Presents activities to demonstrate that current technology allows readily accessible representations in algebraic, numeric, and geometric forms. Argues that integrating these different representations into the curriculum helps students to think more critically about systems. Discusses problem solving using multiple representations, equivalent…

Analyzes didactic problems related to the inseparability of electric charge from the mass, the impossibility of its direct observation, and the meaning associated with the basic concepts of electricity. Contains 44 references. (DDR)

Describes a study that investigates the relationship between secondary students' written responses and the mathematical and cognitive processing used when solving a complex problem. Contains 40 references. (DDR)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Proposes activities that promote students' awareness of the structure of the information involved in their everyday activities, and builds the concept of function from students' mental representations of phenomena. Recommends the use of spreadsheets to provide external representations of these functions. (DDR)

Examines quantitative models in school physics, looking particularly at the degree to which they match the real world. Explores the positive aspects of a mismatch between models and real world conditions. (DDR)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)

Describes a study that explores the instructional influence of presenting pictures at the molecular level when introducing chemistry concepts and solving chemistry problems. Explores the effect of the pictures on students' conceptions and problem-solving abilities. Contains 59 references. (DDR)

Lends support to the idea that the quality of the cases used in problem-based learning affects the nature of student learning in this context. Outlines seven principles adapted from research on learning and cognition that can help guide case design. Contains 22 references. (DDR)

This study of physics problem-solving identifies reasoning mechanisms that enable the problem-solver to achieve the transformation to a physics structure of the problem situation. Elaboration is explored as a mechanism in fulfilling this transformation by providing beginning problem-solvers with elaborations that they failed to infer. A card…