Discusses solving rotation problems and shows that there is an alternative to using mental rotations or their encoding into verbal terms, namely using geometrical properties. Presents an analysis of the functionality and effectiveness of the different kinds of strategies as a function of the task's characteristics. Describes research to improve…

Presents a theoretical proposal of a methodology for the teaching of probability theory. Discusses the importance of the epistemological approach of Lakatos and the perspective of the conceptual change. Discusses research using a proposed didactic method with Spanish high school students (N=6). Concludes that significant differences on all…

Because one of the difficulties with the standard presentation of the Fundamental Theorem of Calculus (FTC) is that essentially all functions used to illustrate this theorem are taken from earlier material, many students never fully appreciate the essential role played by continuity in statement and proof of FTC. Introduces the sim x function that…

Explores the nonsymmetric relationship between percent of increase and percent of decrease. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum. (Author/ASK)

This article describes constructivist principles of learning in geometry specific to children's imaginal anticipations in line measurement and fractions. Application with seven sixth grade students with learning disabilities found that students had difficulty coordinating and imagining second-order and higher nested relationships that could be…

Assessed the strategic flexibility of students in mental arithmetic up to the number 100. Results from 60 Dutch second graders show that students' preference for certain mathematical procedures depend on the number characteristics of the problems, indicating that the students had a good conceptual understanding of numbers and procedures. Actual…

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)

Presents an activity to identify some square-differences on the multiplication table. Discusses these properties using the Pythagorean triangle. (ASK)

Offers an alternative instructional method of constructing cubes based on the use of linking smaller cubes to form triangles. Offers learners insight into algebra by clearly exposing the underlying structure of the problem-solving process. (ASK)

Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)

Presents problems from the Mathematics in Context (MiC) project with a central theme concerning the construction of a variety of formulas by students. (AIM)

Interviews 22 high school precalculus students to examine their understanding of slope as measure. Indicates that students demonstrated a better understanding of slope in functional situations, but many students had trouble interpreting slope as measure of rate of change. Suggests that instruction should focus on helping students form connections…

Examined development of number concepts among participants from the beginning and end of first grade, third and fifth grades, and university. Found that the numerical distance effect appeared in all groups. Found size congruity effect began to appear at the end of first grade. Proposed a model of internal representation of magnitude asserting that…

Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…

Examined whether preschoolers could recognize numerical equivalence for comparisons involving sequentially presented sets. Found that children recognized numerical equivalence for static sets earlier than for sequential sets. Memory of the number of sequentially presented objects emerged earlier than memory for the number of sequential events.…