To identify and describe the basis upon which instructors make curricular and pedagogical decisions, we have developed an artifact-based interview and an analysis technique based on multilayered concept maps. The policy capturing technique used in the interview asks instructors to make judgments about concrete instructional artifacts similar to…

Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

Little research has been conducted on how students work when they are required to plan, build and evaluate artefacts in technology rich learning environments such as those supported by tools including flow charts, "Labview" programming and Lego construction. In this study, activity theory was used as an analytic tool to examine the social…

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying…

The purpose of this study is to investigate the effect of a one-year regular robotic toys (lego) training on school pupils' performance. The underlying pedagogical perspective is the "constructionist theory," where the main idea is that knowledge is constructed in the mind of the pupil by active learning. The investigation has been made…

An investigation was conducted to determine the effectiveness of utilizing analogies to effect conceptual change in mathematics. Forty-one high school seniors participated in a knowledge reconstruction process regarding their beliefs about everyday probability situations such as sports events or lotteries. These mathematics students were given…

Much of the emphasis in this handbook is on helping students develop investigative, problem-solving, and thinking skills, but the importance of students' working together in a cooperative and democratic setting to solve problems is also stressed. Cooperative learning is an instructional tool that can often be used to the student's advantage. Part…

In earlier times, practically everything was taught by apprenticeships. Schools are a recent invention that use many fewer teaching resources, but the computer enables us to go back to the resource-intensive mode of education, in a form called cognitive apprenticeship. This involves the use of modeling, coaching, reflecting on performance, and…

This paper, part of a series of working papers published to provide documentation of research and development efforts associated with the Indigenous Mathematics Project of Papua New Guinea, discusses the role of problem solving in the mathematics curriculum and types and characteristics of good problems, with illustrations. Reasoning by analysis…

The values-in-conflict approach is emphasized as an effective method for developing student understanding of social problems. For journal availability see annotation SO 504 171. (Author/DE)

Social behavior skills were taught to 7- and 8-year-old resource room students through controlled simulation of real-life situations in which students were encouraged to think of various solutions to a problem, evaluate them, and apply the best one. (CL)

This simple example demonstrates the physical significance of similarity solutions and the utility of dimensional and asymptotic analysis of partial differential equations. A procedure to determine the existence of similarity solutions is proposed and subsequently applied to transient constant-flux heat transfer. Short-time expressions follow from…

The author observes that the predictor functions determined geometrically by Ranucci (EJ 090 184) can be algebraically derived, and that capable students might enjoy verifying them. Algebraic formulations and derivations are provided. (SD)

This paper represents one portion of an ongoing effort to elaborate on pedagogical principles based on structural-developmental (largely Piagetian) theory and research. Here, a concept of "problem structure" is developed as a means for identifying physical factors that contribute to children's ability to apply experimental reasoning.…