"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

The present work shows how 4-6-year-old Spanish children interpret numbers and space intervals in the ruler when measuring length. To determine it, 4 ad hoc rulers are designed and used with a sample of 103 children from two schools of Toledo province (Spain). The sample is characterized respecting conservation and measurement with the standard…

Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

The purpose of this study was to examine the effects on four-year-olds' knowledge of mathematics by introducing professional development and center-based mathematics activities around four mathematical domains to early educators' teaching in Head Start programs. Because of the need to provide necessary mathematical experiences to young children to…

Children's literature can play a significant role in integrating math and science concepts into real-world applications. One particularly delightful selection is "Cucumber Soup" (Krudwig, 1998). This book can create a context--making cucumber soup--for weighing and for a real-life on adding fractions. This kind of learning context takes children…

This book demonstrates how K-2 students deepen their mathematical ideas when encouraged to represent and communicate their thinking. Numerous vignettes from actual classrooms and reflective comments from teachers provide a model for how show and tell can enhance classroom teaching and improve children's learning. Examples of students' work and…

Describes a study in which 383 children in grades 1 through 5 were individually interviewed to find out at what point they construct unit iteration out of transitive reasoning. Indicates that most children construct unit iteration out of transitive reasoning by fourth grade. Suggests a better approach to the teaching of measurement that presents…

This discussion of the mathematical potential of classroom events gives many examples of incidents that can be used for learning about topics such as one-to-one correspondence, counting, sets, ordering, time, fractions, money, shape, estimation, measuring, volume, area, number operations, and graphs. (MP)

Several problems are identified: place values, time, even numbers, fractional parts, and temperature. Specific teaching suggestions are discussed. (MP)

A group of 161 kindergarten and first grade children were instructed in mathematics using exercises in linear measurement to increase understanding of unit-quantity relations. A comparison group made up from two adjacent and comparable middle-class schools was taught mathematics without intervention into the mathematics content. Treatment and…

It is argued that number sense develops through meaningful, purposeful activities involving calculating, measuring, and estimating. Understandings that must be developed with each are discussed. More emphasis needs to be placed on thinking about the various procedures that can be used to solve problems and on interpreting the answers. (MNS)

A method for reading Piaget is presented in this guide, written for practicing teachers who want better understanding of Piaget's writings. An account of a Piagetian experiment is given, followed by a discussion of its theoretical and practical implications. Eight topics are explored: number, measurement, knots, perspectives, coordinates, floating…

This discussion of decimals covers topics such as place-value, zero, the decimal indicator, grouping, the metric prefixer, and rules for interpreting dimensions. (MP)

An outline of practical experiences from which the concept of length measurement may be learned. (MM)

Describes a low-tech, hands-on activity to improve student understanding of irrational numbers. Each student creates a number line from adding machine tapes and uses a square and a precisely folded triangle as the only measuring device. (KHR)