It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom.…

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

Personal epistemological beliefs play a key role in teacher engagement with professional learning, so consideration of epistemic cognition is integral to the designing of sustainable professional learning. This qualitative study uses Chinn et al's (2014) model of epistemic aims, epistemic ideals and reliable epistemic processes (the AIR model) as…

The professional character of mathematics teachers is influenced not only by their ability to manage learning but also by their beliefs about the subjects they teach. These beliefs include beliefs about the nature of mathematics (BNM), beliefs about mathematics learning (BTM), and beliefs about assessments (BAM). Together, these beliefs shape the…

In this practitioner-focused article, the authors present a mathematical writing activity for preservice elementary school teachers. The products of this activity, referred to as "journals," are detailed, representation-rich explanations of problems solved in small groups. These journals were originally exchanged across institutions in a…

The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…

The orthogonality of eigenfunctions in problems of unsteady heat conduction in an infinite slab with symmetric and nonsymmetric convective boundary conditions are demonstrated by performing actual integration of the products of the derived forms of eigenfunctions and by implementing the corresponding eigenvalue conditions. The analysis also…

A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using…

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…

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…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

The production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within…

In this paper the author considers the educational experiences and ideas of Émilie Du Châtelet and Maria Gaetana Agnesi, two women mathematicians, scientists and philosophers in eighteenth-century Europe. By tracing their historical emergence as subjects of scientific knowledge, as well as creators of philosophy and culture, the author argues that…

Investigating students' thinking in classroom tasks, particularly in science and engineering, is essential for improving educational practices and advancing student learning. In this context, the notion of "Ways of Thinking" (WoT) has gained traction in STEM education, offering a framework to explore how students approach and solve…