Data on the ability of pupils to deal with measurement concepts at the middle and high school levels are discussed. Results on items related to area and volume concepts indicate that conceptual problems account for most of the errors that students make on these topics. (MP)

This investigation concerns student understanding of the concept of gradient. Six items are discussed from a series of tests constructed for Technical Education Council (TEC) qualification. It is concluded that confusion exists, and a summary of apparent student difficulties is presented. (MP)

The concept and nature of proof in mathematics is examined, and the emerging role of computers in this area is reviewed. The issue is seen to force mathematicians and philosophers to reexamine their assumptions about mathematics and how it is done. (MP)

A method for teaching the product rule of differentiation in calculus is described. (MK)

A discussion outlining the conditions necessary for quantitative literacy is given. (MK)

A method for teaching division of fractions without "inverting" is described. (MK)

This study investigates the use of infinities and limits during the first 12 years of schooling while a secondary study presents ideas and comments on the observations that were made during the primary study. (MVL)

Reviews and analyzes the number-line metaphor in textbooks. Presents examples to show a way to produce an internal critique of mathematical textbooks, a critique that targets the practices in which the notions are involved within the text. Presents the number-line metaphor as the horizon and the tiller of all the enlargements of the notion of…

Provides information on knot theory and its properties. Presents an activity for grades 9-12 on the applications of knot theory and some unsolved questions in the theory. (ASK)

Discusses a unit integrating science, mathematics, and environmental education centered around "The Great Kapok Tree," by Lynne Cherry (1990). Ratios are used to make scale drawings of trees in a rain forest. Other activities include a terrarium and problem-solving activities based on eating habits of rain forest animals. (KMC)

Studied the competence of nine mathematics teachers in Hong Kong and nine in Korea and their pedagogy. Findings show that teachers possessed conceptual and procedural understanding of mathematics, but most of their teaching strategies were procedurally rather than conceptually directed. (SLD)

Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…

Investigated effects of sparse versus real contexts on understanding abstract mathematical concepts regarding the interpretation of linear graphs. Results of four experiments showed that a sparse context facilitated understanding of abstract concepts more than real contexts. Activation of abstract logic-mathematical knowledge structures was…

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Tells a story written by a sixth-grade student to illustrate the various kinds of numbers encountered in elementary arithmetic. (MKR)