Learning by Seeing by Doing: Arithmetic Word Problems

Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty

Design as conversation with digital materials

This paper explores Donald Schön's concept of design as a conversation with materials, in the context of designing digital systems. It proposes material utterance as a central event in designing. A material utterance is a situated communication act that depends on the particularities of speaker, audience, material and genre. The paper argues that, if digital designing differs from other forms of designing, then accounts for such differences must be sought by understanding the material properties of digital systems and the genres of practice that surround their use. Perspectives from human-computer interaction (HCI) and the psychology of programming are used to examine how such an understanding might be constructed.</p

Next steps in implementing Kaput's research programme

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These 'design principles' focus on the evolution of digital representations since the early nineties, and we attempt to take forward our collective understanding of the cognitive and cultural affordances they offer. There are two main organising ideas for the paper. The first centres around Kaput's notion of outsourcing of processing power, and explores the implications of this for mathematical learning. We argue that a key component for design is to create visible, transparent views of outsourcing, a transparency without which there may be as many pitfalls as opportunities for mathematical learning. The second organising idea is that of communication, a key notion for Kaput, and the importance of designing for communication in ways that recognise the mutual influence of tools for communication and for mathematical expression

Peirce's sign theory as an open-source R package.

Throughout Peirce’s writing, we witness his developing vision of a machine that scientists will eventually be able to create. Nadin (2010) raised the question:Why do computer scientists continue to ignore Peirce’s sign theory? A review of the literature on Peirce’s theory and the semiotics machine reveals that many authors discussed the machine;however, they donot differentiate between a physical computer machine and its software. This paper discusses the problematic issues involved in converting Peirce’s theory into a programming language, machine and software application. We demonstrate this challenge by introducing Peirce’s sign theory as a software application that runs under an open-source R environmen

Hedonic and Transcendent Conceptions of Value

In this paper we introduce a conceptual distinction between a hedonic and transcendent conception of value. We posit three linguistic earmarks by which one can distinguish these conceptions of value. We seek validation for the conceptual distinctions by examining the language contained in reviews of cars and reviews of paintings. In undertaking the empirical examination, we draw on the work of M.A.K. Halliday to identify clauses as fundamental units of meaning and to specify process types that can be mapped onto theoretical distinctions between the two conceptions of value. Extensions of this research are discussed

Conceptual spatial representations for indoor mobile robots

We present an approach for creating conceptual representations of human-made indoor environments using mobile robots. The concepts refer to spatial and functional properties of typical indoor environments. Following findings in cognitive psychology, our model is composed of layers representing maps at different levels of abstraction. The complete system is integrated in a mobile robot endowed with laser and vision sensors for place and object recognition. The system also incorporates a linguistic framework that actively supports the map acquisition process, and which is used for situated dialogue. Finally, we discuss the capabilities of the integrated system