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Australian Indigenous students: The role of oral language and representations in the negotiation of mathematical understanding
 In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia
, 2007
"... This paper reports on a small pilot study conducted in an Indigenous P13 school in North Queensland. This pilot study occurred over a two day period with the specific aim of exploring the role of oral language and representations in negotiating mathematical understanding. Implications are drawn for ..."
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This paper reports on a small pilot study conducted in an Indigenous P13 school in North Queensland. This pilot study occurred over a two day period with the specific aim of exploring the role of oral language and representations in negotiating mathematical understanding. Implications are drawn for the implementation of a large study, commencing in 2007 with 4yearold Indigenous students as they transition from home to school. All students in this context either speak Aboriginal English or Creole as their first language. The pilot study occurred in two classrooms, one with 15 Year 6/7 students and the other with fourteen Years 4/5/6 students. The preliminary results indicate that explicit consideration needs to be given to the development of precise mathematical language, strategies for linking school mathematics to home environments, the use of questioning in establishing classroom discourse, and the recognition that many of these classrooms are bilingual.
Pedagogical Practices and mathematics learning
"... This paper explores pedagogies that support Indigenous students learning of mathematics. Three schools in a remote and rural area of Queensland participated in a longitudinal intervention study, extending over a threeyear period (20024), which aimed to improve Indigenous students ’ mathematics out ..."
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This paper explores pedagogies that support Indigenous students learning of mathematics. Three schools in a remote and rural area of Queensland participated in a longitudinal intervention study, extending over a threeyear period (20024), which aimed to improve Indigenous students ’ mathematics outcomes by improving their teachers ’ knowledge and classroom practices. This paper reports on one aspect of the project, namely the pedagogical approaches used by their nonIndigenous teachers before intervention. Results are related to Harris (1980) and indicate that many of the common classroom practices believed to forward mathematics outcomes for Indigenous students simply reflect ‘good ’ mathematics pedagogy for all. The dimensions that were distinctive but absent in these communities were an acknowledgement of the different knowledges of these culturally different students, the nuances and social capital associated with Indigenous English, and the role that parents, caregivers and the community itself plays in young Indigenous students ’ mathematical education. It is conjectured that this could be a result of the inexperience of the teachers in such communities and/or the predominant white view of education prevalent in these three schools. The view, which has prevailed since the time of Plato, is that mathematics represents 'eternal truths', and that it is similarly objective in its portrayal of knowledge. The truthfulness and objectivity of
GSP Mediating the Interplay Between Perception and Reasoning: Some Preliminary Ideas
"... Since antiquity perception and imagination have been relegated to a necessary but secondary place. Philosophers before Kant did not embrace sense experience and imagination in the process of knowing but they were unable to divorce themselves from it. Aristotle, for example said, “The soul never thin ..."
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Since antiquity perception and imagination have been relegated to a necessary but secondary place. Philosophers before Kant did not embrace sense experience and imagination in the process of knowing but they were unable to divorce themselves from it. Aristotle, for example said, “The soul never thinks without an image ” (Aristotle, Posterior Analytics) and “the senses awaken the intellectual soul to understand” (Aristotle, De Anima). Although Aquinas argues that truth cannot be expected from the senses he also acknowledges that “we apprehend the particular through the senses and the imagination …the intellect must turn to sense images in order to look at universal natures in particular things. ” (Aquinas, Summa Theologiae) The reality is that the brain cannot display its functioning capacity without the information of what is going on in time and space. Empiricists tend to assume, in principle, that all knowledge must be derivable from experience. Rationalists tend to assume that all knowledge can be known by the understanding. Both tend to assume, in their own way, that there is only one source of knowledge either sense data or reasoning. For rationalists, knowledge is the product of reasoning; for empiricists knowledge is the