The longitudinal progress of 42 Grade 1 students who participated in a 10-20 week Extending Mathematical Understanding (EMU) intervention program was examined to evaluate the effectiveness of the program for enhancing and accelerating mathematics learning. Overall the students made accelerated progress during Grade 1 and their learning was…

Before starting school, many children reason logically about concepts that are basic to their later mathematical learning. We describe a measure of quantitative reasoning that was administered to children at school entry (mean age 5.8 years) and accounted for more variance in a mathematical attainment test than general cognitive ability 16 months…

Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic…

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

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…

Strategies used by 150 children as they solved addition and subtraction verbal problems were studied over a period of one-and-a-half years. Number size and presence of manipulative materials were variables manipulated in individual interviews given at three separate intervals. Two addition and four subtraction tasks were used. Processes changed…

This paper describes the research program of the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The major interest is in the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children. Three factors…

Solutions to addition and subtraction word problems were studied in a three-year longitudinal study that followed 88 children from grades one to three. They solved problems using a variety of strategies before formal instruction and used invented strategies several years after formal instruction. Four levels of problem-solving ability were found.…

This paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…

Three studies on the development of number concepts (counting, addition, subtraction, and place value) in seven- to nine-year-olds considered low attainers in mathematics were conducted. The search for a descriptive framework, the development of a diagnostic assessment instrument, and a longitudinal study are reported. (MNS)

This paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…

Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…

As part of a 3-year study of arithmetic problem-solving skills in young children, pretests were administered to 180 middle class first grade students. Following each of three instructional units, another achievement test was administered. The three first grade units corresponded to the Developing Mathematical Processes curriculum and involved…

This paper is the second of a series of four reports that document the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to 10 instructional units on sentence-writing for verbal problems and algorithms…