Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the…

Some pedagogical problems in Chinese numeration are described. They involve the teaching and learning of how to speak numerals with fluency in Chinese, using Hindu-Arabic written numbers. An alternative approach which stresses regularity is proposed. (MNS)

The development of a quantitative concept of rational numbers was explored in interviews with 16 fourth and fifth graders in two cities. High performers used a flexible and spontaneous application of concepts of rational number order and fraction equivalence, and a reference point, while low achievers tended not to. (MNS)

In this study, Piagetian theory is extended to explore ways in which children construct their understanding of our notational system and place value. Eighty children aged 4 to 9 were asked to group objects, draw pictures of grouped quantities, write numerals to indicate amounts, and theorize about the relationship between their written numerals…

A mathematics teacher who avoided students' questions about zero, notes that children are able to interpret this concept and any system of numeration in a language that they have made up and can understand. (AM)

The mechanisms, images, and language needed for the development of rational-number ideas are briefly discussed. Such ideas are sophisticated and different from natural-numbers ideas. (MNS)

A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of…

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

The vision of K-12 standards-based mathematics reform embraces a greater emphasis on students' ability to communicate their understandings of mathematics by utilizing adaptive reasoning (i.e., reflection, explanation, and justification of thinking) through mathematics discourse. However, recent studies suggest that many students lack the…

The emergence and differentiation of partitioning as a process that leads young children to construct ideas of rational numbers was traced through clinical sessions with 43 primary children as they manipulated objects. The data analysis led to a five-level theory of the partitioning process. (MNS)

Described is an activity where base-10 blocks are used to develop students' skills in reading, writing, and visualizing large numbers. An activity sheet that helps students with decimal points is included. (KR)

The processes and strategies used by Finnish second graders in solving verbal multiplication and division tasks were investigated, and the relationship of these processes and strategies to Piagetian abilities, memory capacity skills, and rational number concepts was charted. Three categories of strategies were classified: operations based on…

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…

The educational background of students termed "limited English proficient" (LEP) is discussed, with consideration of how that background might affect the LEP student's learning of arithmetic. Reasons why knowledge of background is important are first noted. Then examples of different ways to read and write numerals and differing subtraction and…