Embodiment and embodied design

Picture this. A preverbal infant straddles the center of a seesaw. She gently tilts her weight back and forth from one side to the other, sensing as each side tips downward and then back up again. This child cannot articulate her observations in simple words, let alone in scientific jargon. Can she learn anything from this experience? If so, what is she learning, and what role might such learning play in her future interactions in the world? Of course, this is a nonverbal bodily experience, and any learning that occurs must be bodily, physical learning. But does this nonverbal bodily experience have anything to do with the sort of learning that takes place in schools - learning verbal and abstract concepts? In this chapter, we argue that the body has everything to do with learning, even learning of abstract concepts. Take mathematics, for example. Mathematical practice is thought to be about producing and manipulating arbitrary symbolic inscriptions that bear abstract, universal truisms untainted by human corporeality. Mathematics is thought to epitomize our species’ collective historical achievement of transcending and, perhaps, escaping the mundane, material condition of having a body governed by haphazard terrestrial circumstance. Surely mathematics is disembodied

Learning in a Landscape: Simulation-building as Reflexive Intervention

This article makes a dual contribution to scholarship in science and technology studies (STS) on simulation-building. It both documents a specific simulation-building project, and demonstrates a concrete contribution to interdisciplinary work of STS insights. The article analyses the struggles that arise in the course of determining what counts as theory, as model and even as a simulation. Such debates are especially decisive when working across disciplinary boundaries, and their resolution is an important part of the work involved in building simulations. In particular, we show how ontological arguments about the value of simulations tend to determine the direction of simulation-building. This dynamic makes it difficult to maintain an interest in the heterogeneity of simulations and a view of simulations as unfolding scientific objects. As an outcome of our analysis of the process and reflections about interdisciplinary work around simulations, we propose a chart, as a tool to facilitate discussions about simulations. This chart can be a means to create common ground among actors in a simulation-building project, and a support for discussions that address other features of simulations besides their ontological status. Rather than foregrounding the chart's classificatory potential, we stress its (past and potential) role in discussing and reflecting on simulation-building as interdisciplinary endeavor. This chart is a concrete instance of the kinds of contributions that STS can make to better, more reflexive practice of simulation-building.Comment: 37 page

Research on the reasoning, teaching and learning of probability and uncertainty

In this editorial, we set out the aims in the call to publish papers on informal statistical inference, randomness, modelling and risk. We discuss how the papers published in this issue have responded to those aims. In particular, we note how the nine papers contribute to some of the major debates in mathematics and statistics education, often taking contrasting positions. Such debates range across: (1) whether knowledge is fractured or takes the form of mental models; (2) heuristic or intuitive thinking versus operational thinking as for example in dual process theory; (3) the role of different epistemic resources, such as perceptions, modelling, imagery, in the development of probabilistic reasoning; (4) how design and situation impact upon probabilistic learning

Epistemic Logic for Communication Chains

The paper considers epistemic properties of linear communication chains. It describes a sound and complete logical system that, in addition to the standard axioms of S5 in a multi-modal language, contains two non-trivial axioms that capture the linear structure of communication chains.Comment: 7 pages, Contributed talk at TARK 2013 (arXiv:1310.6382) http://www.tark.or

The technological mediation of mathematics and its learning

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools – physical, virtual, cultural – in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We begin with an appraisal of the role of digital technologies, and our rationale for focusing on them. We present four categories of digital tool-use that distinguish their differing potential to shape mathematical cognition. The four categories are: i. dynamic and graphical tools, ii. tools that outsource processing power, iii. new representational infrastructures, and iv. the implications of highbandwidth connectivity on the nature of mathematics activity. In conclusion, we draw out the implications of this analysis for mathematical epistemology and the mathematical meanings students develop. We also underline the central importance of design, both of the tools themselves and the activities in which they are embedded

Proof-theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets

In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. Rationality here means playing only strategies one believes to be best responses. This involves looking at two formal languages. One is first-order, and is used to formalise optimality conditions, like avoiding strictly dominated strategies, or playing a best response. The other is a modal fixpoint language with expressions for optimality, rationality and belief. Fixpoints are used to form expressions for common belief and for iterated elimination of non-optimal strategies.Comment: 16 pages, Proc. 11th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA XI). To appea

Group Inquiry

Group agents can act, they can have knowledge. How should we understand the species of collective action which aims at knowledge? In this paper, I present an account of group inquiry. This account faces two challenges: making sense of how large-scale distributed activities might be a kind of group action, and understanding the division of labour involved in group inquiry. In the first part of the paper, I argue that existing accounts of group action face problems dealing with large-scale group actions, and propose a minimal alternative account. In the second part of the paper, I draw on an analogy between inquiry and conversation, arguing that work by Robert Stalnaker and Craige Roberts helps us to think about the division of epistemic labour. In the final part of the paper I put the accounts of group action and inquiry together, and consider how to think about group knowledge, deep ignorance, and the different kinds of division of labour