Suggests several hands-on materials for teaching primary students more concretely the concept of fractions. (HTH)

Relates, in story form, how to make geometric and algebraic concepts more accessible to children by using one-dimensional grids. (MKR)

Comprehension and development of the commutative law of addition by children were studied through commutative tasks completed by 72 children aged 5 to 8 years in Madrid (Spain). Results show that children focus mainly on addends in judging equivalence of commuted pairs. A five-level model of understanding of commutativity is proposed. (SLD)

These two articles introduce a new model of probablistic information retrieval (PIR) that is based on the statistical technique of the combination of expert opinion (CEO), which in this model is the opinions of indexers and users. Part 1 presents the conceptual basis, while Part 2 explains the mathematical details. (73 references) (LRW)

Utilizes the notion of a students' proof schemes and outlines categories of proof schemes to evaluate the justifications given by students so that teachers can plan instruction to move them toward more sophisticated ways of reasoning. Contains 22 references. (ASK)

Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)

Offers historical information about square roots. Presents three different methods--Hero's method, visual method, and remainder method--which can be used to teach the finding of square roots and one method for determining cube roots. (ASK)

Discusses what is meant by a process being described as chaotic and how such situations come about. Argues that clarifying this concept is particularly important because understanding chaos helps cure far more fundamental common misconceptions. (ASK)

University students' answers to a "Minds on Physics" problem revealed six distinct approaches to the solution. Discusses implications for teaching and assessment. (Author/WRM)

Focuses on subitizing, the ability to recognize small numbers of objects. Discusses when and how it develops and whether it should be taught. Contains 31 references. (ASK)

Presents an activity using geoboards to recognize similar and different relationships of triangles. (ASK)

Considers a trio of students who collaboratively discover a generalization while doing their calculus homework. Describes the argument as a play which portrays a relatively natural situation cleansed from unrefined mathematical language, errors, and tangential discussions unrelated to the mathematics of the situation. (ASK)

Describes an approach to algebraic thinking based on an extension of the problem-solving tasks typically investigated by elementary and middle school students. Demonstrates how elements of algebraic thinking may be developed in a systematic and coherent way through problem-solving experiences. States that students' pattern-building capabilities…

Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)

Discusses authentic ways to incorporate literature into a first-grade math program. Discusses counting books, number books, storybooks, and concept (informational) books. Cautions teachers not to impose mathematics on a piece of literature--the mathematics should flow from the book. Notes that teachers need to establish a classroom that promotes…