Objectifying early-number : a visual nomenclature to express mathematical domain knowledge
Nutchey, David J. (2010) Objectifying early-number : a visual nomenclature to express mathematical domain knowledge. In First International Conference of STEM in Education, 26th - 27th November 2010 , Queensland University of Technology, Brisbane, QLD. (Unpublished)
To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.
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|Item Type:||Conference Paper|
|Keywords:||knowledge, modelling, early number|
|Subjects:||Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)|
|Divisions:||Current > Schools > School of Curriculum
Current > QUT Faculties and Divisions > Faculty of Education
|Copyright Owner:||Copyright 2010 David Nutchey|
|Deposited On:||25 Oct 2011 22:21|
|Last Modified:||26 Mar 2013 16:05|
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