Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

Linear algebra is gaining increased attention due to its applications in many modern high-tech industries, such as artificial intelligence, machine learning, and robotics. Coordinate systems underlie many concepts in linear algebra and promote students' spatial thinking of key concepts by imposing a visual aspect to courses that may otherwise be…

In this paper, we present a qualitative study on what values students perceive in their abstract algebra course. We interviewed six undergraduates early in their abstract algebra course and then again after their course was completed about what motivated them to learn abstract algebra and what value they saw in the subject. The key finding from…

The paper examined the relations among problem solving, automaticity, and working memory load (WML) by changing the difficulty level of task characteristics through two applications. In Study 1, involving 68 engineering students, a 2 (automaticity) x 2 (WML) design was utilized for arithmetic problems. In Study 2, involving 76 engineering…

Preparing graduates for employment is the goal of postsecondary education. In response to the national quantitative reasoning deficiency, institutions have joined nationwide to align college math content and learning outcomes to meet the needs of common careers and everyday life. The problem addressed in this study is that traditional college math…

The aim of the exploratory method research centered on the presence of mathematical tools in STEM through three main questions: Is mathematics an essential tool in the field of STEM? Can mathematics complete projects solely with mathematical and digital tools? Does understanding mathematical modeling affect STEM teaching? A better understanding of…

This study investigated the role of online applets in early algebra lessons. The effect of two different types of intervention modules on developing students' early algebraic thinking abilities was compared. The first intervention module involved the use of open applets and real-life contexts (open-real). The second intervention module involved…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

Let R be an integral domain with quotient field F, let S be a non-empty subset of R and let n = 2 be an integer. If there exists a rational function ?: S [right arrow] F such that ?(a)[superscript n] = a for all a ? S, then S is finite. As a consequence, if F is an ordered field (for instance,[real numbers]) and S is an open interval in F, no such…

In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason…

Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination,…

In collegiate mathematics, college algebra continues to be a barrier to graduation for students (specifically non-science, mathematics, engineering, and science majors). Each year, nearly half of enrolled students struggle to "pass" this course with a grade of C or better (Herriott, 2006). Using innovative constructed lessons geared…