This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

This study reports on the use of formative, diagnostic online assessments for the topic percentages. Two new item formats (drag-drop and slider) are described. About one-third of the school students (Years 7 to 9) could, using a slider, estimate "80% more than" a given length, in contrast with over two-thirds who could estimate "90%…

Assessments were made of the impact of various overt response modes on the problem-solving process. The Luchins Water Jar Problems were presented to undergraduate university students via interactive cathode ray tube computer terminals under four response mode conditions: Mnemonic Code, Multiple Choice (MC), Numerical List, and Constructed Response…

This report analyzes the discursive interactions of four students to understand what heuristic methods they develop as well as how and why they build isomorphisms to resolve a combinatorial problem set in a non-Euclidian context. The findings suggest that results of their heuristic actions lead them to build isomorphisms that in turn allow them to…

This analysis of 44 research studies concerned with word problems contains: (1) a brief overview; (2) 44 major findings and conclusions; (3) 64 suggestions and questions for further research; and (4) a reference list. The author suggests that the experimental research of the 1980s seemed to focus on the children, the instruction, and the word…

Six division chairpersons at Central Virginia Community College participated in a study designed to develop a problem situation set which can be used to examine academic managers' preferred decision processes; to identify the existing preferred decision processes of chairpersons within the community college setting; and to ascertain how problem…

Problem-based learning (PBL), initiated when learners meet the problem scenarios, develops learners' skills and subject matter content to make the transition from beginner to more expert problem solver. Beginning students might benefit from simple, well-structured problems, in which the understanding of sets of rules and principles results in a…

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

College algebra is currently being taught using graphing calculators such as the TI-81. This document presents exploratory and problem solving activities that have resulted from classroom experiences with the TI-81. The activities have been designed to enhance the learning of some standard college algebra topics through the easy access to…

A comparative analysis is presented of adolescent participation in three-person family problem-solving groups, involving five families with an adolescent diabetic and three families with an adolescent with no diagnosed illness. Observation and interaction analysis of family problem-solving in a laboratory setting were used, as families were asked…

Presented are the results of an investigation of stimulus integration capabilities of three- and four-year-old children in judgments of small and large numbers. There is much evidence that suggested young children have a concept of number for small numbers, but not for large ones. A concept of number was hypothesized by Piaget to rest on the…

This investigation focuses upon the question of: (1) how naive subjects organize and represent knowledge when solving problems; (2) how previous experience of a novice is used in solving a problem; (3) what kinds of information and knowledge are sought as well as overlooked by novices when solving problems; (4) what kinds of strategies novices…

This paper describes the rationale behind and the development and utilization of a bibliographic instruction course which incorporates formal abstract reasoning skills. The limitations of the search strategy technique of bibliographic instruction are discussed as well as the fact that many college students have not developed sophisticated…

This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…