A Popperian consilience : modelling mathematical knowledge and understanding
Nutchey, David J. (2011) A Popperian consilience : modelling mathematical knowledge and understanding. In Clark, Julie, Kissane, Barry, Mousley, Judith, Spencer, Toby, & Thornton, Steve (Eds.) Mathematics : Traditions and [New] Practices (Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia), MERGA, Alice Springs, NT.
Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.
Impact and interest:
Citation counts are sourced monthly from and citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.
|Item Type:||Conference Paper|
|Keywords:||Mathematics, Early-number, Knowledge, Modelling|
|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 Teacher Education & Leadership
Current > QUT Faculties and Divisions > Faculty of Education
|Copyright Owner:||Copyright 2011 [please consult the author]|
|Deposited On:||25 Oct 2011 22:11|
|Last Modified:||19 Aug 2016 04:51|
Repository Staff Only: item control page