For a given rational number r, a classical theorem of Niven asserts that if cos(rp) is rational, then cos(rp) [element-of] {0,±1,±1/2}. In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that.

This literature review covers 42 years and has two main objectives: to identify the obstacles to learning the polar coordinate system and to explore the teaching proposals suggested to overcome them. These questions are answered by locating and analysing articles related to the topic published in research and practitioner journals specialising in…

Problem-based learning (PBL) has the potential to enhance both cognitive and affective engagement but has been criticised for being unsuitable for learners with low levels of knowledge and skills, such as South African learners from poor backgrounds. In such cases, guided problem-based learning (GPBL), which includes direct instruction and teacher…

In this paper, Richard Ollerton presents two alternative approaches to proving the six standard trigonometric angle sum and difference identities. They are suitable for students who have an understanding of rotation matrices.

Helping students to stay motivated by creating an environment that makes them interact is essential to attaining academic achievement. This action research utilizing mixed methods approach explores the flipped classroom's impact on the students' achievement motivation. Also, a significant focus has been on how students interacted with their…

This paper is the result of a research done from the Socioepistemological Theory of Mathematics Education, perspective in which we enquire about the reasons to study trigonometric Fourier series in electrical engineering, and what historical and epistemological conditions can be considered to develop more profound meanings when this topic is…

The goal of the paper is to pay attention to some important techniques and approaches including adequate designations as a tool for unambiguous understanding and a key to success in solving problems, vivid visual images as a mnemonic techniques, and special formulas as a universal tool for solving typical problems, when teaching medical students…

In mathematics, there are countless connections between apparently unrelated topics. Students often find these relationships interesting, and they contribute to expanding their mathematical repertoires. This article describes one of these unusual connections, between the sum of periodic functions and the commensurable and incommensurable numbers.…

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving…

The purpose of this paper is to follow the reasoning of high school students when asked to explain the standard trigonometric limit lim/[theta][right arrow] sin[theta]/[theta]. An observational study was conducted in four different phases in order to investigate if visualization, by means of an interactive technology environment (Geogebra), can…

This case study offers a recounting and analysis of the experiences of one urban educator, in a public high school mathematics classroom setting, working to integrate critical mathematics curricula and pedagogy with youth and in collaboration with a community organization. This project helps to unveil complexities that teachers may experience when…

This article proposes that the reader be nourished by avant-garde elements for new educational practices in the teaching and learning of mathematics. The writing is based on an investigation that was carried out with high school students from Puerto Rico. From a qualitative paradigm with a research design in action, it was explored how students in…

Purpose: Analogical reasoning has been studied using a variety of tasks that generally required consideration of the relationship between the object and its integration to conclude an analog schema. The aim of this study was to describe the model of analogical reasoning schema based on some analogical problems. Research Method: In this study used…

The difficulty in the process of trigonometry teaching, served as a stimulus for the present research, in which the objective consisted of designing and proposing the use of a Trigonometric Cicular Geoplane for the construction of meaningful learning in the area of Mathematics at Israel Technological University. For Its development, a field…

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.