Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…

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 was designed to replicate and extend the work of Steffe on the effect of using different set names as variables in addition problem statements. The behavior of both first- and second-grade students was studied and the usefulness of visual aids in solving addition problems was also investigated. One-hundred twenty first- and second-grade…

A study was undertaken of the effects of formal education and conservation of numerousness on addition and subtraction problem types. Thirty-six kindergarten and 36 first-grade subjects randomly selected from one area of a school district were administered measures of conservation, problem-solving success, and modeling ability. Following factor…

Ten nursery school children who knew how to count but were unacquainted with arithmetic were taught a simple algorithm for solving single-digit addition problems and were then given extended practice. The reaction time on the final block of extended practice suggested that subjects had invented a more efficient procedure to replace the original…

The use of an elaborative process by kindergarten children in the performance of verbally presented arithmetic addition problems was investigated. A static rather than dynamic verbally described relation between stimulus sets resulted in more correct responses for two of nine Developmental Level X Prompt Condition groups, supporting the use of…

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

A teaching experiment involving 30 third graders investigated the transformation of their concepts of numbers. Observations of their notations and problem-solving procedures show development that progresses from a focus on states to a type of reasoning in which changes become quantifiable "objects of awareness." (SLD)