Abstract
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.
Highlights
Low performance in mathematics has been a worldwide challenge for many decades, for instance, in 1989, the president of the International Commission on Mathematics Instruction (ICMI), Dr Hassler Whitney said ‘for several decades we have been seeing increasing failure in school mathematics education, in spite of intensive efforts in many directions to improve matters’
The main purpose of this study was to explore BEd in FP Pre-service teachers (PSTs)’ faulty reasoning in transformation geometry, with a focus on geometric translations. The understanding of these faulty reasoning, as displayed through errors made by students, was to be used to design Van Hiele phase-based instructional activities that were mapped to the errors and misconceptions identified
The instructional design was critical considering the lack of such interventions at the South African primary school level of mathematics education, as well as the scarcity of relevant textbooks for targeted intervention
Summary
Low performance in mathematics has been a worldwide challenge for many decades, for instance, in 1989, the president of the International Commission on Mathematics Instruction (ICMI), Dr Hassler Whitney said ‘for several decades we have been seeing increasing failure in school mathematics education, in spite of intensive efforts in many directions to improve matters’. 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
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