This paper shows how the computational and graphical capabilities of spreadsheets allow for interactive analytic and geometric constructions from numerical modelling of homogeneous Diophantine equations of the second order. Suggested activities, designed for prospective teachers of mathematics and made possible by what is referred to in the paper…

Consider a sequence recursively formed as follows: Start with three real numbers, and then when k are known, let the (k +1)st be such that the mean of all k +1 equals the median of the first k. The authors conjecture that every such sequence eventually becomes stable. This article presents results related to their conjecture.

Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for…

This article considers skills and abilities of young children with number in the areas of cardinality and ordinality. Responses to number tasks by a sample of 3- and 4-year-old children are described to outline their differing approaches to determining the numerosity of a set, and to establish their application of ordinality language to describe…

Three experiments explored the semantics of the mass-count distinction in young children and adults. In Experiments 1 and 2, the quantity judgments of participants provided evidence that some mass nouns refer to individuals, as such. Participants judged one large portion of stuff to be ''more'' than three tiny portions for substance-mass nouns…

In this article, the author explores the concept of "moving one place to the left." A recent investigation by Thompson and Bramald explored the relationship between young children's understanding of place value and their ability to add two-digit numbers. The study took the form of a series of one-to-one interviews with a sample of 144 children…

An exploration of the difference of two squares relates the formula to prime numbers.

This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

This article discusses the challenges students face in making sense of zero as a number. A range of different student responses to a computation problem involving zero reveal students' different understandings of zero.

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Bridge to…

"Singapore Math: Place Value, Computation & Number Sense" is a six-part presentation on CD-ROM that can be used by individual teachers or an entire school. The author takes primary to upper elementary grade teachers through place value skills with each of the computational operations: addition, subtraction, multiplication, and division. She gives…

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of…

The processes and strategies used by Finnish second graders in solving verbal multiplication and division tasks were investigated, and the relationship of these processes and strategies to Piagetian abilities, memory capacity skills, and rational number concepts was charted. Three categories of strategies were classified: operations based on…

Activities for teaching mathematics in kindergarten through grade 8 are included in this guide. Both original ideas and ideas gleaned from various sources, including teachers in the district, are presented. The introduction briefly discusses the importance of developing understanding of concepts, processes, and relationships, the need for…

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…