Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function…

We propose an original machine that traces conics and some transcendental curves (oblique trajectories of confocal conics) by the solution of inverse tangent problems. For such a machine, we also provide the 3D-printable model to be used as an intriguing supplement for geometry, calculus, or ordinary differential equations classes.

It is widely accepted that the classroom teaching practices of in-service secondary mathematics teachers can benefit from the advanced mathematics they learned during their university education. However, pinpointing explicit instances of how this advanced knowledge informs teaching practices has proven challenging for both teachers and…

The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year…

This article presents an instructional technology-based cycle model intended to support and facilitate the teaching and learning of mathematics, particularly calculus. The study used quantitative methods with quasi-experimental research that uses non-randomised assignments of the study group that are categorised into experimental and control…

The five papers published by Hodgkin and Huxley in 1952 are seminal works in the field of physiology, earning their authors the Nobel Prize in 1963 and ushering in the era of membrane biophysics. The papers present a considerable challenge to the novice student, but this has been partly allayed by recent publications that have updated the…

A basic mental model (BMM--in German 'Grundvorstellung') of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific…

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

In this dissertation, we propose a computer-supported method, called insightful learning systems, for tracking student progress that yields human actionable insights. We cover our theories, experiments and applications that aim to pave the way for more effective understanding of student progress, in key skills for a course, by looking at students…

College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…

The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities…

Flipped instruction has been flaunted as a pedagogical strategy that supports improved learning and retentive abilities of students. Nevertheless, one of the twin challenges reported in the literature, students' failing to complete preparatory work, impedes the efficacy of the model. Thus, learners' motivation and attitude to work are essential…

Research using the Anthropological Theory of the Didactic suggests different models of how student learning may evolve in the progression of undergraduate mathematics coursework: from elementary courses in Calculus to more advanced courses in Analysis. An ideal model suggests that the theory-driven learning in the latter serves as a natural…

A central goal of introductory physics for the life sciences (IPLS) is to prepare students to use physics to model and analyze biological situations, a skill of increasing importance for their future studies and careers. Here we report our findings on life science students' ability to carry out a sophisticated biological modeling task at the end…

In high school, students extend understanding of linear and exponential functions and explore trigonometric functions. This includes using the unit circle to connect trigonometric functions to their geometric foundation, modeling periodic phenomena, and applying (and proving) trigonometric identities. These ideas are fundamental for trigonometric…