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 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°.

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…

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

Research shows that teachers influence students' attitudes towards; performance in; and perceptions of a subject. Hence, the need to improve the teaching and learning of many curricular subjects has been well documented for many years. This paper focusses on efforts made to develop competence among out-of-field teachers of mathematics and…

Research into the importance of teachers' use of verbal language in multilingual classes where teaching and learning is done in a language other than the learners' first, is crucial. Such research aimed at improving multilingual learners' access to conceptual understanding of mathematical concepts is becoming increasingly urgent. In this paper, we…

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…

Mathematics educators agree that linking mathematical ideas by using multiple approaches for solving problems (or proving statements) is essential for the development of mathematical reasoning. In this sense, geometry provides a goldmine of multiple-solution tasks, where a myriad of different methods can be employed: either from the geometry topic…

In a typical high school course, the complex physics of collisions is broken up into the dichotomy of perfectly elastic versus completely inelastic collisions. Real-life collisions, however, generally fall between these two extremes. An accurate treatment is still possible, as demonstrated in an investigation of coin collisions. Simple…

Trigonometry is an integral part of the draft for the Senior Secondary Australian National Curriculum for Mathematics, as it is a topic in Unit 2 of both Specialist Mathematics and Mathematics Methods, and a reviewing topic in Unit 1, Topic 3: Measurement and Geometry of General Mathematics. However, learning trigonometric ideas is difficult for…

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…

In 1999, Richard Lee Colvin published an article in "The School Administrator" titled "Math Wars: Tradition vs. Real-World Applications" that described the pendulum swing of mathematics education reform. On one side are those who advocate for computational fluency, with a step-by-step emphasis on numbers and skills and the…

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…

This article describes activities that introduce basic trigonometric functions in a smooth and natural way. The only requirements are basic algebra, the Pythagorean theorem, and the concept of area.