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Title: Developing a more conceptual understanding of matrices and systems of linear equations through concept mapping and vee diagrams
Contributor(s): Afamasaga-Fuata'i, K  (author)
Publication Date: 2006
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Abstract: The paper discusses one of the case studies of a multiple-case study teaching experiment conducted to investigate the usefulness of the metacognitive tools of concept maps and vee diagrams (maps/diagrams) in illustrating, communicating and monitoring students' developing conceptual understanding of matrices and systems of linear equations in an undergraduate mathematics course. The study also explored the tools' role in scaffolding and facilitating students' critical and conceptual analyses of problems in order to identify potential methods of solutions. Data collected included students' progressive maps/diagrams, journals of reflections and justifications of revisions, and final reports and researchers' annotated comments on students' maps/diagrams and anecdotal notes from presentations. Findings showed that students developed more enriched, integrated and connected understandings of matrices and systems of linear equations as a result of continually organizing coherent groups of concepts into meaningful networks of propositional links, critically reflecting on the results against feedbacks from critiques and negotiations for shared meanings, and crystallizing these conceptual changes and nuances where appropriate as revised or additional propositional links. Verifying and justifying solutions were greatly facilitated through the combined usage of concept maps and vee diagrams. Findings suggest that students' classroom experiences in working, thinking and communicating mathematically can be enhanced by incorporating these metacognitive tools into students' repertoire of effective learning strategies.
Publication Type: Journal Article
Source of Publication: Focus on Learning Problems in Mathematics, 28(3-4), p. 58-89
Publisher: Center for Teaching/Learning of Mathematics
Place of Publication: Framingham, Massachusetts, USA
ISSN: 0272-8893
Field of Research (FOR): 130208 Mathematics and Numeracy Curriculum and Pedagogy
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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