Recent research suggests that knowledge is stored in the learner's head as a network of concepts or constructs. Children's mathematical problem-solving strategies become increasingly abstract as they are able to engage in more abstract thinking. An experimental study using an alternative Cognitively Guided Instruction approach is described.…

Reported are early results of a research program that aims to improve children's mathematics learning by developing attitudes and strategies that support processes of interpretation and meaning construction in mathematics. Considerable research shows that many children learn mathematics as symbol manipulation rules, without meaning. Collaborative…

Mathematics is generally regarded as a well-structured discipline by educators and cognitive scientists. This leads to the analysis of the suggestion that practitioners begin investigating possibilities for teaching mathematics as if it were an ill-structured discipline, with more than one interpretation for mathematical statements. The paper is…

Investigated the role of "a priori" ideas in planning experiments and data processing leading to inferences. Thirty-one students (ages 11-13) observed a "combustion/candle in a closed container" experiment and were asked to interpret sets of measurements. Findings, among others, show that children preferentially experiment on…

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…

The purpose of this study was to examine the effects of researcher-developed lessons on students' understanding of two- and three-digit numeration. Digit-correspondence tasks, often used for individual interview assessment of place value understanding, were adapted to be used as problem-solving tasks. The tasks were presented to three classes,…

Investigates fifth-grade students' conceptual changes toward the greenhouse effect and global warming due to sociocognitive interaction developed in small and large group discussion in an authentic classroom context during an environmental education unit. Classroom discussions led the children to integrate new scientific knowledge into their…

The mathematical experiences of elementary students often focus on memorizing facts and rules as opposed to making sense of the subject and developing problem solving skills. Students spend large amounts of time processing, memorizing and sorting collections of data which are tasks well performed by computer technology. To correct this situation,…

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…

The relationship between mental models used in problem solving and strategies children use when problem solving with manipulative materials are discussed. Teaching strategies for bridging the gap between the two are suggested. (CW)

This study explored how regular teachers (N=20) and special education teachers (N=20) think and make instructional decisions about special needs students. Teachers viewed a videotape of a reading comprehension lesson for a small group of third grade students. One student was a target for observation and classified as learning disabled.…

Presents a psycholinguistic analysis of the development of writing skills and reports a developmental study of knowledge effects in writing. A theoretical framework decomposes the requisite knowledge into three main components: (1) generalized, high-level problem-solving plans, (2) content, and (3) discourse. (Author/SED)

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…

An analysis of children's narrative composition and art revealed concurrent development at both a general structural level and at a fine-grained detail level. A three-part study investigated whether this general cognitive pattern would be maintained across a different range of tasks: literary composition, scientific reasoning, and working memory.…

Discusses a new approach to mathematics education that moves away from methods that tell students what to do and toward methods that help students build mental representations of mathematical concepts. Contrasts the previous and emerging views and examines aspects of the new approach. (26 references) (MDH)