This article investigates the interplay of time words with how children position hands on an analog clock. Using a mathematics discourse framework (Sfard, 2008), we analyzed how students interpreted precise (e.g., 2:30) and relative (e.g., half past 11) times, finding that particular words are dynamically interwoven with activity. Interviews with…

This study investigated income group differences in kindergartners' and first graders' (N = 161) arithmetic by examining the link between accuracy and strategy use on simple and complex addition problems. Low-income children were substantially less accurate than high-income children, in terms of both percentage of correctly solved problems and the…

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…

In 4 experiments, we used self-paced reading and eye tracking to demonstrate that readers are, under some conditions, sensitive to the presuppositions of definite versus indefinite determiner phrases (DPs). Reading was faster when the context stereotypically provided a single possible referent for a definite DP or multiple possible referents for…

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an…

This study investigated longitudinal pathways leading from early spatial skills in first-grade girls to their fifth-grade analytical math reasoning abilities (N = 138). First-grade assessments included spatial skills, verbal skills, addition/subtraction skills, and frequency of choice of a decomposition or retrieval strategy on the…

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this…

In this technical report, we describe the development of cognitive diagnostic test items that form the basis of the diagnostic system for Project DIVIDE (Dynamic Instruction Via Individually Designed Environments). The construct underlying the diagnostic test is division of fractions. We include a description of the process we used to identify the…

These materials were written with the aim of reflecting the thinking of The Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. Presented are plans for teaching 15 inequality lessons for above average first grade students. The discovery approach is utilized by the teacher in order to involve…

These materials were written with the aim of reflecting the thinking of the Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. This report deals with some seventh grade mathematical concepts taught at Cambridge Friends' School. The discovery approach was utilized by the teacher in order to…

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. Presented are plans for teaching 23 probability lessons in the elementary grades at Hancock School, Lexington, Massachusetts. The discovery approach was utilized by the…

A BIBLIOGRAPHY OF BOOKS, PAMPHLETS, AND MAGAZINES WHICH WILL ASSIST THE ELEMENTARY SCHOOL TEACHER IN BUILDING A BACKGROUND FOR UNDERSTANDING THE CHANGES IN ELEMENTARY SCHOOL MATHEMATICS IS PRESENTED. NUMBER LINES, FRACTIONS, AND FUNDAMENTAL CONCEPTS ARE IMPORTANT TOPICS IN MANY OF THE PUBLICATIONS. A LISTING OF NINE PROGRAMS FOR TEACHING NEW…

Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we…

The Massachusetts Board of Education recently adopted a 5-year plan to assist Local Education Agencies (LEAs) in the curriculum areas of reading, writing, arithmetic, science, and computer literacy. However, reduction in funds and staff at the LEA level has decreased the ability of local programs to implement marketing and assistance. This manual,…

This report describes comparative evaluations of the Distar I (first grade) and Distar II (second grade) programs which were carried out in 1972-1973. Results showed: (1) the Distar program for first grades had no conclusive advantage over traditional instruction for the development of oral language or reading achievement; and (2) second grade…