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…

Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect…

Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by…

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

Transitional engineering students are those who are academically ineligible to enter a bachelor's engineering program but are enrolled in an associate engineering program with a university. Successful completion of such an associate engineering program allows the higher achievers to transfer to a full bachelor's engineering program. The associate…

This study analyzed the relative importance of different cognitive abilities for solving complex mathematical word problems (CWPs)--a demanding task of high relevance for diverse fields and contexts. We investigated the effects of spatial, verbal, numerical, and general reasoning abilities as well as gender on CWP performance among N = 1282…

Previous studies have suggested that problem-posing activities could be used to improve the teaching, learning, and assessment of mathematics. The purpose of this study is to explore undergraduate engineering students' problem posing in relation to the integral-area relationship. The goal is to help fill a gap in tertiary level research about…

Problem-posing has been recognized for enhancing students' engagement, problem-solving skills, and mathematical knowledge, which leads to higher mathematics achievement. This research is experimental research with a randomized comparison groups pre-test and post-test design, which aims to examine the effect of using online problem-posing to…

This introduction presents Active Learning Methodology, surveying its history, main existing tools and supporting evidence, with an emphasis on mathematics and higher education, in particular engineering studies. This work is part of the DrIVE-Math project, developing innovative mathematical teaching strategies in engineering studies.

The development of mathematical skills for future engineers is essential. Game-based learning (GBL) and gamification have been widely used in elementary education, but less applied in higher education. The objective of this article was to evaluate the effect of didactic strategies mediated by games in the teaching of mathematics in first-year…

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

Laplace transform (LT) is an essential mathematical tool for solving linear ordinary differential equations (ODE) with boundary values, by transforming differential equation into algebraic equations which are easier to manipulate. In this article, we analyse the errors students make and misconceptions they have in solving linear ODE using LT…

In this note, some variants of Cauchy's mean value theorem are proved. The main tools to prove these results are some elementary auxiliary functions.

The literature describes different stances concerning the focus on how mathematics should be taught, with some preferring a conceptual knowledge approach and others a procedural knowledge approach. The current study investigated the relationship between students' conceptual and procedural knowledge in a calculus context. To better understand the…

This article shows results on the simulation of partial differential equations such as the heat equation, the Laplace equation and the wave equation in a course called mathematical methods at a university in Bogotá Colombia. In this course, the concept of partial differential equations and different solution methods were explained to them, both in…