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…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

Computer algebra system (CAS) calculators are becoming increasingly common in schools and universities. While they offer quite sophisticated mathematical capability to teachers and students, it is not clear at present how they may best be employed. In particular their integration into students' learning and problem-solving remains an issue. In…

The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…

If equivalent operations are performed on the left term and right term of an equation, a new equation results. This principle allows one to produce equations with a variable isolated on one side and its value(s) on the other. It also underlies problem-solving in situations where equations are not explicitly used, but the problem calls for…

The author provides an example of obtaining the correct answer to a problem through a so-called nonsense solution. The conditions under which this incorrect method will yield a correct solution are examined. (JP)

Discussion is focused on standard teaching procedures that contain the elements of modern mathematics. Of the various methods which have been tested, it is concluded that the solving of problems remains the most effective basic activity. A sample collection of problems is presented to indicate relationships and the principles they illustrate. (RP)

Two problem-solving strategies involved in finding the area of a particular square formed on a geoboard are described in detail. (MP)

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.

This article describes Comer's Method, a student's discovery of an alternative approach to solving the determinant of a 3x3 matrix.

In this paper, a contextual approach to teaching Mathematics at the pre-university level is recommended, and an example is illustrated. A "context" in the form of a real common mathematical problem is presented to the students. Different approaches to tackle the problem (from topics within and outside the syllabus) can be elicited from students.…

Algebra has been identified as the foundational course for all other mathematics courses. Yet, research has shown that African-American students are low achievers in all strands of mathematics (NCES, 2001). Computers, on the other hand, have been marketed as an instructional tool to teach and reinforce classroom instructions. This study…