Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning

This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53 The final publication is available at www.springerlink.com Published version: http://dx.doi.org/10.3758/BF0321390

Reoccurring patterns in hierarchical protein materials and music: The power of analogies

Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and function. As a comparative tool here we apply hierarchical ontology logs (olog) that follow a rigorous mathematical formulation based on category theory to provide an insightful system representation by expressing knowledge in a conceptual map. We explain the process of analogy creation, draw connections at several levels of hierarchy and identify similar patterns that govern the structure of the hierarchical systems silk and music and discuss the impact of the derived analogy for nanotechnology.Comment: 13 pages, 3 figure

Increasing cognitive inhibition with a difficult prior task:implications for mathematical thinking

Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2 processing. In two studies, we demonstrate that giving participants a difficult task (Raven’s Matrices) before a task that requires the inhibition of intuitive responses (the Cognitive Reflection Test) significantly improves performance. Our findings suggest that encountering a difficult task that requires Type 2 processing before completing a task that requires inhibition of Type 1 processing may encourage an enduring ‘Type 2’ mindset, whereby participants are more likely to spontaneously use Type 2 processing for a period of time. Implications for mathematics education are discussed