The expectation for doctoral research to contribute to knowledge is closely related to examiners' attention to conceptual and theoretical components in the thesis. These components require abstract thinking and familiarity with a number of research ideas that are difficult to teach and learn. We argue that these can be made more accessible to…

A growing body of research has examined the experiential grounding of scientific thought and the role of experiential intuitive knowledge in science learning. Meanwhile, research in cognitive linguistics has identified many "conceptual metaphors" (CMs), metaphorical mappings between abstract concepts and experiential source domains,…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

The purpose of this study was to compare traditional classification training for a set of abstract concepts with multiple-relations training consisting of inference practice and the use of a content diagram. To examine this, 200 undergraduate and graduate psychology students completed a Web-based tutorial covering the abstract concepts of a…