Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

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)

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…

The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

A selected bibliography of research studies and books related to mathematics and early childhood education. Studies cited pertain to the development of mathematical thought in children, teaching strategies, age-appropriate mathematical content, and assessment and evaluation of mathematical learning. Only materials published in the last five years…

One group of elementary education majors received an algebraic instructional treatment of a unit on linear absolute value equations while another received a geometric treatment. The hypothesis of an aptitude-by-treatment interaction was statistically confirmed. (MN)

This book shows students how to increase their power to analyze problems and comprehend what they read. First it outlines and illustrates methods that good problem solvers use in attacking complex ideas, then it provides practice in applying these methods to a variety of comprehension and reasoning questions. The "Whimbey Method" of teaching…

A workshop concerned with Dienes' six stages in the process of abstraction and generalization is described. One of the logic games used with children in one of the demonstration lessons is explained in detail. (DT)

Contrasts students' presymbolic and symbolic procedures in generalizing activities. Uses the semiotic-cultural theoretical approach and focuses on the role of body, discourse, and signs when students refer to mathematical objects. Identifies types of generalizations and discusses a specific kind of rupture in the ostensive gestures and…

Presents young children's concepts related to probability grouped by definite, possible, and definitely not. Discusses the teaching methods of the probability concepts. (YP)

Discusses the spatial aspects of Greeno's model of conceptual domains and applies the theory to geometry learning. Examines the relationship between mathematical and spatial thinking in light of Greeno's environmental/spatial view of learning. (Contains 16 references.) (MDH)

(MDH)

Conducted to extend a series of earlier aptitude treatment interaction studies in the area of mathematics learning, this study was designed to determine if spatial and general reasoning abilities interact with instructional treatment. The aptitudes used included spatial and general reasoning ability. One hundred and twenty students enrolled in…