Studies of discourse are prevalent in mathematics education, as are investigations on facilitating change in instructional practices that impact student attitudes toward mathematics. However, the literature has not sufficiently addressed the operationalization of the commognitive framework in the context of Calculus I, nor considered the…

Research results from this study reveal students have difficulties understanding and using of the concepts of average rate of change and the derivative function. Students in this study held multiple approach to understand the concepts that made it difficult to develop a strong understanding of the average rate of change and derivative function. In…

This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense…

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…

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…

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

We collected data on students' self-assessment behavior from four sections of a Calculus II course. Students were asked to write their expected scores on each of the weekly in-class quizzes and problems in the exams, immediately after they completed them. They were then asked to justify their expectation in writing. One-on-one interviews were…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

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.…

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 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…