What is meant by "normal science" is described, the first three steps in the "route to normal science" are outlined, and an example is given in which the trend toward research consensus is apparent. This involves current work on learning addition and subtraction. (MNS)

Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

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…

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…

Determined whether 11 third-grade children, differing in cognitive processing capacity, solve addition and subtraction word problems differently. Results, among others, show that children who differ in cognitive processing capacity also differ in strategies they use to solve the same verbal problems and differ in their success in finding correct…

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…

This paper reports the results of the second of a series of collaborative studies examining how children acquire the skills to represent and solve verbal addition and subtraction problems. The purpose of this study was to identify the cognitive processing capabilities of a group of Tasmanian (Australian) children. Fifteen cognitive tests were…

Findings from five related studies carried out in Tasmania, Australia in 1979-80 are summarized. The first study attempted to determine the memory capacity of a cross-sectional population of children aged 4-7, while the second study was designed to portray differences on a variety of mathematically related developmental tasks for the same…

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…

The purpose of this study was to identify the working memory capacity (M-space) for a group of 139 children (4 to 8 years of age) enrolled at Sandy Bay Infant School in Hobart, Tasmania, Australia. Four M-space tests -- The Counting Span Test (Case and Kurland, 1978), Mr. Cucui Test (DeAvila and Havassy, 1974), the Digit Placement Test (Case,…

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 reports the results from one of a series of related, collaborative studies carried out in Sandy Bay, Tasmania, Australia, in 1979 and 1980, examining how young children acquire the skills to represent and solve addition and subtraction problems. The purpose of this study was to relate children's cognitive processing capabilities and…

Data are reported for the classroom observational portion of a cross-sectional study conducted in Tasmania, Australia to examine the acquisition and development of addition and subtraction skills in young children. During the study, a group of students in grades l, 2, and 3 who differed in cognitive processing skills were observed during…

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…