Metaphors are recognized as bridging scientists' challenges in communication with the public. In mathematics, however, which often involves abstract concepts and relations, less attention has been paid to the role of metaphors in public communication. In this article we examine the metaphors appearing in the discourse of 10 mathematicians in five…

'Bothways' was an expression first utilised by Yolnu educators in the late 1980s to convey the profound intercultural epistemological foundations of Yolnu society that should also apply to modern "Balanda" (white) schooling systems. Despite the pressures from national, standardised curriculum and assessment regimes, 'Bothways' has not…

This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three…

Even though reflective symmetry is heavily embedded in the everyday, learners continue to experience challenges when they mathematize concepts from this informal/everyday context. In this article we argue that symmetry exists in nature, it can also be symbolized algebraically and it can be abstracted into the world of axioms and theorems. We…

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…