Toward an Anthropology of Mathematizing

This essay investigates the practical ways that artists and craftspeople cultivate mathematical sensibilities through their practical immersion in making and problem-solving. Mathematical sensibilities refer to skilled kinds of perception and heightened levels of attention and discernment regarding the qualitative properties of an object or composition, such as its shape, proportion, balance, symmetry, centredness, alignment or levelness. It also includes an ‘intuitive’ quantitative sense of volume, mass, weight, thickness and dimension. The objective of the investigation is not to describe the ways that a maker’s existing knowledge and training in formal mathematics is put into practice, but rather to elucidate the ways that their practices of making produce kinds of ‘non-formalised’, context-dependent mathematical understanding and knowledge. The starting point for exploring embodied mathematizing is therefore not from the cognitive or neurosciences, psychology or formal mathematics, it is argued, but rather from a phenomenological approach – ‘an opening on the world’ – that attends to person, materials, tools and other physical and qualitative features that make up the total environment in which activity unfolds

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Abstract Certainly one of the most powerful and important modeling languages of our time is the Calculus. But research consistently shows that students do not understand how the variables in calculus-based mathematical models relate to aspects of the systems that those models are supposed to represent. Because of this, students never access the true power of calculus: its suitability to model a wide variety of real-world systems across domains. In this paper, we describe the motivation and theoretical foundations for the DeltaTick and HotLink Replay applications, an effort to address these difficulties by a) enabling students to model a wide variety of systems in the world that change over time by defining the behaviors of that system, and b) making explicit how a system's behavior relates to the mathematical trends that behavior creates. These applications employ the visualization and codification of behavior rules within the NetLogo agent-based modeling environment (Wilensky, 1999), rather than mathematical symbols, as their primary building blocks. As such, they provide an alternative to traditional mathematical techniques for exploring and solving advanced modeling problems, as well as exploring the major underlying concepts of calculus