Assuming that dynamic features of Dynamic Geometry Software may provide a basic representation of both variation and functional dependency, and taking the Vygotskian perspective of semiotic mediation, a teaching experiment was designed with the aim of introducing students to the idea of function. This paper focuses on the use of the Trace tool and…

Proof is a fundamental aspect of mathematics. Without the notion of proof, mathematics would not exist as a separate subject, as it would be essentially indistinguishable from science. Yet proof is often reserved for "high ability" students in schools or those studying mathematics in further education. The author's own memories of…

This article presents a rich geometry problem and discusses its solution. A variety of mathematically correct justifications for this answer are provided. (Contains 2 figures.)

The general factor of mental ability ("g") may reflect general biological fitness. If so, "g"-loaded measures such as Raven's progressive matrices should be related to morphological measures of fitness such as fluctuating asymmetry (FA: left-right asymmetry of a set of typically left-right symmetrical body traits such as finger…

This paper provides students with many interesting observations regarding the nature of magic squares, magic rectangles, and quasi-magic squares and provides tools for teachers to group students into ability-balanced cooperative learning groups.

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies…

How can the secondary Geometry course serve as an opportunity for students to learn to "be like" a mathematician--that is, to acquire a mathematical sensibility? In the first part of this dissertation, I investigate what might be meant by "mathematical sensibility". By analyzing narratives of mathematicians and their work, I identify a collection…

A teacher narrates from activities and discussions that arose among undergraduates and herself while doing critical explorations of mirrors. Surprised by light's behaviors, the students responded with curiosity, losing their dependence on answers as the format of school knowledge. Inadequacies in how participants supposed light works emerged in…

The aim of this study was to examine the views of pre-service mathematics teachers on the use of webquests in teaching and learning geometry with reference to a theoretical framework developed by Dodge in 1995. For this study the researcher identified four groups containing nineteen pre-service mathematics teachers, which were then assigned to…

The authors investigated the effects of student spatial ability, as measured by Raven's Progressive Colored Matrices (J. C. Raven, 1938) and type of instructional program on geometry achievement. Sixth-grade students worked through either 6 instructional activities in Geometer's Sketchpad (Key Curriculum Press, 1993), a dynamic geometry program,…

Secondary special educators are in desperate need of progress monitoring measures in mathematics that appropriately reflect their students' instructional content. As educators across the country respond to increasing standards for challenging curricula, growing numbers of students with disabilities are participating in more advanced mathematics…

This study documents problem solving approaches that high school students develop as a result of using systematically Cabri-Geometry software. Results show that the use of the software becomes an important tool for students to construct dynamic representations of the problems that were used to identify and examine different mathematical relations.…

This instructor's guide consists of materials for use in teaching a course in geometry designed for students enrolled in postsecondary vocational or technical education programs. Covered in the individual units of the guide are the following topics: basic terms, straight line combinations, angular conversion, circles, polygons, and geometric…

In this document, detailed objectives for the following courses are listed: Algebra I, Algebra II, Geometry, Trigonometry, Analytic Geometry, Advanced Mathematics, Personal Business Mathematics, and Business Mathematics. Each objective is keyed to an expected level of achievement: awareness, knowledge, application, mastery, reinforcement, and…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…