In this article, we propose a family of second derivative Adams-type methods (SDAMs) of order up to 2k + 2 ("k" is the step number) for initial value problems. The methods are constructed through a continuous approximation of the SDAM which is obtained by multistep collocation. The continuous approximation is used to obtain initial value methods,…

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the…

This article details the results of testing an e-book in two differential calculus classes. Although we, as math instructors, were drawn to the components of the e-book that promote conceptual understanding--such as the interactive figures--the students reported liking the assessment support most. We found that students were initially excited…

This article presents a problem-based approach that prepares students for future learning in the classroom. In this approach, students complete problem-based activities before coming to class to familiarize themselves with the topics to be covered. After the discussion on how the use of these activities relate to the learning and transfer…

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits…

Historically, what people can learn is co-determined by the "representational infrastructure" for knowledge building. When Latin was the required medium of knowledge building, few could engage in scholarly activities; without the change to the vernacular, nearly universal access to higher education would not be possible. The highly…

The collection of chapters in this special book examines educational practices during the COVID-19 viral outbreak. This special book brings together a variety of studies and scholars in an effort to exemplify how the COVID-19 shapes the learning and teaching processes in different countries. The twelve chapters selected for this special book…

The collection of chapters in this special book examines educational practices during the COVID-19 viral outbreak. This special book brings together a variety of studies and scholars in an effort to exemplify how the COVID-19 shapes the learning and teaching processes in different countries. The twelve chapters selected for this special book…