The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…

Research on the characteristics of individuals who have demonstrated a high level of ability in mathematics is presented. The importance of structure in mathematical thinking is stressed and implications for teaching are detailed. (MNS)

This monograph is a comprehensive presentation and discussion of the 1972-73 National Assessment mathematics data. It is a report from the National Council of Teachers of Mathematics Project for Interpretive Reports on National Assessment. The report examines data from four age groups (nine, thirteen, seventeen, and adult) and evaluates…

This study investigated: (1) the relationship between the development of information processing capacity and certain Piagetian logical reasoning abilities; and (2) how the development of these cognitive abilities related to acquisition of certain measurement concepts. Forty first-grade children were individually administered tests of conservation…

This material is designed to examine the research on how children acquire basic addition and subtraction concepts and skills. Two major lines of theories of the development of basic number concepts, called logical concept and quantification skill approaches, are identified. Major recurring issues in the development of early number concepts are…

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…

Forty-three first-grade children, who had received no formal instruction in addition and subtraction, were individually administered 20 problems that could be solved using addition or subtraction. The problems were selected to represent the following semantic types: joining, separating, part-part-whole, comparison, and equalizing. Responses were…

This study was presented at the 1979 meeting of the American Education Research Association (AERA), San Francisco. It investigated the relationship between the structure of simple addition and subtraction problems and the types of processes children use to solve them prior to receiving formal arithmetic instruction. Specific strategies which young…

The study investigated children's ability to write number sentences for simple addition and subtraction word problems. The results suggest that open number sentences may provide mathematical symbolism that allows young children to build on informal strategies for presenting and solving simple word problems. (Author/PK)

Results from the third national mathematics assessment indicate that the decline in performance of 17 year olds between 1973 and 1978 has leveled out over the last four years, and 13 year olds' performance improved significantly between 1978 and 1982. However, most gains were on lower-order skills. (MNS)

National assessment data on student performance in several phases of algebra are reported. It is noted that this performance has not reached the point of mastery even for most students with two years of algebra and a year of geometry. However, the data are not thought to suggest complete failure. (MP)

This review synthesizes research on relationships between performance on mathematics learning tasks to determine whether Piagetian tasks make useful readiness measures. Results indicated such tasks do not make useful measures, and suggested success on these is not necessary for many mathematics tasks. (MP)

Data from the second mathematics assessment of the National Assessment of Educational Progress shows little difference between males and females in overall mathematics achievement at ages 9 and 13. However, at age 17, females are not achieving as well in mathematics as males. (MP)

Data from the 1977-78 mathematics assessment of the National Assessment of Educational Progress (NAEP) on the use of calculators are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

First-grade children's solution processes for addition and subtraction were studied. Their processes tended to represent the relationships or actions described in individual problems. (MP)