This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

This article describes an activity that incorporates 9 of the 10 National Council of Teachers of Mathematics (NCTM) Standards. Students explore a stacking garden containing multiple layers. The garden allows students to focus on finding the amount of border material needed and the amount of space available for planting. The problem balances the…

Background: Research about sport pedagogy has recently emerged as a significant interest in student reflective practice within the PE teaching/learning system. This learning process is considered as a type of knowledge of co-construction in action. This epistemological assumption postulates that the "knowledge-in-action" is the result of an active…

A comparative study was conducted to compare two approaches to engineering design curriculum between different schools (inter-school) and between two curricular approaches, "Project Lead the Way" (PLTW) and "Engineering Projects in Community Service" (EPIC High) (inter-curricular). The researchers collected curriculum…

The purpose of this study was to describe a process of preparing technology education teachers to teach engineering design concepts in the context of technology education. This process was identified through a study of professional development activities that were organized and conducted by technology teacher education partner universities of the…

Cooperative learning allows individuals with varying abilities to work alongside their peers. Students are placed into achievement levels based on placement test scores. The Regular College Preparatory (RCP) level is a score of 59% or lower and Academic College Preparatory (ACP) level is a score of 60-92% on the placement test. The purpose of this…

This study integrates the purposes of communication, i.e. in-class and on-line discussions, with problem solving skills in the process of learning professional knowledge of pre-service teachers. It attempts to foster both comprehension of professional knowledge and the attitude of contextualizing knowledge with situational factors. More…

This paper will explore a problem finding task the authors developed as one component of the Mission to Mars curriculum, an inquiry-based science unit developed by Petrosino & The Cognition and Technology Group at Vanderbilt (CTGV). The paper also attempts to address evolving conceptions of the problem generation task, primarily from that of…

The use of a visual representation in learning about proportional relations was studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability…

Designed by classroom teachers who, through repeated experimentation, identified activities that proved successful in developing students' understanding of citizenship, this unit contains 12 lessons that focus on the multicultural dimensions of citizenship. Each lesson includes objectives, procedures, and materials designed to involve students…

In this book, 10 strategies that are widely used in problem-solving both in mathematics and real-life situations are examined. Approximately 200 problems are selected to illustrate these strategies. Chapters include: (1) Introduction To Problem-Solving Strategies; (2) Working Backwards; (3) Finding a Pattern; (4) Adopting a Different Point of…

A conditions-based approach to the development of microlevel organizational strategies for instruction is explored. The conditions model reflects the idea that differences in learning tasks, primarily qualitative differences in the cognitive processing required of different learning tasks, can suggest different ways by which instruction can either…

This 5-section report summarizes the results of a project concerned with how novices learn to become creative educational computer users. Based on a cognitive analysis of elementary programming statements in BASIC and calculator language into conceptual units, the project builds on previous research on learning BASIC programming. A general…

Geometry students were randomly assigned to treatments in which they received (1) instruction in general problem solving procedures in addition to geometry or (2) regular geometry instruction. No significant differences attributable to treatments were found on a subsequent problem solving test. (SD)

The background, characteristics, and rationale for problem solving using "real" rather than academic problems are discussed. Criteria for choosing "real" problems, theories basic to problem solving, and the implementation of problem solving in the classroom are also covered. (JH)