In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

Playing games holds an important role in learning and development. While designing and using digital game-based learning (DGML) environments becomes more appealing to educators, there is a disconnect between the goals that educators try to achieve and the design strategies they utilize to achieve their goals. The inclusion of game elements alone…

Based on a detailed reading of Graham Wallas' "Art of Thought" (1926) it is argued that his four-stage model of the creative process (Preparation, Incubation, Illumination, Verification), in spite of holding sway as a conceptual anchor for many creativity researchers, does not reflect accurately Wallas' full account of the creative…

This is the fourth paper in our Light-Emitting Diodes series. The series aims to create a systematic library of LED-based materials and to provide readers with the description of experiments and the pedagogical treatment that would help their students construct, test, and apply physics concepts and mathematical relations. The first paper provided…

Design-thinking is an inductive and participatory process in which designers are required to manage constraints, generate solutions, and follow project timelines in order to complete project goals. The researchers used this exploration study to look at how designers in various disciplinary fields approach design projects. Designers were asked to…

In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order…

The Magic Mathworks Travelling Circus is a touring maths lab--in and of itself, a good thing. When children enter it, they find particular pieces of apparatus captioned with particular challenges--which is perhaps not such a good thing. Students are faced with an apparatus that can do only one thing, and so are not encouraged to look again at…

Human expert problem-solving in science is defined and used to account for scientific discovery. These ideas are used to describe BACON.5, a machine expert problem solver that discovers scientific laws using data-driver heuristics and "expectations" such as symmetry. Implications of BACON.5 type research for traditional science education…

Methods used to investigate problems in the sciences include building-up strategies, insight, and change (or serendipitous discovery). Discusses appropriate learning experiences for the undergraduate science students so they are more likely to benefit from the second method of scientific discovery as they make a career in their chosen field. (JN)

People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear-system problems as part of a game. Although none of the participants initially…

Discusses the development and use of flowcharts to involve students in the major stages of experimental design and hypothesizing. The progress of stages attempts to simplify the complexity involved during problem-solving in science investigations. Several illustrative flowcharts are included. (JN)

Discovery learning, defined as intentional learning through problem solving and under the supervision of the teacher, is discussed in terms of its advantages and disadvantages, with suggestions for its application. (JMF)

Describes guided discovery and problem-solving programs, providing a buyer's guide for same. The guide includes program name, source, current price, type (such as learning module, simulation, adventure), brief description, and whether the program has graphics and sound effects. (JN)

Presents a historical overview of visualization as a cognitive strategy in human creativity, discovery, and problem-solving. Highlights include visualization as a cognitive strategy for solving everyday problems; visualization by scientists and inventors; counter examples; and implications for multimedia learning environments, instructional…

Critical thinking alone is reactive, in that it lacks the creative elements necessary for social progress. Accordingly, the author has developed the CoRT (Cognitive Research Trust) program to teach the two aspects of perception: breadth (developing a perceptual map) and change (using the map to discover solutions). (TE)