@article {1191, title = {AN EXPLORATION OF HIGH SCHOOL LEARNERS{\textquoteright} UNDERSTANDING OF GEOMETRIC CONCEPTS}, journal = {Problems of Education in the 21st Century}, volume = {77}, year = {2019}, month = {February/2019}, pages = {Continuous}, type = {Original article}, chapter = {82-96}, abstract = {There is much concern in South Africa about the poor performance of learners in mathematics, particularly in geometry. The aim of this research was to explore the understanding of basic geometry concepts by grade 10 and grade 11 learners in terms of the van Hiele{\textquoteright}s levels of geometry thinking. The participants of the research were 147 learners from three high schools in a rural area in the south of KwaZulu Natal, South Africa. The results showed that the learners had difficulties with problems involving definitions of geometric terms, interrelations of properties and shapes, class inclusion and changing semiotic representations. It was also found that most of the learners were operating at the visual and the analysis levels of the van Hiele levels of geometric thinking. It is recommended that teachers should provide learners with tasks that require movements between semiotic representations, and to also focus attention on improving learners{\textquoteright} skills in proving aspects of mathematical relations.}, keywords = {class inclusion, geometry, high school, mathematical proof, necessary and sufficient conditions, van Hiele theory}, issn = {1822-7864}, doi = {https://doi.org/10.33225/pec/19.77.82}, url = {http://oaji.net/articles/2019/457-1550425157.pdf}, author = {Harrison Ngirishi and Sarah Bansilal} } @article {1179, title = {PRE-SERVICE MATHEMATICS TEACHERS{\textquoteright} KNOWLEDGE OF MATHEMATICS FOR TEACHING: QUADRATIC FUNCTIONS}, journal = {Problems of Education in the 21st Century}, volume = {76}, year = {2018}, month = {December/2018}, pages = {Continuous}, type = {Original article}, chapter = {847-863}, abstract = {Many researchers and education stakeholders in South Africa point to the need to develop teachers{\textquoteright} personal knowledge of the mathematics concepts that they teach to their learners. In this research study we explore the understanding of 42 pre-service mathematics teachers of one aspect of school level mathematics, that of quadratic functions. Data were generated from the written responses to an assessment as well as semi-structured interviews. The purpose was to explore the methods used by pre-service mathematics teachers to derive a symbolic equation for a quadratic function expressed in graphical form. Furthermore, we looked at whether the pre-service teachers were able to use different methods to generate the symbolic equation. The results showed that 25 participants were able to determine the equation of a parabola using one method, while 11 of them were able to use two different methods. The most common method used was based on the intercept form of the equation. Some students identified different forms that the equation of a quadratic function could be expressed as but were unable to apply this to derive the equation. These results indicate that these students are not yet ready to teach these school level concepts even though they have studied advanced mathematics topics as part of their pre-service training. The study recommends that pre-service teachers should also be provided with more structured opportunities to help develop pedagogic content knowledge of the school level content as part of their teacher training programme.}, keywords = {graphical representation, parabola, pre-service mathematics teachers, quadratic functions, symbolic representation}, issn = {1822-7864}, doi = {https://doi.org/10.33225/pec/18.76.847}, url = {http://oaji.net/articles/2017/457-1545497857.pdf}, author = {Ifunanya Julie Adaobi Ubah and Sarah Bansilal} } @article {1007, title = {PHYSICAL SCIENCE TEACHERS{\textquoteright} PERCEPTIONS OF AN ADVANCED CERTIFICATE IN EDUCATION}, journal = {Problems of Education in the 21st Century}, volume = {70}, year = {2016}, month = {April/2016}, pages = {Discontinuous}, type = {Original article}, chapter = {21{\textendash}33 }, abstract = {Advanced Certificate in Education programmes was offered by many South African universities to provide opportunities for teachers to upgrade their positions. The purpose of the study was to explore Physical Science teachers{\textquoteright} perceptions of their professional development. In this study we considered three domains of professional development which are content knowledge, pedagogic content knowledge and teacher beliefs and attitudes. This study used a mixed method approach using the form of an embedded design. The study was conducted with 156 students enrolled in an ACE Physical Science programme. The teachers stated that their content knowledge and pedagogic content knowledge had not only improved, but also their engagement with actual laboratories, and conducting experiments contributed to their teaching experiences. Hence, their self-confidence of physical science teaching evolved. The authors recommend that the ACE programme should also include a mentoring system with teaching practicum via school leadership and subject advisers.}, keywords = {content knowledge, pedagogic content knowledge, physical science teachers, professional development, teacher beliefs, teacher confidence}, issn = {1822-7864}, doi = {https://doi.org/10.33225/pec/16.70.21}, url = {http://journals.indexcopernicus.com/abstract.php?icid=1203601}, author = {Sarah Bansilal and Angela James} } @article {1008, title = {REFLECTIONS OF SOUTH AFRICAN TEACHERS TEACHING UNDER ADVERSARIAL CONDITIONS}, journal = {Problems of Education in the 21st Century}, volume = {70}, year = {2016}, month = {April/2016}, pages = {Discontinuous}, type = {Original article}, chapter = {34{\textendash}44 }, abstract = {Teachers often teach under difficult conditions of which they do not have oversight. In order for teacher development programmes to be responsive to teachers{\textquoteright} needs, it is necessary to understand the teaching contexts of their participant teachers. Accordingly the purpose of the research was to identify the problems of practice reported by 41 Mathematical Literacy teachers who teach under impoverished conditions in South Africa. The participants identified their problems of practice and focused on one problem which they tried to address during a two-week teaching intervention. They were required to generate a reflective research report based on their teaching intervention, which formed the primary data source. The findings indicate that of the 305 citations of problems, 174 were attributed to socio-economic factors, 111 to pedagogic factors and 51 to school management factors. With most of these problems being out of their locus of control, these teachers are forced to spend time dealing with the consequences of these problems, instead of focusing their energy to find ways to improve their pedagogic practice. Teacher development agencies need to consider how such teachers could be more appropriately supported.}, keywords = {classroom practice, non-prototype classes, problems of practice, teacher learning}, issn = {1822-7864}, doi = {https://doi.org/10.33225/pec/16.70.34 }, url = {http://journals.indexcopernicus.com/abstract.php?icid=1203603}, author = {Sarah Bansilal and Thelma Rosenberg} }