The paper discusses how complex mathematical behaviors might possibly be accounted for in terms of a finite set of rules. Behaviors involved in knowing mathematical systems are extended to logical interrelationships between properties of mathematical systems. (JG)

Research reported deals with measuring attitudes of college students enrolled in a terminal mathematics course. Attitudes about mathematics learning, mathematics as a process, the place of mathematics in society, and school and learning in general were measured. The instrument used was specifically designed for the study. (JG)

Research reported deals with the effects of activity instruction in the learning of multiplication in grade 3. Procedures, data analysis, and conclusions are presented. (JG)

Research reported deals with developing objective item types which measure the same abilities measured by student-produced formal proofs in geometry. Procedures and findings are included. (JG)

Research reported deals with the effects of using negative instances in the teaching of eighth-grade general mathematics on achievement, reasoning ability, perceptual speed, and tendency to overgeneralize. Procedures, data analysis and conclusions are presented. (JG)

A review of research involving the utilization of manipulative materials in improving mathematics learning is presented. Subsequent assessment and discussion is included. (JG)

A critique is given of the use of an efficiency ratio to reexamine the data of the International Study of Achievement in Mathematics. A reply to this and an earlier critique of the analysis is included. (JG)

Reported is the development of an instrument to assess knowledge of mathematical information by entering kindergarten pupils. Subscales are developed for the areas of geometry, measurement, money, numbers, pattern identification, recall, and mathematics vocabulary. Reliability estimates, intercorrelations of subscales and a factor analysis of…

Scales were developed to measure dimensions of belief about mathematics and mathematics instruction. (MM)

Learning of games related to the mathematical Klein group is studied with adolescent girls. (MM)

Stimulus conditions were found to interact with conservation level and relation type. (MM)

A review of 25 years of Piagetian research in intellectual growth as it pertains to the learning and understanding of mathematics and implications for teaching. (MM)

A study of conservation of length concepts covering the symmetric, asymmetric, reflexive, nonreflexive, and transitive relations. Their order of development was traced during the course of a 15-lesson sequence of related instruction. (MM)