Describes an activity for introducing elementary school students to the surprising Mobius band. Incorporates elements of experimentation and exposes the deceptively simple Mobius band as a rich resource for discovery. Provides an opportunity for young learners to participate in the process of scientific inquiry within a mathematical framework.…

Elementary number theory is investigated with the main focus on the concept of divisibility and its relation to division, multiplication, prime and composite numbers, factorization, divisibility rules, and prime decomposition. Preservice teachers' responses indicated dispositions toward procedural attachments even when conceptual understanding was…

Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)

Describes a very successful attempt to teach fractions to year 5 pupils based on pupils making their own fraction pack. Children decided for themselves how to make the fractional slices used in the activity using colored cardboard sheets and templates of a paper circle consisting of 24 equal slices. (Author/NB)

Studied the effects of four instructional methods on the mathematical reasoning and metacognitive knowledge of 384 eighth graders. Results show that cooperative learning plus metacognitive training outperformed other combinations of individual and cooperative learning and metacognitive instruction or learning without metacognitive instruction.…

Examined patterns of conceptual and procedural knowledge of addition in 5- to 8-year-olds. Found that children were more successful in noticing that addends had been reordered rather than decomposed and in noticing the decomposition of addends presented with objects rather than with symbols. Also found that profiles of procedural competence were…

Presents vocabulary building strategies to assist young adolescents in better understanding the mathematical concepts being presented to them. Specifically describes: (1) a verbal and visual word association strategy; (2) concept circles strategy; and (3) use of the strategies. Notes that the modified vocabulary strategies have positive results…

Elementary combinatorial problems may be classified into three different combinatorial models: (1) selection; (2) partition; and (3) distribution. The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. Gives an analysis of variance of the…

Illustrates the qualitative nature of the differences between reform courses and traditional courses based on the types of student questions and comments generated in reform classes ranging from college algebra to multivariable calculus. (AIM)

Describes an activity which provides a starting point for exploring geometric concepts through language. The activity incorporates three general ideas: (1) relating to personal experience; (2) integrating with other disciplines; and (3) requiring students to express their ideas. A sample activity would include writing a story about what life would…

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. Develops a mathematical function to describe these gestalts in scientific literature and discusses structural characteristics of…

This article discusses the benefits of using a combined model of academic instruction that includes both explicit and strategic instructional procedures for teaching students with mathematics learning disabilities. It presents an overview of division instruction and interventions for teaching division that include explicit and strategic…

Considers how students' mathematical thinking evolves as a result of their actions and everyday experiences and from increasing reliance on introduced mathematical principles and representations. Exemplifies how 8- to 10-year-olds' personal representations come to face with representations involving algebraic concepts. Explores implications for…

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Discusses ways in which teachers can use the appealing study of quilts as a tool for teaching mathematics concepts and connecting multicultural history, literacy, and art. (Author/NB)