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…

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…

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…

This study reveals the content and methodological features of professionally oriented training of engineering students in higher mathematics. The authors provide examples of applied tasks for students of different technical specialities. The relevance of this article is determined by the fact that a modern higher educational institution sets…

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…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

Core maths (CM) qualifications were introduced into the post-16 curriculum in England in 2014, with first assessments in 2016. They are a suite of qualifications aimed at students who achieve a grade 4 (originally a grade C) or higher at GCSE Maths but do not go on to take AS or A level Maths. This group comprised around 40% of all students in…

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for…

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…

Deaf and hard of hearing (DHH) students' performance on fraction story problems is a cause for concern given that knowledge of fractions in the elementary grades is essential for learning Algebra in secondary school and advanced mathematics in college. Using grounded theory, the current study investigated DHH college students' cognitive strategies…

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus…

The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in…

The aim of this study is to improve the quality of the mathematics curricula in Saudi universities by investigating the required changes in mathematics curricula in order to satisfy the demands of the Saudi Vision 2030. The researcher used qualitative methods to answer the research questions by randomly selecting a sample composed of some faculty…

The main objective of this paper is to propose a didactic framework for teaching Applied Mathematics in higher education. After describing the structure of the framework, several applications of inquiry-based learning in teaching numerical analysis and optimization are provided to illustrate the potential of the proposed framework. The framework…