Identifies seven new axes (or dimensions) of variation in mathematics education analogous to the formal-informal and instructionist-constructivist dimensions. (AIM)

This investigation designed for grades three through six centers on the relationship between area and perimeter when solving a problem related to designing a garden. Goals include using area and perimeter in an authentic situation, generating hypotheses, and exploring congruence. (AIM)

Reports a study of mathematical interactions and developing attitudes of children in transition from preschool to school. Two episodes of construction play were analyzed to suggest a model of autonomous learning. Access to self-regulatory social relations was closely linked to accessibility of mathematical meanings. Contains 59 references. (FDR)

Examines 199 middle school students' understanding of percent, focusing on number sense. Reports that students performed better interpreting a quantity expressed as a percent given a pictorial continuous region than when a pictorial discrete set of circles was given. Students had difficulty interpreting a quantity expressed as a percent of a…

Describes an experimental approach to determining the speed of light in water using some simple observations and Fermat's principle. Enables students to integrate mathematical techniques and encourages mathematical exploration in which the students have control over what mathematics and technology to use and when to use them. Presents extensions…

Presents responses to a problem that appeared in the May 2000 issue. The problem was to determine different ways to divide 8 cookies between 3 people. Includes student work from grades 1, 3, and 5. (KHR)

Explores the influence of student teachers' subject matter knowledge on the process of pedagogical reasoning and the influence of images of mathematics, teaching, and learning on student teachers' organization of subject matter. Four student teachers differed in subject-matter knowledge both in aspects of concepts they emphasized and in the use of…

The construction of both natural and formal infinities are products of human thought and may be considered in terms of embodied cognition. Forwards the viewpoint that formal deduction focuses as far as possible on formal logic in preference to perceptual imagery, developing a network of formal properties that do not depend on specific embodiments.…

This classroom study supported and documented the emergence of multiple senses of mathematical similarity. Findings showed a shift toward modeling, which introduced an epistemological dissonance between mathematics and science. Postinstructional interviews suggested that most children came to appreciate the mathematical generalizations afforded by…

Describes a model of cognitive and motivational processes in mathematics learning and relates the model to Brazilian street mathematics and abacus operation. Proposes instructional strategies for motivating conceptual understanding in school mathematics learning. (RJC)

Discusses the term concept and claims that the use of certain strategies to overcome the loss of multiplication facts due to brain damage is evidence of conceptual knowledge and that infants have rudimentary arithmetical knowledge. (MKR)

Discusses epistemological specificities of unifying and generalizing concepts in mathematics, such as axiomatic theory or groups; analyzes their influence on teaching; and presents a theoretical framework used to draw conclusions about theoretical questions of evaluation in a teaching experiment. Contains 37 references. (MKR)

Provides tips and guidelines for teaching students how to speak the universal language of mathematics. Recommends the unlearning of faulty vocabulary, adopting workable strategies to teach math language, and teaching appropriate names of operations, shapes, and angles. Emphasizes need for mastering math vocabulary to be able to communicate in…

The common goal of the empirical studies discussed in this analysis was to assist children in developing a meaningful understanding of the rational number construct, founded on durable fraction concepts. Some research has focused on partitioning; some on ratio and proportion. Contains 59 references. (Author/MKR)

Probability terms were scaled by 3 methods as a result of a survey of undergraduate students (n=194): rank order, percentage estimate, and successive interval. Discusses implications for the selection and placement of probability terms on rating scales in the development of assessment instruments. (JPS)