University of Macau / Faculty of Education

The aim of this study was to explore the effects of a problem-solving heuristic instructional method on Grade 6 learners’ achievements in algebra. Two main theories inspired the design of this teaching method, namely the modelling and modelling perspective, and action, process, object, schema (APOS) theory. Modelling and modelling perspectives guided the development of modelling-eliciting activities used in the teaching method and the APOS theory guided the sequence of activities used to develop Grade 6 learners’ conceptions in algebra. The impact of the problem-solving heuristic instructional method was investigated with 198 Grade 6 learners from four different primary schools in the Zululand district of Kwazulu-Natal that were conveniently sampled. A mixed-method approach was used in this study and a hypothesis was formulated to investigate the effects of the teaching method on the learners’ achievements in algebra. The qualitative component consisted of a pre-intervention class observation of mathematics lessons of all four mathematics educators in the schools used for this study. The design and implementation of the problem-solving heuristic instructional method and the quantitative component employed non-equivalent control group design with pre-test and post-test measure. The main instruments for data collection were an observation schedule to document sequence of events in the classroom during the class observation, a standardized achievement test in algebra used to measure effects of the problem-solving heuristic instructional method and modelling-eliciting activities used as a medium of interaction between learners and the researcher during the implementation of the problem-solving heuristic instructional method. Findings from the class observation indicated all four schools made use of comparable traditional methods of instruction. The implementation of the problem-solving instructional method gave insights into how a problem-solving heuristic instructional method can be developed and used in Grade 6 algebra lessons, and the factors that could influence learners’ conceptual development in algebra. The findings from the quantitative component supported the initial hypothesis that improved scores in algebra are achieved through participation in the problem-solving heuristic instructional method. Quantitative data was analysed using the t-test, analysis of covariance, Johnson-Neyman (J-N) technique and the effect size. / Mathematics Education / D. Phil. (Mathematics Education)

Philosophical inquiry as a pedagogical approach develops higher order thinking and problem solving skills. Inquiry-based learning is an important approach for sustainable development, considering the fact that today’s societies has to deal with everyday challenges. Philosophical inquiry is a powerful educational approach that has cognitive, social and practical benefits. This study examined the challenges faced by the Nyadire Teachers’ College (NTC) student teachers in Mashonaland East Province in Zimbabwe in engaging pupils in philosophical inquiry and ways of overcoming them. The study employed the qualitative design because of its focus on participants’ perceptions and actions. The researcher viewed participants as reflective beings whose actions were influenced by their thoughts. The study sample comprised forty student teachers on campus who had just completed their Teaching Practice (TP), eight student teachers on TP and ten lecturers from various departments. The data were collected through individual interviews, focus group discussions, non-participant observation of lessons and document analysis. The evidence from literature indicates that philosophical discourse and pedagogy develop learners’ ability to be responsible and accountable for their actions. It has also indicated teachers’ inability to introduce children to thoughtful discussion as one of the barriers to the use of philosophical inquiry as a pedagogy. The findings of the study indicated that NTC student teachers lacked skills and dispositions to engage pupils in philosophical inquiry. This was attributed to lack of critical pedagogy in teacher education at NTC. The findings also indicated that there were challenges in practicing schools. The study established knowledge and competence gaps amongst NTC student teachers as one of the challenges. The study suggested that NTC teacher education should expose student teachers to theory and practice of critical pedagogy. It also suggested in-service education on mentoring for teachers in schools, as mentoring demands more skills and knowledge than mere teaching. / Educational Studies / D. Ed. (Philosophy of Education)

A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is described using van Zee and Manogue's (2010) ethnography of communication. Bing's (2008) epistemic framing model is used to illuminate how students are framing what they are doing and whether or not they see the problem as geometric. Kuo, Hull, Gupta, and Elby's (2010) blending model and Krutetskii's (1976) model of harmonic reasoning are used to illuminate ways students show problem-solving expertise. Sayer and Wittmann's (2008) model is used to show how resource plasticity impacts students' geometric reasoning and the degree to which students accept incorrect results. / Graduation date: 2013

This study examined “problem solving skills in circle geometry concepts in Euclidean Geometry. This study was necessitated by learners’ inability to perform well with regards to Euclidean Geometry in general and Circle Geometry in particular. The use of naturalistic observation case study research (NOCSR) study was employed as the research design for the study. The intervention used for the study was the teaching of circle geometry with Polya problem solving instructional approach coupled with social constructivist instructional approach. A High School in the Northern Cape Province was used for the study. 61 mathematics learners (grade 11) in the school served as participants for the first year of the study, while 45 mathematics learners, also in grade 11, served as participants for the second year of the study. Data was collected for two consecutive years: 2018 and 2019. All learners who served as participants for the study did so willingly without been coerced in any way. Parental consent of all participants were also obtained. The following data were collected for each year of the research intervention: classroom teaching proceedings’ video recordings, photograph of learners class exercises (CE), field notes and the end-of-the- Intervention Test (EIT). Direct interpretations, categorical aggregation and a problem solving rubric were used for the analysis of data. Performance analysis and solution appraisal were also used to analyse some of the collected data. It emerged from the study that the research intervention evoked learners’ desire and interest to learn circle geometry. Also, the research intervention improved the study participants’ performance and problem solving skills in circle geometry concepts. Hence, it is recommended from this study that there is the need for South African schools to adopt the instructional approach for the intervention: Polya problem solving instructional approach coupled with social constructivist instructional approach, for the teaching and learning of Euclidean geometry concepts. / Mathematics Education / M. Sc. (Mathematics Education)