The performance and learning difficulties of Grade 10 learners in solving euclidean geometry problems in Tshwane West District
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Authors
Olabode, Adedayo Abosede
Issue Date
2023-01-31
Type
Dissertation
Language
en
Keywords
Geometrical thinking , Learner performance , Learning difficulties , Parallelograms , Congruency , Parallel lines , Interaction , Quality Education , SDG 4 Quality Education
Alternative Title
Abstract
There is a growing trend of declining performance in the final year (Grade 12) mathematics examinations in the South African public school system. The study aimed to evaluate Grade 10 learners in the Tshwane West District on their performance and learning difficulties in solving Euclidean Geometry problems. The study utilized a mixed method approach under a pragmatic paradigm to determine the achievement and the challenges experienced by learners when solving Euclidean geometry problems. The Van Hiele levels of geometry thinking and constructivist theory, underpinned the theoretical framework used to determine the actual performance and how they understand geometry concepts. The population was Grade 10 learners, and the sample size was 80 learners, purposively selected from two secondary schools in the Tshwane West district in the Gauteng Province. The Geometric Achievement Test instrument was used to determine firstly, the overall performance of learners in Euclidean geometry, secondly, the level of Grade 10 learners on Van Hiele levels of thinking and lastly to specify the area where learners have the most difficulties when engaging with geometry problems. A semi-structured interview guide and class observation checklist were used to further understand the challenges experienced by grade 10 when they are faced with Euclidean geometry questions.
The findings from this study showed the underperformance of learners in three Euclidean geometry topics: these included parallel lines, congruency, and parallelograms. The findings further indicated that the low performance was a result of a lack of understanding of the computational and spatial thinking that characterises Euclidean geometry. These findings were supported by the quantitative findings of the study.
The pass mark stipulated in Euclidean geometry is 30%; less than 10% of the participants in the GAT obtained 30% and above. The findings of the study showed that less than 5% of the learners obtained a score of 38 on the achievement test, which was the highest score obtained. Of the 80 participants, 1,25% (1 of 80) obtained a score of 2. Euclidean geometry requires learners to use their spatial and logical skills in solving mathematical questions; for this sample, making connections and comprehending the visual and spatial aspects of parallel lines, congruency, and parallelograms were found to be difficult. The findings also showed that learner lack an understanding of the properties of parallel lines, resulted in difficulties in calculating the magnitudes of unknown angles using these properties. The findings further indicated that Grade 10 learners have difficulty solving geometry requiring knowledge of corresponding, alternating, and co-interior angles. A notable difficulty was that for the learners to apply the conditions of congruency and execute the proof for parallelograms, learners must understand parallel lines and its properties. Teachers must ensure that learners understand the procedures of naming angles correctly. The understanding of properties of parallel lines, congruency, and proof of parallelograms is essential for enhancing learner abilities in Euclidean geometry.