Mathematics, Science and Technology Education
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Browsing Mathematics, Science and Technology Education by Author "Bayaga, A."
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- ItemAnalysis of matlab instruction on rural-based pre-service teachers' spatial-visualisation skills and problem solving in vector calculus.(University of Zululand, 2019) Amevor, Godfred; Bayaga, A.; Bossé, M.Studies from interdisciplinary have noted positive correlation between spatial-visualization skills and mathematical problem solving. However, majority of these studies that interrogated this shared link between spatial-visualization and problem solving were carried in the urban settings only few interrogated rural settings. Also, studies have identified family social economic status (SES) which mainly described one’s geographical settlement to be one of the major effects on cognitive development. Thus, research finding from cognitive discipline revealed that students from poor SES background are less advantagous to cognitive activities (e.g., problem solving) compare to their counterpart. However, one of research achievements is providing evidence-based that cognitive skills can be enhanced through computer technology and spatial activities hence, the integration of several graphical tools such as: MATLAB, GeoGebra, and many other computer environments in mathematics education. These graphical tools are believed to enhance students’ conceptual and procedural knowledge in problem solving in mathematics areas such as: Euclidean geometry, multivariate calculus, and trigonometry which require more spatial skills in their problem solving. However, little has been researched on vector calculus even though vector calculus by its definition is accompanied by spatial reasoning. Students find it easy to evaluate a given vector integral using analytical techniques for integrations but struggle to visualize and transform it from one coordinate system to another. Objectives Based on the background, the current research employed the theoretical frameworks of Duval semiotic representation and the visual-analyser (VA) proposed by Zazkis et al., to analyse MATLAB instruction on rural-based pre-service teachers' spatial-visualisation skills and problem solving in vector calculus. The examination was guided by the analysis of the dynamic software MATLAB instruction on Spatial-Visualization, problem solving, and achievement in Vector Calculus. The three objectives were to 1) Analyse how rural-based v pre-service teachers apply their spatial-visualisation skills in problem solving in vector calculus. 2) To investigate the degree to which rural-based pre-service teachers’ spatial-visualisation skills correlate with their vector calculus achievement and 3) To assess how a dynamic software environment such as MATLAB influences rural-based pre-service teachers’ spatial-visualisation skills.
- ItemApplication of geogebra on euclidean geometry in rural high schools - Grade 11 learners(University of Zululand, 2015) Mthethwa, M.Z.; Bayaga, A.This research aims to establish the level of students’ cognitive skills using GeoGebra, and investigates whether GeoGebra as a technological tool helps in improving poor performance in respect of Euclidean geometry or geometry of the circle. Students’ interests, in learning about circle geometry in mathematics, are also being tested. GeoGebra is an innovative, dynamic mathematics software which integrates algebra, geometry and calculus to aid students during the learning process. The specific sample in this research consists of 112 Grade 11 secondary school learners within the UMkhanyakude district, Hlabisa circuit, under the Empembeni and Ezibayeni wards. During this research, GeoGebra and the concept of circle geometry were introduced to students. Afterwards, students had to answer several geometry of the circle questions, entailing key theorems as prescribed by the National Mathematics pacesetter for Grade 11 and Grade 12. As students answered the above questions, they solved problems and conducted discussions among themselves. At the end, students were individually required to answer questionnaires which consisted of 15 closed items relating to views on GeoGebra and its impact on Euclidean geometry and mathematics, as well as three open-ended questions which asked learners about their reflections on the application of GeoGebra. The above methods provided a strong base to explore whether GeoGebra as a tool helps students in the learning process. The results showed that students endorsed the use of GeoGebra as a technological tool in the teaching of Euclidean geometry. Some students even suggested that GeoGebra be used in other mathematical topics. Students overall enjoyed the use of GeoGebra, finding it user-friendly and a highly significant learning motivator.
- ItemErrors and misconceptions related to learning algebra in the senior phase – grade 9(University of Zululand, 2019) Mathaba, Philile Nobuhle; Bayaga, A.Algebra is a mathematical concept that explains the rules of symbol operations, equations, and inequality. Algebra is a combination of logic and language; hence common mistakes and conceptions are either attributed to logic or language problems, or both. There is also ongoing debate about the fact that learners come to class with different ideas that result in errors and misconceptions when they solve algebraic equations and expressions. Based on this debate concerning both errors and misconceptions in solving algebraic equations and expressions, the purpose of this study was to investigate the errors and misconceptions committed by learners when learning Algebra. The study answered the following research questions: What are the types and the sources of errors and misconceptions committed by Grade 9 learners in Algebra learning? How do the types and the sources of errors and misconceptions influence errors in Grade 9 learners’ cognition when learning Algebra? Which strategies work to avoid errors? What are the sources of the errors and misconceptions in Algebra? Unlike the predominant existing studies, which are urban-based, this study was based in rural schools in the King Cetshwayo District of UMlalazi and Mtunzini Municipality. The structure of the observed learning outcome (SOLO) theory was adopted to observe, examine and analyse learners’ misconceptions in rural-based secondary schools.