A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

This work was developed to present constructive steps of multiple integrals using the open-source software Geogebra. The main focus was directed towards creating three-dimensional graphs of integrals through Riemann sums in two variables. Some practical examples are developed to demonstrate the reliability of the presented results, which are…

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

This study investigates the impact of GeoGebra, a dynamic, accessible, and easy-to-use mathematics software, on student confidence and perceptions of its helpfulness in the context of Calculus III courses. A quasi-experimental design was employed to compare four sections of Calculus III, with two sections integrating GeoGebra for in-class…

Graphical analysis of the relationships between pairs of integrals and their corresponding derivatives resulted in the development of a procedure one may describe as 'pictorial integration'. The arctangent of the derivative of various functions was analysed to confirm that this accurately reports the magnitude of angles made by integral functions…

This article presents an instructional technology-based cycle model intended to support and facilitate the teaching and learning of mathematics, particularly calculus. The study used quantitative methods with quasi-experimental research that uses non-randomised assignments of the study group that are categorised into experimental and control…

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

Multiple representations cultivate students' mathematical mindset. However, research results have reported that students do not benefit from these tools due to lack of representational fluency. This study was designed to determine the impact of GeoGebra assisted multiple representations approach on students' representation translation performance…

In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

Learners in the 21st century need technological support in the learning process because of the advancements made in technology for teaching and learning. A GeoGebra-oriented classroom uses one of these technologies that can be implemented in the classroom. The new developed cycle model implemented in the study and explored the effect of using…

In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed. This is due to the impossibility of expressing, in terms of simple elementary functions, the solutions of the nonlinear differential equation (NLDE) that models the pendulum, which is why the authors usually choose the linearized…