If this is our mathematics, what are our stories?
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If this is our mathematics, what are our stories? Lulu Healy Æ Nathalie Sinclair
Published online: 20 February 2007 Springer Science+Business Media B.V. 2007
Abstract This paper sets out to examine how narrative modes of thinking play a part in the claiming of mathematical territories as our own, in navigating mathematical landscapes and in conversing with the mathematical beings that inhabit them. We begin by exploring what constitutes the narrative mode, drawing principally on four characteristics identified by Bruner and considering how these characteristics manifest themselves in the activities of mathematicians. Using these characteristics, we then analyse a number of examples from our work with expressive technologies; we seek to identify the narrative in the interactions of the learners with different computational microworlds. By reflecting on the learners’ stories, we highlight how particular features, common across the microworlds—motion, colour, sound and the like—provided the basis for both the physical and psychological grounding of the behaviour of the mathematically constrained computational objects. In this way, students constructed and used narratives that involved situating mathematical activities in familiar contexts, whilst simultaneously expressing these activities in ways which—at least potentially—transcend the particularities of the story told. Keywords Narratives Æ Expressive technologies Æ Microworlds Æ Ideational and conceptual mathematics Æ Dynamic mathematisations This paper was inspired by words spoken on behalf of the Gitxsan people of British Columbia, quoted in the title of Ted Chamberlin’s book ‘‘If this is your Land, where L. Healy (&) Programa de Estudos Po´s-Graduados em Educac¸a˜o Matema´tica, Pontifical Catholic University of Sa˜o Paulo, Rua Marqueˆs de Paranagua´, 111, Consolac¸a˜o, 01303-050 Sao Paulo, SP, Brazil e-mail: [email protected] N. Sinclair Faculty of Education, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6 e-mail: [email protected]
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are your stories’’. These words come from an episode in which a Gitxsan Elder is questioning the rights other groups have claimed to the land he sees as belonging to his people. If others want to claim the land, then surely they must have stories and myths that reflect their ties to it. The question is meant to assess whether the land really means something to them; if it does, they will have stories to prove it. Over the past few decades, there has been an increasing emphasis on the relationship between stories and knowledge construction and a questioning of the kinds of stories students might have about their school mathematics. Many have lamented the pervasiveness of sad and fearful stories told by learners of mathematics, such as the one that follows—stories suggesting that rather than wanting to stake any claim, many experience mathematics as a forbidding and inaccessible land, a land that they would not call their own. And on the eighth day, God created mathematics.
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