Described are three activities and variations that can help students to understand the concept of place value. Allowing students to use concrete materials and helping them to bridge the gap between manipulatives and paper-and-pencil tasks are emphasized. (KR)

The influence that number naming grammar has on the understandings of two-digit numbers and place value of kindergarten children of European and Asian background was examined. Results indicate that Asian verbal/numerical representation patterns naming tens and units in order may be associated with distinctive place value concepts that support…

Research on cognitive representation of numbers and understanding of place value of U.S. and Japanese first graders was extended to France, Sweden, and Korea (118 subjects; approximately 24 from each of the 5 countries). Basic differences in children's cognitive representations of number are influenced by characteristics of their languages. (SLD)

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

Examines two days of teacher-led large group discussion in a 5th grade class about a mathematical question intended to support student exploration of relationships among fraction and decimal representations and rational numbers. Illuminates the teacher's work in supporting student thinking through the use of a mathematical question embedded in a…

This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students' work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions…

Whenever teachers of young children get together there will be differences of opinion about how far children should be taught to count. Some will argue that the focus should be on small numbers to 9, building up the notion of what, say, the name 5 means, what it looks like, and how it can be represented. Others argue that with ice blocks retailing…

A study was conducted with forty-seven preservice childhood (elementary) education teachers (42 F, 5 M) enrolled in two mathematics methods classes taught by the same instructor to determine the effect of these college students making curriculum materials appropriate for upper elementary students on the preservice teachers' knowledge of…

This article details problems and instructional approaches intended to promote preservice teachers' understanding of the reasoning underlying whole number multiplication. (Contains 9 figures.)

This paper discusses a study that explored the mental models of fifth (n=35) and sixth (n=49) graders attending two urban public elementary schools in South Korea in word problem solving. Two levels of mental models (problem model and mathematical model) constructed in the process of word problem solving were investigated. Coding categories for…

This dictionary of Ahtna, a dialect of the Athabaskan language family, is the first to integrate all morphemes into a single alphabetically arranged section of main entries, with verbs arranged according to a theory of Ahtna (and Athabascan) verb theme categories. An introductory section details dictionary format conventions used, presents a brief…

This guide contains a collection of alternative techniques for teaching arithmetic that have proved useful in teaching both children and adults with various learning problems. Discussed first are several underlying principles of instructing individuals with learning disabilities, problems, and differences and special accommodations for…

This competency analysis profile contains eight lists of mathematics skills that have been identified by employers and verified by math-certified instructors as being core competencies for eight groups of occupational areas. Each list is organized into subsections dealing with the following: numbers and number relations, measurement, data analysis…

This document is a collection of 77 shared teaching ideas from the "From the File" department that appears regularly in the "Arithmetic Teacher." The ideas are reproduced in file-card size and categorized for easy use and handling. This useful source of activities and problems is designed to help elementary and middle school…

This document presents Core Course Proficiencies for the State of New Jersey whose purpose is to ensure that all students have equal access to the fundamental knowledge and skills critical to achieving success in mathematics. After an introduction providing rationale and background, the Core Course Proficiencies are presented in three sections.…