We view the (real) Laplace transform through the lens of linear algebra as a continuous analogue of the power series by a negative exponential transformation that switches the basis of power functions to the basis of exponential functions. This approach immediately points to how the complex Laplace transform is a generalisation of the Fourier…

The purpose of this study is to conduct a bibliometric analysis of the research published in the field of mathematics misconception from 1947 to 2023, to determine the general knowledge structure and participation in research publication. An analytical approach was used based on Scopus database data. This study used mixed methods; quantitative…

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…

This paper examines prospective mathematics teachers' knowledge of asymptotes and asymptotic behaviour of functions in calculus. They are university students and future facilitators of knowledge in upper secondary education. We constructed a "reference epistemological model" to describe the knowledge about asymptotes for upper secondary…

We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students' errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

We investigated understanding of the linear independence concept based on the type and nature of connections displayed in seven non-mathematics majors' interview responses to a set of open-ended questions. Through a qualitative analysis, we identified six categories of frequently displayed connections. There were also recognizable differences in…

This study analyses a standards-based textbook series to investigate how slope is presented across seven sequential textbooks in a secondary mathematics curriculum. Analysis of the expository content across the textbooks shows that slope is covered in all seven books, is frequently described as a "Constant Parameter" or…

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus.

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…

In this study, the conceptualizations used by prospective middle school mathematics teachers when defining, representing, and exemplifying the slope concept and relating it with other mathematical situations were examined. Participants' conceptualizations were identified by Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. [(2013).…

Despite the use of axiomatic definitions for mathematical concepts, scholars struggle to produce a single definition of angle that does not have some limitations. Textbooks' treatment of angle and its measure reflects this multifaceted nature of the angle concept while informing the different ways learners conceive of these concepts. In this…

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…