Reports research designed to explore the possibility that conceptually different forms of common-fraction understanding can be identified. Such forms may be associated with differences in fraction problem solving-performance. Contains 50 references. (DDR)

Explores the development of understanding of the concept of average with students from grades 3 to 9 through interviews. Observed six levels of response based on an hierarchical model of cognitive functioning. Documents usage of ideas associated with the three standard measures of central tendency and representation as strategies for problem…

Teachers need to assist students in understanding what they read in science textbooks. Presents effective reading as a basis for good problem solving skills. (DDR)

The relation of knowledge for solving problems to understanding of general principles in a subject-matter domain is discussed. Theoretical representations, called "conceptual competence," are presented to represent principles that are believed to be understood implicitly by individuals. Implications for problem-solving procedures can be…

Presents a revised working definition of schema, lists four types of knowledge that individuals have (i.e., identification, elaboration, planning, and execution), and outlines issues in schema theory. The usefulness of schema in problem solving and information problem solving is discussed, and implications for teachers of information literacy are…

Presents evidence indicating that spontaneously generated analogies can play a significant role in expert problem solving. Focuses on an evaluation strategy known as bridging that has been observed in solutions to both science and mathematics problems. Contains 23 references. (DDR)

An appreciation of the relationship between novice and expert knowledge frameworks may help develop an understanding of the process of transition from one to the other. Recommends the use of concept mapping. (DDR)

An alternative is suggested to conventional and propositional ways of thinking about curriculum matters. Curriculum theory is conventionally presented as statements of propositional knowledge even though the significance of tacit, non-propositional knowledge has been recognized in philosophy. It is suggested that attention be paid to how teachers…

Describes a study that investigated probabilistic intuitions held by students (N=98) from grade 7 through college through the use of a questionnaire. Of the misconceptions that were investigated, availability was the only one that was stable across age groups. Contains 20 references. (DDR)

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

Presents two cognitive models that illustrate the commonalities between reading for meaning and solving mathematical problems with meaning. Discusses the importance of number sense in the prior knowledge component of the solving with meaning model and the implications of the models in teaching mathematics. (MDH)

This article proposes that the behavior of teachers conducting small-scale evaluations of their own programs is analogous to the behavior of students solving curriculum-specific problems in classrooms and that teaching methods for training students in problem-solving skills can be usefully adapted to training teachers in evaluation skills.…

The early stages of a microcomputer-based project to integrate managerial knowledge and practice are described in this report. Analysis of the problem-framing process that effective principals use to reduce complex problems into more manageable ones forms the basis of the project. Three cognitive-mapping techniques are used to understand the…

Research has revealed distinct differences in the problem-solving approaches of high- and low-aptitude students. As a consequence, content area teachers can focus on thinking skills by having students describe their mental processes and giving them feedback on erroneous or incomplete reasoning. (TE)