In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with…

Calculus is a required course in most engineering programmes and is intended to provide students with tools they will use throughout the rest of their training. However, research seems to indicate that calculus is not very prevalent in the engineering workplace or in university engineering courses. To shed some light on how calculus is actually…

Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…

The preparation gap [Salehi et al., Phys. Rev. Phys. Educ. Res. 15, 020114 (2019)] refers to gaps in students' prior knowledge that can negatively affect their learning as they engage in introductory physics courses. To better characterize the gap, the current study distinguished the impact of various prior knowledge components on learning gains.…

Physical chemistry students often lack conceptual understanding of the measurable quantities derivatives and integrals represent in particular problems. Also, two-parameter equations of state exhibit horizontal inflections at the critical point in the "PV" isotherms, and students must employ the mathematical properties of inflections to…

Background and Context: Computer Science has traditionally had poor student retention, especially among women. Prior work has found that student attitudes are a key factor to retention, especially with "weedout" courses such as Calculus. Objective: To determine how student attitudes towards CS 1 and Calculus change over active-learning…

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service…

This study aims to prepare an educational program based on integrating Science, Technology, Engineering and Mathematics (STEM) to develop students' mathematical thinking skills. It also aims to provide proposals that could have a major role in rebuilding some of the general features on which mathematics curricula can be built according to the STEM…

Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of…

The current COVID-19 pandemic has largely impacted the academic performance of several college students. The present study is concerned with the effects of the COVID-19 pandemic on students pursuing a STEM (science, technology, engineering, and mathematics) degree. We collected weekly survey data (w=9) of students (n=53) taking calculus courses…

Background: Applied Calculus courses serve hundreds of thousands of undergraduates as quantitative preparation and gatekeepers across diverse fields of study. The current study investigated how motivational factors are associated with students' learning outcomes in Applied Calculus courses from the perspective of self-determination theory--a sound…

The multi-faceted nature of mathematics knowledge for teaching, including pedagogical content knowledge (PCK), has been studied widely in elementary classrooms, but little research has focused on senior secondary mathematics teaching. This study utilised the Knowledge Quartet (Rowland et al., "Research in Mathematics Education," 17(2),…

The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…

According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean…

We investigated understanding of the linear independence concept based on the type and nature of connections displayed in seven non-mathematics majors' interview responses to a set of open-ended questions. Through a qualitative analysis, we identified six categories of frequently displayed connections. There were also recognizable differences in…