This paper presents some critical perspectives regarding pedagogical approaches to the method of reversing the order of integration in double integrals from prevailing educational literature on multivariable calculus. First, we question the message found in popular textbooks that the traditional process of reversing the order of integration is…

The next generation of life science professionals will require far more quantitative skills than prior generations. Calculus is important for understanding dynamical systems in biology and, therefore, is often a required course for life science students. However, many life science students do not understand the utility value of mathematics to…

We conducted a semester-long ethnographic study of group work in a physics class that implemented the investigative science learning environment approach. Students' conversations were videotaped while they were engaged in group learning activities. Our primary research goal was to better understand what factors made some groups more effective than…

Education research has repeatedly shown that active learning in physics is pedagogically more efficient than traditional lecture courses. Widespread application of the active learning is slowed down by the lack of data on the performance of the active learning in widely varying circumstances of different educational systems. We measured the level…

In this paper, we present a "route of activities" mainly addressed to first and second year engineering students attending the basic mathematics courses. These activities are intended to be a tool both for students and teachers. On the one hand, they should help the students to acquire a deeper understanding of the mathematical ideas and…

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

Over the past few decades there has been increased attention on instructional practices that incorporate and build on student thinking. To effectively implement these practices, it is essential for an instructor to demonstrate responsiveness to student thinking. Although important, responsiveness is not well-understood at the post-secondary level.…

A more effective math education has never been more pressing than in today's world. However, it is no mystery that students continue to struggle with basic mathematics concepts, let alone more advanced math such as Pre-Calculus. Thus, in the present study, two Pre-Calculus math classrooms were randomly assigned to either a flipped classroom model…

The transition of the educational system in the Philippines vastly affects basic and higher education. A mismatch of pre-requisite Mathematics learning competencies from the basic education level occurred when the student reached higher education. This descriptive-developmental method of the study utilized the developed contextualized learning…

Mathematics is a discipline that exists within a social context, a context that influences how the subject is taught and learned. Women's performance in mathematics has been shown to be vulnerable to stereotype threat, and psychologists have developed interventions aimed at reducing the effect of stereotype threat on women's mathematics…

This study aimed to explore the effects of an instructional intervention in which GeoGebra and the think-pair-share method were used to teach the relationship between the graph of a parametric curve and the derivatives of its component functions. The participants in the study were 19 prospective mathematics teachers. To assess the understanding of…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

In this article we present the results of a qualitative investigation into the teaching and learning of Taylor series and local approximations. In order to perform a comparative analysis, two investigations are conducted: the first is historical and epistemological, concerned with the pedagogical evolution of semantics, syntax and semiotics; the…

Rubric has been associated with the term assessment used for grading and/or scoring. However, it might observe less, but it is also designed as students 'learning tool. This study was conducted to provide empirical facts on its effectiveness as a learning tool in teaching Applications of Derivatives in Basic Calculus. It used the…