There are diverse ways to construct instructional activities that teachers can use to foster their students' development of mathematical thinking. It is argued that the use of computational tools offers teachers the possibility of designing and exploring mathematical tasks from distinct perspectives that might lead their students to the…

This paper reports on an exploratory study of the mathematical beliefs of a group of ninth and tenth grade students at a large, college preparatory, private school in the Southeastern United States. These beliefs were revealed using contemporary metaphor theory. A thematic analysis of the students' metaphors for mathematics indicated that students…

The process of examination marking is complex, requiring examiners to engage in a variety of cognitive operations. While consideration has been given to marking practices in a few specific contexts, those of General Certificate of Secondary Education (GCSE) examiners have yet to receive serious attention. This study's aims, therefore, were: first,…

The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

This research examines students' use of graphics calculators and investigates the extent to which the students' use meets their teachers aim when using graphics calculators in the classroom. The teacher's use of her graphics calculator was analysed over a week using Key Record software. The teacher was questioned about her aims and expectations…

Reform in secondary mathematics education has created changes regarding how to educate teachers. It is time to check the result of such changes. This study provides a snapshot look at the commonalities of ten pre-service teachers in regards to their mathematics knowledge and their attitudes about mathematics and mathematics education. Four themes…

Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

Throughout much of the world, boys continue to outscore girls on standardized mathematics tests. For example, in most of the 57 countries that participated in the Programme for International Student Assessment (PISA) 2006, boys' performance was significantly higher than girls on the mathematics scale. This fact alone can harm girls' opportunities…

This article describes an activity done by eighth grade students using data that was gathered from sun-shadow observations. (Contains 5 figures.)

Central to the standards-based assessment validation process is an examination of the alignment between state standards and test items. Several alignment analysis systems have emerged recently, but most rely on either traditional rating or matching techniques. Little, if any, analyses have been reported on the degree of consistency between the two…

Thoughts of diverse individuals concerning mathematics are reprinted. Quotations are presented in four categories: philosophical, aesthetic and creative, emotional, and scientific. The author opines that the classroom use of such quotations can provoke thought about the nature of mathematics. (SD)

By introducing elementary trigonometry earlier in a geometry course, a teacher can demonstrate how a variety of techniques can be brought to bear on the same problem. Eight theorems illustrate this. (Author/KM)

Some concerns are expressed about many students who lack mathematics preparation for understanding college physics. Several possible solutions are identified. (RH)

Providing for original and creative thinking by geometry students is discussed. Techniques for discovering theorems are suggested, and examples of places in geometry where these methods can be used are given. (DT)