Examined the nature of numerical knowledge in 5-month-olds to inform the debate whether numerical abilities result from capacities dedicated to numerical cognition or to more general perceptual capacities. Found that 5-month-olds could determine the number of collective entities, moving groups of items, when non-numerical perceptual factors such…

Aims to help children understand difficult concepts according to their own particular learning styles and to keep students learning while maintaining their interest in and excitement about mathematics. Presents everyday mathematics games for students at every ability level to practice important mathematical skills. (ASK)

Explores the study of ordered pairs to allow students to demonstrate their own creativity, apply previously learned computer skills, evaluate their own work, and draw connections to other mathematical strands. Using a spreadsheet, students construct a drawing composed of connected ordered pairs, the inverse, and the negative of the drawing. (ASK)

Presents a joint work of mathematics and science educators that suggests that many responses that literature describes as alternative conceptions are interpreted as if they evolved from a small number of intuitive rules. Demonstrates the explanatory and predictive power of these intuitive rules. (Contains 36 references.) (Author/ASK)

Presents five mathematics activities to celebrate the 100th Day of School. Lists the full set of activities that relate to mathematics, art, music, physical education, science, social studies and history, English, and creative writing. (ASK)

Examined role of spontaneous gesture in 2- to 4-year-olds' counting and assessment of counting accuracy. Found that correspondence of children's speech and gesture varied systematically across age. Children adhered to one-to-one correspondence principle in gesture prior to speech. Counting accuracy related to correspondence of speech and gesture,…

Two experiments examined preschoolers' performance on test relying on the uniqueness principle for using evidence from a miscount in inferring a counterfactual cardinal number, with subtests probing associated number-skills. All the 5-year-olds and half the preschoolers passed the test. Results suggest that a crucial preschool step is to start…

Explores the meanings of millennium, century, and decade, and introduces the notion of millennial age as one's precise age on 1 January 2000. Asks students to estimate their millennial age and explores various other computation and estimation activities using the idea. (ASK)

Reacts to the publications "Curriculum Guidance for the Foundation Stage" and "National Numeracy Strategy: Framework for Teaching Mathematics from Reception to Year 6" published by the Department for Education and Employment in Great Britain. Makes the case for the marrying of formal and informal, abstract and concrete…

Offers teaching suggestions for activities using the TI-73 graphing calculator in middle schools. Topics include the number line, data handling, and algebraic thinking. (MM)

Describes the constructs of referents, relationships, and modes and illustrates how these constructs may be reflected in students' written responses to a decimal task that requests an explanation. Examines sets of responses from two classrooms using the proposed framework to illustrate the type of information that teachers may acquire through the…

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

Thousands of years ago, mathematicians thought about numbers in terms of geometry. Numbers had shapes, and by thinking about the shapes, mathematicians could do a lot of things with numbers that are now recognized as algebra. This document contains a lesson plan for students to learn the relationship between numbers--all while developing algebraic…

If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

This article presents a new model of transcoding numbers from verbal to arabic form. This model, called ADAPT, is developmental, asemantic, and procedural. The authors' main proposal is that the transcoding process shifts from an algorithmic strategy to the direct retrieval from memory of digital forms. Thus, the model is evolutive, adaptive, and…