Original Research

Understanding students’ misconceptions: An analysis of final Grade 12 examination questions in geometry

Kakoma Luneta
Pythagoras | Vol 36, No 1 | a261 | DOI: https://doi.org/10.4102/pythagoras.v36i1.261 | © 2015 Kakoma Luneta | This work is licensed under CC Attribution 4.0
Submitted: 07 March 2014 | Published: 30 June 2015

About the author(s)

Kakoma Luneta, Department of Childhood Education, University of Johannesburg, South Africa


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Abstract

The role geometry plays in real life makes it a core component of mathematics that students must understand and master. Conceptual knowledge of geometric concepts goes beyond the development of skills required to manipulate geometric shapes. This study is focused on errors students made when solving coordinate geometry problems in the final Grade 12 examination in South Africa. An analysis of 1000 scripts from the 2008 Mathematics examination was conducted. This entailed a detailed analysis of one Grade 12 geometry examination question. Van Hiele levels of geometrical thought were used as a lens to understand students’ knowledge of geometry. Studies show that Van Hiele levels are a good descriptor of current and future performance in geometry. This study revealed that whilst students in Grade 12 are expected to operate at level 3 and level 4, the majority were operating at level 2 of Van Hiele’s hierarchy. The majority of students did not understand most of the basic concepts in Euclidian transformation. Most of the errors were conceptual and suggested that students did not understand the questions and did not know what to do as a result. It is also noted that when students lack conceptual knowledge the consequences are so severe that they hardly respond to the questions in the examination.

Keywords

Geometry; van Hiele levels; misconceptions; errors; coordinate goemetry

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Crossref Citations

1. The obstacles of geometric problem-solving on solid with vector and triangle approach
F Alghadari, T Herman
Journal of Physics: Conference Series  vol: 1132  first page: 012046  year: 2018  
doi: 10.1088/1742-6596/1132/1/012046