Children's number sequence progress through several developmental changes that are brought about through adaptations in the children's counting activities. Introduces key psychological aspects of number sequences, pre-numerical counting schemes, an initial number sequence, a tacitly-nested number sequence, explicitly-nested number sequence, and…

Educators define number sense as a set of conceptual relationships between quantities and numerical symbols. The instructional principals of teaching number sense and number worlds program are mentioned.

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…

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…

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…

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.

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

Previous research has demonstrated that both hearing adults and hearing children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Here, the possibility is explored that the same phenomenon can be confirmed in deaf adults who have acquired a signed language as their first language. Results…

This article describes an example of a fourth-grade lesson from Taiwan in which number sense is developed through real classroom interactions.

Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a fifth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human…

This study examines a wide range of numerical representations (i.e., quantity, knowledge of multiplication facts, and use of parity information) in adult deaf signers. We introduce a modified version of the number bisection task, with sequential stimulus presentation, which allows for a systematic examination of mathematical skills in deaf…

This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 4 figures.)

This article describes an instructional sequence intended to help students think about why integer operations work the way they do. It introduces the idea of an integer as a composite unit and embeds the well-known debit/credit model in an "allowance" context. (Contains 3 figures.)

This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

Examines questions about reported findings that the natural number concept derives from a prior understanding of ordination rather than a prior understanding of cardination. (GO)