Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were…

Twenty-seven supplemental lessons for primary students involving mathematical thought problems on addition, subtraction, and comparison (e.g., greater than and less than) are presented. Each of the lessons contains 10 or more problems which students either hear or read and then respond to either orally or on written answer sheets. The materials in…

Over the past few years a substantial body of research has yielded evidence that the semantic structure of elementary arithmetic word problems influences children's strategies to solve them. The study reported in this document considered three other task characteristics in addition to semantic structure: (1) the order of presentation of the two…

Summarized are the findings from five studies carried out in Australia in 1979-80. First was a cross-sectional survey designed to determine the memory capacity of a population of children in grades 1-3. The second study investigated performance differences on a variety of mathematically related developmental tasks for the same group. Data from…

This practicum was designed to improve and increase the problem-solving skills of third-grade students. Using a specially designed 20-item test consisting of mathematical word problems, a preassessment was made of the addition and subtraction skills of 843 third-grade students from high, middle, and low socioeconomic levels in four Florida…

This study investigated children's representation of addition and subtraction problems with canonical and noncanonical number sentences, to see whether children would directly represent the structure of a problem if both types of sentences were available. Subjects were 22 first graders and 41 second graders randomly assigned either to a Canonical…

The purpose of this study was to relate children's cognitive processing capabilities and their grade level to their performance and to the strategies they used when working addition and subtraction problems. From two sets of data which assessed memory capacity and cognitive processing capacities, six groups of children with different cognitive…

The focus is on the problem-solving behaviors of primary age children on one-step verbal or story problems involving addition and subtraction. When children are given a simple word problem for which they have not learned the necessary algorithms, they are often able to derive a solution on their own. This report focuses on the child-invented…

Presented are four interpretive reports and a list of current publications of the Mathematics Work Group at the Wisconsin R&D Center. The first interpretive report gives a brief overview of their work. Reports two through four are concerned with individual interviews, carried out during a longitudinal study, in which primary children are asked to…

To ascertain if children's use of manipulatives and/or the teacher's presentation of the problem in parts (chunking) affect children's ability to model and/or solve addition and/or subtraction problems, 146 first-grade subjects were administered the Houston Addition and Subtraction Problem-Solving Test which provided accuracy and modeling scores…

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

This is a first-grade manual for teachers using SMSG elementary school text materials. For each chapter background information is given; for each section, objectives, vocabulary, materials, suggested procedures, and further activities are listed. Chapter topics include: (1) pre-number experiences; (2) recognizing geometric shapes; (3) building…

THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE (1) ADDITION AND SUBTRACTION WITH WHOLE NUMBERS, (2) PATTERNS AND…

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) number patterns, (2) measuring the interior and exterior angles…

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) addition, subtraction, and multiplication in modulo seven…