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.

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…

Two important pedagogical techniques for developing deeper mathematical understanding are to prove a given theorem in different ways and to unify the proofs of different theorems. Trigonometric angle sum and difference identities are introduced in Unit 2 of Specialist Mathematics in the Australian Curriculum (Australian Curriculum, Assessment and…

Transitional engineering students are those who are academically ineligible to enter a bachelor's engineering program but are enrolled in an associate engineering program with a university. Successful completion of such an associate engineering program allows the higher achievers to transfer to a full bachelor's engineering program. The associate…

Teaching mathematics by project-based learning (PBL) method on the use of educational technology offers an innovative teaching pedagogy at college. The "World Culture Art Created with Calculus Graphs of Equations" poster project was designed by the first author and was completed in the pilot Calculus course during the spring 2016…

Researchers promoting the inclusion of technology for teaching and learning have recently called for the integration of mathematical technologies into the preparation of future teachers. This report analyzes the dynamic geometry sketches produced by preservice secondary mathematics teachers when investigating trigonometric relationships. We…

Science and engineering instructors often observe that students have difficulty using or applying prerequisite mathematics knowledge in their courses. This qualitative project uses a case-study method to investigate the instruction in a trigonometry course and a physics course based on a different methodology and set of assumptions about student…

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

Many studies argue that dynamic features of the artefact Cabri may function as instruments of semiotic mediation. Our study is situated in this perspective and aims to observe the impact of the use of the technological artefact Cabri in a teaching experiment that introduces the notion of a trigonometry function, through the articulation of the…

Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…

The kinematics teaching strategy is a teaching method that stimulates kinesthetic intelligence and thus offers students an unconventional approach for exploring mathematical ideas through movement. This article describes how to use the kinesthetic approach to introduce radian measure. The article includes detailed descriptions of easy-to-use…

The mathematics methodology subjects the author undertook in the early 1980s encouraged him to adopt a very expository style of teaching in which each new concept is introduced by its formal definition. The teacher should then explain a few carefully chosen examples for students to copy into their books, and then provide plenty of graded practice…

Over the years the technology behind displaying the image of the unit circle has changed, but the defining features remain constant. The key question for the author as a teacher is this: are the relationships embodied in the image simple, memorable and rich enough to be grasped by any KS3 student at his school? It needs to be simple enough to…

By selecting certain special triangles, students can learn about the laws of sines and cosines without wrestling with long decimal representations or irrational numbers. Since the law of cosines requires only one of the three angles of a triangle, there are many examples of triangles with integral sides and a cosine that can be represented exactly…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…