This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…

We sometimes teach our students a method of finding all integral triples that satisfy the Pythagorean Theorem x[squared]+y[squared]=z[squared]. These are called Pythagorean triples. In this paper, we show how to solve the equation x[squared]+ky[squared]=z[squared], where again, all variables are integers.

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.

When students take General Chemistry there are substantially fewer molecular images than they will encounter in Organic Chemistry. The molecular images Organic Chemistry students see in their textbooks are ones that use dashes and wedges to represent 2D and semi 3D views, ball and spoke, ball and wire, and structural formulas, to name just a few.…

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

This article describes how a series of lessons might be used to allow students to discover the size of the Earth, the distance to the Moon, the size of the Moon, and the altitude of Mount Piton on the Moon. Measurement with a sextant, principles of geometry and trigonometry, and historically important scientists and mathematicians are discussed.

The study was conducted to investigate the relation of adolescent students' mathematics motivation and achievement to their appropriate help-seeking and inappropriate guessing behaviour while using instructional software. High school students (n = 90) completed brief assessments of mathematics motivation and then worked with software for geometry…

This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

A whimsical mathematics event for children and adults, derived from Lewis Carroll's Alice's Adventures in Wonderland, was held at the Providence Children's Museum in Rhode Island. NCTM's Standards were the basis of all the activities. (Contains 10 figures and 1 table.)

Presents a unit to review geometric concepts and problem solving by having students work cooperatively to discover geometric shapes constructed from two congruent right triangles obtained from cutting a rectangle along its diagonal. Students report their findings both orally and in writing. (MDH)

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This article describes a multifaceted program that improves the mathematics instruction in a school district's 10 lowest-performing schools. This program includes seven support components--including monetary incentives for teachers, professional development, education technology, and reduced class sizes. After three years, results show that the…

This paper discusses insights for using geometry sketching software to teach geometric concepts for kindergarten to grade 4. The authors created hands-on resources that incorporate technology in a user-friendly environment. When working with "Geometer's Sketchpad" with middle and high school students, the teacher educators noticed the…