Abstract
Three-dimensional (3D) trigonometry combines basic trigonometry, 2D and 3D shapes, reduction formulae, sine rule, cosine rule, area rule, compound, and double angles. The National Senior Certificate (NSC) diagnostic report states that errors in 3D trigonometry displayed by grade 12 mathematics learners contribute to poor performance. Three-dimensional trigonometry concepts have been a prevalent trend in mathematics curricula across grades in South Africa. However, the preparation of high school mathematics learners has not received similar attention, and the learning opportunities provided for this trigonometry section are often insufficient to allow learners to conceptualize 3D trigonometry. How can mathematics teachers effectively use a blended teaching approach to enhance the teaching and learning of 3D trigonometry concepts? The study also explored how grade 12 mathematics teachers identify learners’ misconceptions and associated errors responsible for them in the Chris Hani West Educational District.
This study used an explanatory sequential mixed-method research design. A sample of 381 grade 12 learner scripts (learners) was used to collect quantitative data. Additionally, 30 learners and three mathematics teachers provided qualitative data. The research instrument was a validated NSC Mathematics Paper two September 2021, question 7 on 3D trigonometry. The t-test, ANOVA, and regression indicators were employed for data analysis. The collected data were also treated with Mathematical Language Errors, Procedural Errors, Conceptual Errors, and Application Errors (MPCA).
Results revealed that blended teaching increases the percentage pass mark by 20% compared with the traditional approach. Schools with 100% access to technology-based aids (WhatsApp and YouTube) had fewer procedural errors than schools with 40% access (Traditional). Conceptual errors accounted for 65.70%, making them the most prominent error type, followed by procedural errors at 10.84%. Blended learning is acknowledged as fundamental to success; however, the lack of infrastructure is a barrier. For better performance with 3D trigonometry, concrete models and hybrid teaching were shown to be more beneficial.
The results indicated a statistically significant difference in the overall mean achievement scores for learners taught through blended learning rather than those
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taught face-to-face. The results indicated that most learners have access to smartphones, yet, integrating technology into mathematics teaching to ease the learners' lives presents a problem. Mathematics teachers may use YouTube videos of mathematics content on WhatsApp group platforms to supplement their presentations. The study further suggests that including error analysis as part of mathematics teachers' lesson planning enhances teaching and learning.
Keywords: 3D Trigonometry, Blended Teaching Method, MPCA Error Analysis