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…

Mathematical reasoning with algebraic and geometric representations is essential for success in upperdivision and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to…

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

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…

Trigonometry is a well known branch of Mathematics. The study of trigonometry is of great importance in surveying, astronomy, navigation, engineering, and in different branches of science. This paper reports on the discovery of flaws in the traditional definitions of trigonometric ratios of an angle, which (in most cases) make use of the most…

Must two triangles with equal areas and equal perimeters also be congruent? This question was introduced in "Mathematics Teacher" ("MT")by Rosenberg, Spillane, and Wulf in their article "Heron Triangles and Moduli Spaces" (2008), which also described the authors' subsequent investigation of a particular moduli…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…

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…

The study of trigonometry suffers from a basic dichotomy that presents a serious obstacle to many students. On the one hand, there is triangle trigonometry, in which angles are commonly measured in degrees and trigonometric functions are defined as ratios of sides of a right-angled triangle. On the other hand, there is circle trigonometry, in…

Today's classrooms pose many challenges for new mathematics teachers joining the teaching force. As they enter the teaching field, they bring a wide range of mathematical experiences that are often focused on calculations and memorization of concepts rather than problem solving and representation of ideas. Such experiences generally minimize what…

How to determine when there is a unique solution when two sides and an angle of a triangle are known, using simple algebra and the law of cosines, is described. (MNS)

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…

Algebraic and transcendental curves are discussed, with attention focused on computing the area of some special regions bounded by the curves. (MNS)