The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

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)

Discusses convergence between instructional practices suggested by research on achievement motivation and practices promoted in mathematics-instruction reform literature by focusing on fourth- through sixth-grade students (N=624) and their teachers (N=24). Concludes that the instructional practices suggested in the literature of both research…

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language…

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Two studies dealing with length conservation and measurement indicate that caution needs to be used when one looks at and makes claims about children's cognitive ability and development with regard to conservation. (MP)

Ninth-grade students were given a battery of cognitive aptitude tests and randomly assigned to verbal or figural mathematics instruction. Learning and retention were correlated with the aptitude measures and other fixed variables; regression analysis indicated the importance of memory, semantic factors, and sex difference. (SD)

Studies the co-emergence of teaching and children's construction of specific conceptions that support the generation of improper fractions in a constructivist teaching experiment with two fourth-grade students posing and solving tasks in a computer microworld. Reports that examination of the teacher's adaptation of learning situations (tasks) and…

Report provides new data concerning children's accuracy as measured by previous studies and clarifies progress of first graders during entire year on difficult single-digit addition and subtraction problems. Discussion focuses on advantages of an adding on interpretation of subtraction and the importance of emphasizing conceptual understanding…

Described are the general problem-solving strategies and their nature and functions. The importance of integrating different types of general problem-solving strategies with content-specific teaching in mathematics classes is discussed. (KR)

Increased use of cooperative learning methods is a visible change in mathematics education in the last decade. Research questions on cooperative learning concerning different models employed, their effectiveness compared to traditional methods of instruction, their effects on student achievement, and cognitive and affective benefits gained during…

Reviews chapters of this book on probability in mathematics education. Topics discussed in the chapters include a historical perspective of probability, an epistemological perspective of probability, an overview of the psychological research on probability learning, computers in probability education, and an analysis of the probability curriculum.…

Six classes received problem-centered mathematics instruction for two years in second and third grade. Results indicate that students in these classes scored significantly higher than students in traditional classes on standardized measures of computational proficiency and conceptual understanding. (TO)

Examines how one teacher's way of knowing mathematics was reflected in language used in teaching concepts of rate to one student. The teacher's conceptualizations of rate were encapsulated in the language of numbers and operations which undermined his effort to help the student understand rates conceptually. (Contains 27 references.) (Author/MKR)

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)