Browsing by Author "William, Hlako Mmachuene"

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    Information communication technology interventions in TVET mathematics N4 integral calculus
    (2018) William, Hlako Mmachuene
    Technical and Vocational Education and Training (TVET) College engineering students experience many challenges in the deep learning of calculus and the definite integrals in particular. This research identified the types of errors and misconceptions TVET engineering students showed on the definite integral and its applications. The study further explored how Information Communication Technologies (ICT) tools could help diminish these errors and misconceptions. The study is underpinned by constructivism learning theory and hints bridging theories such as Actions-Process-object and System (APOS) theory, Concept image and concept definitions, Kilpatrick `s five strands of mathematical proficiency, Mathematics content knowledge, etc. Data collection was done in four stages which consisted of First-Test Task, interviews, correction session coupled with feedback, class discussions and re-teaching of topic using ICT tools and Follow up-Test Task. The tasks consisted of carefully selected questions aiming at probing and soliciting error types and misconceptions of students in this section of Calculus. An intervention strategy used to re-teach the topic through the use of ICT tools was implemented. A follow-up test task was written. This was done to determine the extent this intervention helped to diminish observed errors and misconceptions. The results of the ICT intervention showed a great improvement as less errors and misconceptions were committed. It is therefore recommend that ICTs be used in the teaching and learning of calculus in TVET Colleges and further research be conducted on the TVET N4 mathematics background knowledge of calculus before learning definite integral
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    Technical and vocational education and training (TVET) mathematics teachers` professional noticing of students` productive struggle in calculus tasks
    (University of the Witwatersrand, Johannesburg, 2024) William, Hlako Mmachuene; Makonye, P.J
    Research has shown that mathematics students have difficulties understanding calculus concepts. This situation is mainly attributed to the poor and ineffective traditional methods of teaching and learning mathematics in schools and institutions of higher learning. In attempting to improve this situation, mathematics education researchers are calling for research on innovative constructivist methods of mathematics teaching and learning. This study explored productive struggle and professional noticing as new pedagogical strategies of teaching and learning of Technical and Vocational Education and Training (TVET) College mathematics, calculus in particular. Three constructivist theories of APOS, Concept Image and Concept Definition and Self-directed learning are discussed, merged and used in the study. Two groups of TVET College lecturers were formed with one as the experimental group and the other as a control group. Experimental group lecturers underwent training on productive struggle and professional noticing new strategies of TVET College mathematics teaching and learning. The control group did not get training on these new teaching strategies and was kept as the benchmark point of comparison. These participating lecturers from the two groups were purposefully sampled as lecturers offering TVET College mathematics in exiting levels of N5 and N6 mathematics classes. Data collection was done through a triangulation approach of using observations, interviews and document analysis in the form of term test scripts. This study found that productive struggle and professional noticing strategies of teaching and learning mathematics were superior to traditional methods of mathematics teaching and learning and were also found effective in enhancing calculus understanding in students. The study has put up a pedagogical framework that can be used by TVET College mathematics lecturers when teaching complex calculus topics. This study recommended in-service training for TVET College lecturers on productive struggle and professional noticing new teaching strategies. Again, the department of higher education and training should make bursaries available for these TVET College lecturers to further their studies in mathematics education.