This model is useful in identifying specific learning problems and in providing techniques for the teacher to motivate and teach students at all levels. What it is and how it can be used are discussed, illustrated by specific strategies for geometry and science. (MNS)

Students solve a geometric problem of measuring polygons with the help of proportional reasoning. Thus the importance of conceptual reasoning is emphasized as a highly efficient technique for teaching and strengthening mathematical content.

A Mandelbrot mathematical set is an object with endless borders, and in the present exercise a graphing calculator is used to identify and examine the set points. The significance and power of technology is also displayed in the understanding and solving of problems.

As geometry involves lot of graphics, it acts as a link between mathematical model and real-world phenomena. An effective tool like geometry software can help students to explore the ellipse.

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

In this article, the authors talk about transformation geometry being treated as little more than a set of tricks rather than as a mathematically rigorous topic. This appears to lead to pupils seeing little point in studying "reflections, rotations and translations" as other than examinable items in some future test. Following the argument…

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.

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…

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…

This article describes the work of outreach mathematicians introducing the topic of complex variables to eighth and ninth grade students (13- to 15-year-olds) in the US. Complex variables is an area of mathematics that is not typically studied at secondary level. The authors developed seven lessons designed to stimulate students' interest in…

Different computational tools may offer teachers and students distinct opportunities in representing, exploring and solving mathematical tasks. In this context, we illustrate that the use of dynamic software (Cabri Geometry) helped high school teachers to think of and represent a particular task dynamically. In this process, the teachers had the…

Computer-assisted instruction systems have been broadly applied to help students solve math word problem. The majority of such systems, which are based on an instructor-initiating instruction strategy, provide pre-designed problems for the learners. When learners are asked to solve a word problem, the system will instruct the learners what to do.…

This submission contains the Proceedings of the 2009 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at York University in Toronto, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group…

Describes activities that use the geometric construction capabilities of the Geometer's Sketchpad computer software to explore triangles. Topics investigated include angle measurement, the sum of the measures of the angles of a triangle and a five-pointed star, triangle classification, and area and perimeter of a triangle. (MDH)

For boys and girls who are prepared in the essential elements of arithmetic this later book proposes extended instruction in percentage and commercial transactions, and in the elements of geometry. It is one of a series of handbooks for pupils, and consists of progressive lessons, arranged mainly in topics, either reviewing the treatment in…