In this paper the authors described the influence of the computer-based environment on students' learning achievement of the multidimensional calculus, in particular double integrals. The research was conducted with the second year students at the University of Kragujevac, Serbia, with two groups of students: the experimental and the control one.…

This article explores the parallels between improvisational theater, commonly known as improv, and active teaching. Specifically, it focuses in the impact of improv techniques on instructor and teaching assistant professional development. The implementation of an active teaching seminar is analyzed, where improv techniques were used in developing…

In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.

Background: Many engineering students fail to proceed through required prerequisite mathematics courses. Since these courses strongly influence engineering student attrition, we should examine to what degree these courses truly serve as prerequisites for following engineering coursework. Purpose/Hypothesis: We examined two research questions:…

This article includes a case study describing our innovative teaching technique of assigning reading journals in a first semester calculus course (Calculus I), as well as an exposition about and recommendations arising from our subsequent experiences implementing similar methods in Junior and Senior mathematics courses. In the primary case study…

Recently a teacher friend enquired about the S-I-R equations for disease spread, and what follows was stimulated by that exchange. COVID-19 provides an opportunity to put mathematical flesh on verbal bones such as "self-isolation", "lockdown", "herd immunity", "flattening the curve", "closed…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

This paper reports the results of three questionnaires applied to sixty-seven students preparing to become university-level mathematics teachers; the questionnaires were focused on knowing their conceptions and their mastery of the representations of functions in the development of power series. The theoretical and methodological background rests…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

In high school, students extend understanding of linear and exponential functions and explore trigonometric functions. This includes using the unit circle to connect trigonometric functions to their geometric foundation, modeling periodic phenomena, and applying (and proving) trigonometric identities. These ideas are fundamental for trigonometric…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

This article covers how a computer algebra system (CAS) "wxMaxima" can be explored for teaching single-variable and multivariable calculus to Korean digital natives. We present several examples where "wxMaxima" can handle calculus problems easily, not straightforwardly but still successfully with some human intervention, and…

Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge for teachers and students in their academic careers. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and…