Current research and learning theory suggest that a hierarchy of proportional reasoning exists that can be tested. Using G. Vergnaud's four complexity variables (structure, content, numerical characteristics, and presentation) and T. E. Kieren's model of rational number knowledge building, an epistemic model of proportional reasoning was…

External representations have a great impact on what and how students learn. One key manner in which environments can operate upon novices' knowledge is through helping them ground their problem solving in an understanding of the situation embodied by the problem. In this paper, students' difficulties in microeconomics problem solving were…

Performance in concrete and abstract tasks is examined systematically by varying the degree of abstractness of problem-solving and concept formation tasks. Four forms of a problem solving test were constructed. Each form of the test presented problem situations through four different modes: verbal stories, picture-book, color slides,…

Describes a study of the mental processes college students use in thinking about speed. Piagetian-type tasks dealing with speed, time, and distance were used in an individual interview format. Males outperformed females on tasks relating to speed, but not on the other tasks. (TW)

Six experiments with 42 kindergartners, 190 first graders, and 15 second graders in Germany investigated why arithmetic word problems with an unknown reference set are more difficult for children than are problems with an unknown compare set. Lack of access to flexible language use makes these problems so difficult. (SLD)

Information about how Graduate Record Examination (GRE) examinees solve verbal analogy problems was obtained in this study through protocol analysis. High- and low-ability subjects who had recently taken the GRE General Test were asked to "think aloud" as they worked through eight analogy items. These items varied factorially on the…

This paper describes seven interrelated studies concerned with children's understanding of sequential actions and with the effects of observing a model on this understanding. A total of 546 elementary and secondary school students served as subjects for the studies. The tasks for all of the studies involved deriving the pattern for a sequence from…

Twenty learning-handicapped and 20 nonhandicapped intermediate-grade children worked on a mathematics problem-solving task on a microcomputer. Their social and instructional interactions were compared as group configuration (individual, homogeneous dyad, and heterogeneous dyad) and task difficulty changed. The computer's effect on the conversation…

Scholastic achievement tests and mental ability tests normally consist of a set of multiple choice items, all of which are assumed to measure school-relevant cognitive abilities. The presumption, in a given test situation, is that the answers/solutions to the given tasks represent cognitive capabilities on the part of the examinees. The purpose of…

In assessing the quality of science teaching for an effort such as the National Assessment of Educational Progress (NAEP), it is important to understand what is meant by scientific thinking--the search for explanations. Instruction should involve higher-order cognitive skill development, but it is difficult to measure reasoning and understanding…

A pilot study on the development and administration of a test using a spatial reasoning problem, the 15-puzzle, is described. The test utilizes on-line capabilities of a real-time computer to record an examinee's progress on each problem through a sequence of problem-solving "moves", and to collect additional on-line data that might be…

Reports on a study designed to assess the kinds of learning opportunities students had as they dealt with science content and the problems teachers faced in managing different kinds of assignments. Management strategies associated with these assignments are described and the effects of these strategies are considered. (Author/TW)

This report builds a case for survey feedback as a useful method of assisting schools to respond actively, rather than passively, to uncertainty and complexity in the school environment. The main argument is that passive responses, such as defensiveness and buffering, reduce educational effectiveness. Planning, an active response, creates…

New information and communications technologies and research in cognitive science have led to new ways to think about and implement learning environments. Among these new approaches to instruction and new methods to support learning and performance is an interest in and emphasis on complex subject matter (e.g., complex and dynamic systems…

The cognitive processes students use in doing the 1996 science assessment of the National Assessment of Educational Progress (NAEP) were studied using two booklets from the 1993 NAEP science field test. Blocks of items from these booklets, a hands-on task block and either a conceptual/problem solving block or a theme block, were administered to 16…