Original Research

Mapping pre-service teachers’ faulty reasoning in geometric translations to the design of Van Hiele phase-based instruction

Nokwanda P. Mbusi, Kakoma Luneta
South African Journal of Childhood Education | Vol 11, No 1 | a871 | DOI: https://doi.org/10.4102/sajce.v11i1.871 | © 2021 Nokwanda P. Mbusi, Kakoma Luneta | This work is licensed under CC Attribution 4.0
Submitted: 06 May 2020 | Published: 30 September 2021

About the author(s)

Nokwanda P. Mbusi, School of Early Childhood Development, Faculty of Education, University of Mpumalanga, Siyabuswa, South Africa
Kakoma Luneta, Department of Childhood Education, Faculty of Education, University of Johannesburg, Johannesburg, South Africa

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Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs’ faulty reasoning displayed in errors they make.

Aim: The aim of this study was to explore the use of Bachelor of Education (BEd) students’ faulty reasoning in geometric translations, in designing a Van Hiele phase-based instructional programme that could address such faulty reasoning.

Setting: The setting for the study was a newly established rural university in South Africa.

Methods: Tests on geometric translations were administered to BEd Foundation Phase students, followed up by interviews to explore errors made when responding to the test items. The errors were then mapped to the design of a Van Hiele phase-based instructional programme.

Results: The results revealed that the students had several misconceptions with geometric translations. The misconceptions were delineated into the errors that the students displayed and these were classified under two themes. The first theme was incorrect properties of transformation and under this theme, the errors were coded as confusing translation with rotation, wrong translation method, incorrect interpretation of coordinates and confusing the x and y axis. The second theme was errors involving basic mathematics operations including wrong diagrammatic representation of coordinates and incorrect calculations.

Conclusion: The study showed that if the students’ misconceptions and the resulting errors are mapped to specific instructional approaches, their faulty reasoning in geometric transformations is addressed and effective learning is enhanced.


errors and misconceptions; Van Hiele theory; instructional design; geometric translations; intervention


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