Extends O'Callaghan's computer-intensive algebra study by using his component competencies and the process-object framework to investigate the effects of a graphing-approach curriculum employing the TI-82 graphing calculator. Concludes that students in the graphing-approach classes demonstrated significantly better understanding of functions on…

Utilizes a psychological-constructivist perspective to examine the transitions that students make from arithmetic to algebra in the context of problems that, from an expert's perspective, involve the concept of linear inequality. Reports that students who completed a transition to algebra operated at higher levels of reflective abstraction than…

Provides a brief synopsis of the development of the National Fire Danger Rating System along with an explanation of how it works and possible ways to use it in a modeling or problem-solving unit in a secondary mathematics classroom. (ASK)

Addresses the difficulties students have in acquiring graphical problem-solving skills. Presents some techniques and concepts intended to help students overcome them. Contains 15 references. (Author/ASK)

Adopts several strategies for successful teaching and learning of linear algebra, which consist of a set of computer projects allowing students to explore new concepts, make conjectures, apply theorems, and work on applied projects of their choice. The resulting improvement in student learning has been remarkable. (Contains 12 references.)…

Presents a case study of one high school student's experiences in a first-year algebra course. Emphasizes the use of technology and how it changed the mathematics curriculum. (ASK)

Presents a problem and its solution on generating the complete set of triples of given sides of a triangle. Determines that students who work through the problem stand to learn a great deal more than just which particular triangles fit the given requirements. (ASK)

Offers a matrix to assist mathematics-curriculum planners and teachers around the world in developing multicultural learning materials. Contains 22 references. (ASK)

Given only correlation coefficient, one cannot infer causality. This lesson has been lost on Secretary of Education Richard Riley, who recently intoned that "taking rigorous mathematics courses ... early in secondary schools is a gateway to college and future employment." Students taking such classes have probably already been identified…

Discusses the rationale behind the technique of rationalizing the denominator in algebra. Argues that the importance of this technique is greatly exaggerated and is usually unnecessary. Examines an appropriate application of rationalizing the denominator. (ASK)

Suggests that the differences existing between the view of algebra as a mandated course at a specified grade level and the view of algebra as a way of mathematical thinking and reasoning developed gradually over time must be positively integrated to help students develop a genuine capacity for algebraic thinking and reasoning. (AIM)

Explains the approach of integrating notions of algebra in problem-solving experiences and the design of instructional activities that integrate nonroutine, nontraditional problems. Presents some problems and students' interpretations, conjectures, and generalizations about the patterns they discovered. (AIM)

Presents a problem included on the 1992 National Assessment of Educational Progress in mathematics at grade eight in the content area of algebra and functions. Collects and examines a set of responses to this problem and discusses some examples of strategies that students used to determine the answer to the problem. (ASK)

Focuses on the implications of key findings and theoretical positions from social and cognitive developmental psychology of the use of information technology (IT) tools to support learning in algebra. Presents evidence from a small-scale study of graphics calculators in Hong Kong that supports the feasibility of the UK Cognitive Acceleration…

Presents a comparative study of the effects of feedback on students who learned to solve algebraic factorization problems in an intelligent learning environment. Concludes that when the same error comments were used in both experiments, similarities were observed in the learning paths of the respective student groups. Contains 41 references.…