A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers' collaborative…

SProblem solving has a long and successful history in mathematics education and is valued by many teachers as a way to engage and facilitate learning within their classrooms. The potential benefit for using problem solving in the development of algebraic thinking is that "it may broaden and develop students' mathematical thinking beyond the…

Social promotion is defined as the practice of allowing students who failed to meet performance standards and academic requirements the opportunity to pass on to the next grade with their peers. Although the A+ Educational Reform Act abolished the use of the practice, social promotion continues to occur in numerous school districts across one…

Problem-solving processes used by concrete- and formal-operational eighth-grade pupils were investigated through interviews. Formal-operational pupils used a larger variety of processes. Also, a larger variety of processes were used on more complex problems. (MP)

A unit analysis approach, advocated by science teachers, teaching students to solve proportions, is described. (JT)

Thirty-five students from all ability levels in the first and second year of secondary school were interviewed to determine their understanding of appropriate application of number operations. Results of the interviews are classified into five different levels of understanding. (DT)

Student comments about having time in class to think and solve problems are presented. Stressed are teaching methods which allow students to familiarize themselves with the problem, think about solution processes, work through the solution process, and reflect while solving a problem. (CW)

This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

This paper directs attention to the use of the EQUATIONS game as a research tool to study certain kinds of mathematical behavior, for example, the kinds of mathematical problems which players prefer to consider and to force their opponents to consider. Mathematical equations that meet certain game rule constraints constitute a problem space. A…

Described are the general problem-solving strategies and their nature and functions. The importance of integrating different types of general problem-solving strategies with content-specific teaching in mathematics classes is discussed. (KR)

Problem-solving strategies which use reflective thinking and inference in mathematics are discussed. Examples are provided with discussions of the learning process. The advantages of this approach are stressed. (CW)

This study investigates the role of basic elements of a learning context namely: the given tasks, the nature of the provided tools, and the pupils' gender in their choice of tools provided by an open problem-solving computer environment. Pupils' choice of tools is discussed through the description of an experiment involving the interaction of (30)…

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…

Problem solving is defined and characteristics of good problem solvers are highlighted. The cognitive processes used in problem solving are discussed. Suggestions for methods which can be used to teach problem solving are provided. Research implications from mathematics education are listed. (CW)

This study used 152 grade eight students ranging in age from 12 to 14 years from a suburban middle school in central New Jersey. The investigations gave particular attention to the identification of variables that represent understanding of fundamental mathematical structures. The first year of the research took place during the 1978-1979 school…