This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

This article explores the educational and philosophical contributions of Nikolai V. Bugaev, a prominent 19th-century Russian mathematician and founder of the Moscow philosophical-mathematical school. The study specifically focuses on Bugaev's textbook, "Arithmetic of Whole Numbers," analyzing Bugaev's pedagogical approaches within the…

The author discusses Professor Henry A. Bent's presentation regarding the nature of the difficulty that many college and university students have with arithmetic reasoning involving division. (HM)

The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part: part notion of ratio, and the "between" and "within" relationships in ratio were emphasised.…

An examination of the status of teaching mathematics to deaf students showed that teachers ignore the hands-on exploration of objects that promotes conceptualization of basic mathematic principles. An arithmetic teaching strategy is proposed which is activity-based and is derived from Piaget's theory of intellectual development in children.…

It is argued that Australian elementary mathematics curricula have been influenced by earlier British and United States educational movements and theories and are out of touch with current research emphasizing a constructivist approach. A new model of young children's numerical development is offered, and recommendations for improving mathematical…

With the aim of viewing children as individuals and not as psychological problems or creatures to be taught, The Children We Teach examines the roles of child and teacher as they relate to one another and as they relate to the subject matter and learning tasks of early school years. Included are discussions of relationships among children, of…

METHODS OF MEASUREMENT AND A SUITABLE CURRICULUM WERE DEVELOPED AND ASSESSED FOR ELEMENTARY SCHOOL CHILDREN GIFTED IN ONE OR MORE OF THE FOLLOWING RESPECTS--SPACE CONCEPTUALIZATION, VOCABULARY, NUMBER ABILITY, LOGICAL REASONING, AND SCIENTIFIC INFORMATION. EXPERIMENTAL AND CONTROL GROUPS WERE ESTABLISHED OVER A 2-YEAR PERIOD. EVALUATION OF SOCIAL…

Presents a developmental framework for the study of culture and cognition in which cultural practice is a key organizing construct. Argues that systematic analysis of either cultural change or cognitive development requires that they be understood relative to one another in a single integrative treatment. (Author/SD)

This article discusses the challenge mathematics educators face in deciding what and how mathematics is to be taught, and offers some suggestions for teachers of young children based on Piaget's developmental theory of mathematics. Piaget's cognitive stages are briefly described and the concrete stage, which spans the age range included in early…

This study was undertaken to ascertain the degree of stability of significant gains made in intellectual functioning by a group of children who attended Head Start programs and two groups of children who did not attend preschool programs. Data collected and analyzed at postkindergarten showed nonsignificant differences between performance levels…

The cognitive determinants of number analogy performance were studied by systematically manipulating the processing demands imposed by the items. To explore sources of developmental differences in analogical reasoning, subjects were included from two age levels, grades 4 and 5 and college. To allow the investigation of individual differences in…

Twenty culturally deprived children planning to enter first grade in the fall attended an 8-week half-day summer program in which a systematic classroom management program utilizing token reinforcement and isolation techniques was combined with a strong academic program. One hour and 40 minutes was allotted daily to pre-reading and language…

The report presents information on intellectual development and school achievement of youths in relation to selected socioeconomic and demographic factors. Estimates were based on data collected by the National Center for Health Statistics from 1966-70. The survey sample consisted of 6,768 adolescents aged 12-17 years. Measurement instruments were…