What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...) arithmetic, and mathematics in general, have unique features—precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world—that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and “laws” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education. (shrink)

Purpose – The purpose of this article is to use entrepreneurship to bridge the traditional – progressive education rift. Design/methodology/approach - The rift between traditional and progressive education is first deconstructed into five dualisms. Conceptual question-based analysis is then applied to determine if and how three entrepreneurial tools could contribute to bridging this rift; effectuation, customer development and appreciative inquiry. Finally, pattern based generalizations are drawn from this analysis. Findings – Patterns in the analysis motivate the articulation of an overarching (...) educational philosophy – learning-through-creating-value-for-others – grounded in entrepreneurship and capable of bridging the educational rift. Research limitations/implications Only three entrepreneurial tools were included in the conceptual analysis, signifying a need to explore whether other tools could also help teachers bridge the traditional - progressive education rift. Entrepreneurial tools and the new educational philosophy manifesting entrepreneurship could also need to be further contextualized in order to be useful in education. Practical implications - The tentatively new educational philosophy has been shown to be capable of bridging five dualisms in education which are currently problematic for teachers in their daily practice, and to remedy teacher challenges such as complexity, lack of resources, assessment difficulties, and student disengagement. Originality/value – An educational philosophy grounded in entrepreneurship has arguably not been proposed previously. Contrasting existent educational philosophies, this new philosophy goes beyond learning-through to also emphasize creating-value-for-others. This could facilitate bridging between traditional and progressive education, one of the most important challenges in education. It could also be used to facilitate the infusion of entrepreneurship into general education. (shrink)