Presents a way of interpreting mathematics classrooms, by advancing the notion of sociomathematical norms, to account for how students develop mathematical beliefs and values and how they become intellectually autonomous in mathematics. Includes episodes from a second-grade classroom to clarify the processes by which sociomathematical norms are…

Sixteen middle school students ranked the lengths of various paths in problem-solving interviews. Every student invoked at least one of four intuitions that originated from their everyday experiences: compression, detour, complexity, and straightness. Students continued to use their inadequate intuitions in the posttest before applying learned…

Analyzes instructional actions designed to help a student understand distance, time, and speed. Focuses on the mathematical knowledge that guided instructional decisions and actions and discusses implications for content preparation of teachers. Contains 48 references. (Author/MKR)

Interviews with 107 children, ages 4-7, about uncounted quantities, counted quantities, and numerical equations showed that the ability to predict changes to counted quantities increased with age. Only 7-year olds were able to use covariance and compensation in the purely numerical context of derived equations. (Author/MKR)

Children (n=336) in grades 1-5 were interviewed individually using a Piagetian task to study development from additive to multiplicative thinking. Multiplicative thinking was found to appear early (in 45% of second graders) but to develop slowly (only 48% of fifth graders used consistently solid multiplicative thinking). (Author/MKR)

Discusses the role of language in mathematical understanding, focusing on a classic debate between two leading writers in hermeneutics, Gadamer and Habermas. Suggests that personal learning of mathematics is inseparable from the social practices within which learning occurs. (Author/MKR)

Inservice (n=36) and preservice (n=67) mathematics teachers were asked for a commutative, nonassociative binary operation. Responses were analyzed for correctness, productiveness, mathematical content, and underlying difficulties. Both groups exhibited a weak concept by failing to produce an example and using a limited content search space.…

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)

Explores cognitive operations such as coordination, integration, and structuring as manifested in a spatial context. Relates spatial thinking to enumeration strategies. Interviews with 45 third graders and 78 fifth graders suggest that students initially see arrays of cubes as uncoordinated sets of faces, later as space-filling structures. (FDR)

Middle school teachers (n=53) and prospective secondary teachers (n=28) posed problems related to billiards before and after solving a sample problem. Found systematic problem generation and more problems posed before solving a sample problem. Posed problems were not always solvable. (MTE)

Validates a framework for assessing children's thinking in multidigit number situations and uses the framework to evaluate instructional programs. Key constructs--counting, partitioning, grouping, and number relationships--appear stable within each of 5 levels across 12 case studies, suggesting a possible hierarchy of thinking. (DF)

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)

This constructivist teaching experiment investigated the role of whole-number knowledge in fraction learning. Two nine-year-old students worked for one year with a computer program (Copycat) and demonstrated that the development of whole-number knowledge and rational-number knowledge is interdependent. Contains 59 references. (KMC)

Videotaped 14 mother-infant dyads during book sharing to examine categories of information mothers provided when talking about the book. Found a substantial amount of discussion about the books. Mothers modeled information structures of varying levels of cognitive demand, most frequently modeling the simplest of labeling pictures, with decreasing…

Explored development of interpersonal understanding by observing two four-year-old boys as they played checkers. All interactions were coded and conflicts were isolated and coded for resolution. Found a decrease in impulsive strategies and an increase in reciprocal strategies during the year, and increased ability to resolve conflicts and a…