A LONGITUDINAL STUDY OF THE DEVELOPMENT OF MATHEMATICS STRATEGIES AND UNDERLYING COUNTING SCHEMES

The purpose of this study was to determine whether patterns of strategy use in second, third and fourth grade children’s arithmetic supported Steffe’s model of numerical development. In addition to student-generated strategies, we looked at commonly taught algorithms not considered in Steffe’s model to determine whether these algorithms reflected underlying schemes. 206 children were assessed on their strategy use while solving arithmetic problems in the second grade, the third grade and again in the fourth grade. Factor analyses indicated some support for Steffe’s model, but there were exceptions. Not all children progressed in their number knowledge and strategies as a function of schooling and schooling appeared to affect the types of strategies children use independent of underlying schemes.     

Diversity as a natural occurrence: an enrichment strategy of peer learning

Business educators are concerned with integrating diversity-related topics and seek methods by which to teach them. This paper suggests that as classes become more heterogeneous, the opportunity to examine diverse perspectives and experiences naturally arises in the course of class assignments and activities. The differential experiences of majorities and minorities are revealed when students discuss and write about their own experiences related to the content of various business courses. The issues of self and group identity and perceptions of others emerge in the context of small group discussions when students share their experiences as recorded in learning logs, personal cases, research assignments, and typical class discussions. The opportunity for community learning in heterogeneous groups provides a forum for diverse perspectives and experiences to be shared. Students and professors learn about different perceptions and reactions to personal and current events as well as their own perspectives, creating a culture of inclusion in the class. Implications and suggestions for a wider application of our methods to a global context are also offered.     

Cognitive Development in Gifted Children: Toward a More Precise Understanding of Emerging Differences in Intelligence

To truly understand gifted performance, it is necessary to merge research on giftedness with current thinking in cognitive development and intelligence. This article presents traditional research on gifted children's cognitive development then considers how the application of newer models and theories from the field of cognitive development can be combined with research on giftedness to change the way people think about gifted performance. First four factors that have often been associated with giftedness are discussed from the perspectives of cognitive developmental psychology and gifted education. Next, emphasis is placed on investigating the strategic development of gifted children. Specifically, R. S. Siegler's (Emerging Minds: The Process of Change in Children's Thinking, Oxford University Press, New York, 1996) model of strategy development is addressed in terms of what it may contribute to understanding gifted cognition. Finally, future lines of research using models from cognitive development and complex systems models of development are recommended.