This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

The main focus of the study was to identify the the effects of the ACE teaching cycle approach on students' engagement in learning of Elementary Linear Algebra. The Elementary Linear Algebra course was delivered at the Mathematics Education Study Program of State University of Padang, Indonesia. An action research methodology was adopted for the…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

This paper reports on themes that arose in an investigation of university lecturers' views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course?…

We introduce learning modules in cryptography that can be crafted to motivate many abstract mathematical ideas, and we illustrate with a sample module. These modules can be used in a variety of ways, such as the core for a cryptography course or as motivating topics in other courses such as abstract and linear algebra or number theory.

Proof has a prominent place in the linear algebra curriculum, teaching and learning but in first-year courses it continues to be challenging for both instructors and students. While an introduction to new concepts through definitions and theorems adds to the complexity of the course, proof remains the number one hurdle for many students. How do…

Mathematical modelling has acquired relevance at all educational levels in the last decades since integrating this activity in instruction provides significant contexts for improving students' learning, including in linear algebra courses that have a notable presence in many undergraduate courses from different fields, including engineering and…

Contribution: This article compares student success via different pathways in which students take mathematics courses required for engineering degrees. Background: Mathematics courses are an integral part of engineering curriculum. Many institutions require or recommend the order in which students take Calculus II, Multivariable Calculus,…

Theon's ladder is an ancient method for easily approximating "n"th roots of a real number "k." Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We extend this work using techniques from linear algebra. We will show that a ladder associated to the quadratic…

Limited research exists to target algebra instruction for students with intellectual and developmental disabilities (IDD). In this study, researchers compared the use of concrete -- with scaffolds added by researchers -- and virtual algebra tiles -- with inherent scaffolds -- to support the acquisition, fluency, and generalization of linear…

Articulated pedagogical and didactic strategies allow improving academic quality and strengthen individual and institutional cognitive processes such as student retention. Mathematical modelling, articulated with complementary actions, contributes to teaching and learning processes within situations that go beyond the classroom since they are…

Inquiry-oriented teaching is a specific form of active learning gaining popularity in teaching communities. The goal of inquiry-oriented classes is to help students in gaining a conceptual understanding of the material. My research focus is to gauge students' performance and conceptual understanding in inquiry-oriented linear algebra classes. This…

In this study, we look at student perceptions of a first course in linear algebra, focusing on two specific aspects. The first is the statement by Carlson that a fog rolls in once abstract notions such as subspaces, span and linear independence are introduced, while the second investigates statements made by several authors regarding the negative…

Multicomponent solution calculations can be complicated for students and practiced chemists alike. This article describes how to simplify the calculations by representing a solution's composition as a point in a "concentration space," whose axes are the concentrations of each solute. The graphical representation of mixing processes in a…

Linear algebra is a crucial part of mathematical training for engineering students and there are many problems in the application of this subject in engineering, physical, and even mathematical disciplines. In this scope, a study on the sustainability of learning this subject and how it can be improved is considered necessary. This article aims to…