Comparison of the comprehension of proverbs of 200 students (50 each in Grades 6, 8, 10, and 12) found growth in proverb comprehension was most pronounced at two transitional points in development: when students move from late childhood into early adolescence, and again when they move from late adolescence into adulthood. Implications for…

Suggests an elementary school activity and questions to promote five types of mathematical thinking including modeling, logical analysis, inference, optimization, and abstraction. Discusses evaluating activities for mathematical reasoning opportunities. (ASK)

Explores strategies to encourage students' understanding of proportional reasoning. Conducts a study to compare the proportional reasoning of students studying one of the new standards-based curricula with that of students from a control group. (ASK)

Clarifies how students' mathematical reasoning as acts of participation are analyzed in the mathematical practices established by the classroom community. Presents episodes from a recently completed classroom teaching experiment that focused on statistics. Discusses change, diversity, and equity. (Contains 66 references.) (Author/ASK)

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

This paper examines how emerging materials and associated methods became inscribed within and have shaped developing patterns of practice in environmental education. In so doing, it gives attention to how materials and methods have informed methodological narratives and shaped abstracted propositions used in professional development activities.…

According to construal level theory (N. Liberman, Y. Trope, & E. Stephan, in press; Y. Trope & N. Liberman, 2003), people use a more abstract, high construal level when judging, perceiving, and predicting more psychologically distal targets, and they judge more abstract targets as being more psychologically distal. The present research…

Similarity underlies fundamental cognitive capabilities such as memory, categorization, decision making, problem solving, and reasoning. Although recent approaches to similarity appreciate the structure of mental representations, they differ in the processes posited to operate over these representations. We present an experiment that…

Recognizing similarities between our relationship to music and to other people reveals significant educational implications. Emotional responses are inseparable from the understanding which is a necessary condition for any fully educational activity. This brings out the importance of reasoning in music education. Such importance is usually…

Is the idea of the liberal university dead, has the postmodern university any chance of being emancipatory, has the theory-practice divide merely collapsed in an era of "new knowledge work", or has the university just become one aspect of market states and global capitalism? Knowledge-based economies locate universities as central to the…

Trouche's [Third Computer Algebra in Mathematics Education Symposiums, Reims, France, June 2003] presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing…

To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

"What does deep ethical understanding look like and how can we measure the progression of this aptitude?" Qualitative and quantitative data collected from students in Contemporary Moral Problems courses over two successive semesters revealed that the development of moral reasoning skills is a slow process. The progression of moral…

One of the missions of education is to prepare children for complex tasks that occur in their cultural environment. By means of abstracting, the effects of this complexity can be reduced. Recent research and theoretical development show us that young children already seem to be able to think abstractly. The acknowledgement of this potential in…

This study documented the ways in which the spontaneous narratives of a focus group of young children reflected the ways in which these children constructed meaning about their world and their place in it. Participants were six kindergartners who engaged in extended episodes of imaginary, dramatic play and produced complex descriptive narratives…