The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)

Presents examples in which the graphing calculator can provide students with particularly valuable insights into some major statistics ideas such as random numbers. (ASK)

Describes three activities of imaging, including constructing an image, representation-presenting the image, and transforming the image. Discusses a link between imaging and number sense, teaching students to image, and assessing imaging. Contains 25 references. (ASK)

Surveys texts of grades 6 through 9 and makes quantitative and qualitative analyses of the instructional emphasis on selected concatenations in written mathematics. Indicates much curricular emphasis on unsigned (without negative signs) numeral forms and integers as compared to minimal curricular emphasis on signed (with negative signs) fraction,…

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.

This article concludes the serialization of the Royal Statistical Society's Schools Lecture for 2004, on "Lies and statistics".

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.