Original Research

South African teachers’ conceptualisations of gradient: A study of historically disadvantaged teachers in an Advanced Certificate in Education programme

Vimolan Mudaly, Deborah Moore-Russo
Pythagoras | Vol 32, No 1 | a25 | DOI: https://doi.org/10.4102/pythagoras.v32i1.25 | © 2011 Vimolan Mudaly, Deborah Moore-Russo | This work is licensed under CC Attribution 4.0
Submitted: 16 August 2011 | Published: 15 September 2011

About the author(s)

Vimolan Mudaly, University of KwaZulu-Natal, South Africa
Deborah Moore-Russo, Department of Learning and Instruction, Graduate School of Education, University at Buffalo, The State University of New York, United States

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This study looked at how a group of South African secondary school mathematics teachers regarded the concept of gradient (slope). Results are reported from nine free-response items on a paper-and-pencil test administered to practising teachers who were pursuing qualifications to teach Grades 10–12 mathematics through an Advanced Certificate in Education (ACE) programme. The findings suggest that teachers’ understanding of gradient varies greatly. A number of teachers in the study demonstrated very little to no understanding of this important concept, whilst others demonstrated a strong understanding of gradient and were able to conceptualise it in many different ways. Implications for teacher professional development are considered.


slope; average rates; pedagogical content knowledge; common content knowledge


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