The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to…

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

This article draws on a multi-phase study of collaboration in tertiary education programmes. This commenced with a survey of 111 students in Engineering and Creative Arts, contrasting their experiences of the teaching of collaboration in different faculties. This led to an iterative action research cycle, in which the conceptual boundaries that…

At the undergraduate level, the composite motion of simple harmonic vibrations has always been the main content of physics as well as several other scientific disciplines. Many textbooks tell us clearly that when the frequency ratio [omega][subscript 1]/[omega][subscript 2] of two perpendicular vibrations is simple integer ratio n[subscript…

An electric motor converts electrical energy into mechanical work and an electric generator converts mechanical work into electrical energy. The symmetry between the motor and generator naturally leads to questions about creating a perpetual motion machine. The allure of this question has inspired textbook problems, physics education articles, and…

There is a growing interest in the value of teachers guiding students to generate their own representations to support conceptual learning in science and across complementary subjects such as mathematics. However, this approach to an interdisciplinary focus poses challenges for programme design and learning assessment. In this paper, we report on…

There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…

This paper presents a study aimed at investigating the didactic potentiality of the combined use of two different kinds of artefacts for the purpose of constructing and conceptualizing mathematical meanings related to the notion of axial symmetry. In our view, the process of meanings construction can be fostered by the use of adequate artefacts,…

To better understand the role of neuroendocrinological regulation in adolescent mental health, stress reactivity needs to be analyzed through both the autonomic nervous system (ANS) and the hypothalamic-pituitary-adrenal (HPA) axis. Accordingly, this study examined how adolescents' internalizing and externalizing mental health symptoms are…

We investigate three 8th-grade students' mathematical meanings developed in the context of using linked representations to generate animations of figural models tuned in musical rhythm in "MaLT2," a programmable Turtle Geometry in 3D resource affording dynamic manipulation of variable values. We adopted a modified version of the UDGS…

This article engages with methodological concerns connected to insider education research and the "race-symmetry" shared between the researcher and teacher participants. To do this, race critical reflexive strategies are utilized to show how and why this practice productively contributed to the knowledge about race making constructed in…

We investigated the extent to which one elementary school child with working-memory differences made sense of number as a composite unit and advanced her reasoning. Through ongoing and retrospective analysis of eight teaching-experiment sessions, we uncovered four shifts in the child's real-time negotiation of number over time: (a) initial…

Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of…

This article discusses a 2021 survey of French as a second language (FSL) teacher candidates (TCs) in Faculties of Education in Ontario whose practice teaching experiences were affected by the COVID-19 pandemic, pivoting them into remote FSL teaching and learning. The survey, which formed a component of a larger mixed method SSHRC-funded research…

The development of creative processes within the framework of music and dance constitutes an opportunity to promote and integrate learning from different subject areas. In these activities, the moments of knowledge transfer between the different parts of the curriculum emerge as key moments in the process. This article identifies and analyses the…