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The nature of errors and their significance for learning and teaching mathematics

Welna, B. (1999) The nature of errors and their significance for learning and teaching mathematics. PhD thesis, Murdoch University.

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This dissertation is a study of the nature of errors and their potential significance for learning and teaching mathematics. It is consistent with the new positive attitudes towards errors, suggesting that errors are a natural occurrence of all learning, rather than an indication of inadequacy. The general method of this inquiry involves a conceptual analysis. The analysis draws upon a substantial body of literature in mathematics education and other related disciplines, and uses secondary data sources comprising empirical and analytical research on students’ mathematical errors. These literature sources central to the study concern errors directly, as well as historical perspectives on the development of mathematical ideas and studies related to humour.

The study shows that to approach errors from both the historical and the individual learner’s perspectives, in a humorous way, can provide us with deep insights into their nature. This study reveals that a combination of errors, history and humour can be a potential tool in learning and teaching mathematics at all levels, in particular, in overcoming cognitive and epistemological obstacles in order to attain a deeper understanding of mathematical ideas and mathematics itself. This is of significant importance in the light of the last few decades of empirical research, rich in evidence of the depth and persistence of students’ errors, misconceptions, unhelpful intuitions and conceptual difficulties in understanding mathematical ideas at all educational levels.

The dissertation consists of two parts. In the first part, the arguments for the usefulness of considering errors, history and humour together are developed on the grounds of the general considerations from a range of dimensions: philosophical, historical, epistemological, psychological, linguistic, humorous and others. In the second part, attention is turned to particular mathematical ideas as a context in which such considerations, as discussed generally in the first part, appear to be profitable for mathematics educators, teachers and learners themselves.

Item Type: Thesis (PhD)
Murdoch Affiliation(s): Division of Social Sciences, Humanities and Education
Notes: Note to the author: If you would like to make your thesis openly available on Murdoch University Library's Research Repository, please contact: Thank you.
Supervisor(s): Willis, Sue and Kissane, Barry
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