Technical and vocational education and training (TVET) mathematics teachers` professional noticing of students` productive struggle in calculus tasks - William, Hlako Mmachuene (University of the Witwatersrand, Johannesburg, 2024)
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.
A research report submitted in fulfillment of the requirements for the Doctor of Philosophy, In the Faculty of Humanities, Wits School of Education, University of the Witwatersrand, Johannesburg, 2024
Keywords: UCTD; Productive struggle and Professional noticing; Strategies; College Calculus; Mathematics knowledge for teaching; SDG-4: Quality education