Presents three open-ended problems as a basis for discussing concerns and possible hazards in their solution, including partial answers or unjustified guesses, and considers the appropriate use of these types of problems. Appendices include problem solutions. (MKR)

Some ideas are presented about the ways in which the three domains of metacognition, affective factors, and beliefs influence the cognitive activities of seventh graders as they solve mathematics problems. The research project, initiated in 1981, is first described. Theoretical considerations are then discussed, with sections on affects, beliefs,…

Discussion of how to teach thinking and problem-solving skills focuses on a study of seventh graders that attempted to convey expertlike behavior using LEGOLogo to explain how a washing machine operates. Topics addressed include concept representation and mental models; cognitive apprenticeship; and LEGOTClogo as a learning environment. (Contains…

The efforts of Cleveland's intermediate level mathematics teachers to change their curriculum from computation to a dual emphasis on application and computation are described. This paper reports on the second year of a project to enhance mathematics instruction. A natural history ethnography was conducted, which focused on the work of seven…