Investigating conceptual teaching of word problems through visualisation processes: a case of selected Grad 9 mathematics teachers - John, Ssennyomo Bernard (Rhodes University, Faculty of Education, Department of Education, 2020)
This study investigated how selected grade 9 mathematics teachers used visualisation strategies to conceptually teach Pythagoras' theorem word problems as a result of an intervention program. This research project is an integral component of the ViProMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. This case study of mathematics teachers in the John Taolo Gaetsewe (JTG) District in the Northern Cape Province, used a social constructivist theory. The study is grounded within an interpretive paradigm and used an explanatory sequential mixed methods design. It surveyed eighty-seven mathematics teachers from all the secondary schools in the JTG District, focusing on their experiences when using visualisation approaches to teach Pythagoras' theorem word problems. After the survey, three teachers purposively selected from three different schools in the district took part in the intervention programme. I used a survey questionnaire, classroom observations and interviews to collect the data from the study participants. The data were analysed quantitatively and qualitatively. The findings from survey data revealed that while teachers in the JTG District acknowledge the importance and value of visualisation strategies in the teaching of Pythagoras' theorem word problems, many of them are either using visuals minimally or not using them at all. Challenges such as lack of resources in schools, time constrains, a lack of support from subject advisers, among others were noted. This thus necessitated a need for an intervention with some teachers in the district, specifically focusing on the use of visualisation tools and skills to teach Pythagoras' theorem word problems for conceptual understanding. Lessons observations showed that all observed teachers used visual models to generate images and used the models to develop mathematical ideas. The teachers used the images to create platforms for classroom discussions. The discussions were driven by questions which teachers asked both for ascertaining learners' prior knowledge and for finding out if they understood what the teachers were teaching. Interviews revealed that teachers' perceptions had changed because they now know how to make and use different models to build on learners' prior knowledge, extend what they are teaching to real life and make sense of Pythagoras' proposition in multiple ways and to establish connections among a rich set of mathematics concepts when teaching Pythagoras' theorem word problems. This study concludes that the use of visual strategies has the potential of enhancing conceptual teaching of Pythagoras' theorem word problems. The implications for teachers are that learners need to be taught how to create visual representations (both internally and externally) of the relations between objects in a word problem as this will help them in maximising understanding. Furthermore, it is hoped that the results of this study could be used by various stake holders who include inter alia, mathematics subject advisers and teacher training institutions to improve the teaching of Pythagoras' theorem word problems.
Keywords: Mathematics -- Study and teaching (Secondary) -- South Africa; Pythagorean theorem -- Study and teaching (Secondary); Mathematics teachers -- South Africa; Visualization