Focuses on metacognition as a process from the subjectivity of knowledge to its objectivity. Designs a mathematical class of problem situation learning about numbers on a calendar in which students need to generalize the numerical relations of the calendar. (Author/ASK)

Introduces addition, subtraction, multiplication, and division of fractions using area models such as rectangles and circles, or linear models such as the number line and fraction strips. (ASK)

Presents a probability activity addressing students' misconceptions regarding the Law of Large Numbers. Provides students with better conceptual understanding of the Law of Large Numbers. (ASK)

Discusses an algorithm that converts a fraction in simplest form into a terminating decimal and allows students to explore the efficacy and conceptual bases of a mathematical algorithm. (ASK)

Examined analog number representations in 5- to 7- year-olds. Found that subjects accurately estimated rapidly presented groups of 5 to 11 items. Children's data were qualitatively and to some degree quantitatively similar to adult data, with one exception. The ratio of the standard deviation of estimates to mean estimates decreased with age.…

Describes two card games to motivate students to understand number sense concepts that can be used at the 2nd-5th grade levels. (ASK)

Discusses linguistic influence on children's numerical development. Describes and reviews recent papers that address the relationship between number naming systems and children's numerical concepts. (Contains 20 references.) (ASK)

In a course on proofs, a number of problems deal with identities for Fibonacci numbers. Some general strategies with examples are used to help discover, prove, and generalize these identities.

The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

A result known as the Borel-Cantelli lemma is about probabilities of sequences of events. This article presents an example in which it appears that the hypotheses of the lemma are satisfied but the conclusion is not. The explanation of why not combines elements of probability theory, number theory, and analysis.

The number Pi has a rich and colorful history. The origin of Pi dates back to when Greek mathematicians realized that the ratio of the circumference to the diameter is the same for all circles. One is most familiar with many of its applications to geometry, analysis, probability, and number theory. This paper demonstrates several examples of how…

This article illustrates the misconceptions that students have when using the equals sign and describes a lesson used to give students the foundation for an accurate conception of equivalency.

Research addressing the effectiveness of feedback for learning has focused on many dimensions of feedback, including the timing (Kulik & Kulik, 1988), type (Mory, 2004), and amount of available information (Dempsey et. al, 1993). Much of the feedback research in education has tacitly assumed that the available information is perceived, and any…

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…

In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…