An exploration of in-service teachers’ understanding of teaching mathematics in Grade R classrooms: A case study of Grade R in Lesotho University of KwaZulu-Natal, South Africa (original) (raw)
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2014
Research have indicated that young learners are capable to learn mathematics because they are born with innate core of mathematical knowledge. Teachers of young learners are therefore, expected to offer mathematical curriculum which exposes learners to deep and explicit knowledge of high mathematics which embraces all five major content areas of mathematics in order to lay a solid foundation of the learning of mathematics in the future grades. This study focuses on in-service teachers teaching Mathematics in Grade R classes. The dissertation is aspired to explore their understanding of the teaching of Mathematics in Grade R class. Shulman's theoretical framework of seven domains of knowledge that teachers must have in order to be able to teach any subject, guided this study. The objectives of this study were to understand in-service teachers' understanding of the teaching of Mathematics in Grade R class and to examine how in-service teachers' understanding of the teaching of Mathematics influences their teaching of Mathematics in Grade R class. To explore this, a qualitative approach and case study design were employed. I sampled five in-service teachers from four districts of Lesotho namely Maseru, Berea, Mohale's hoek and Leribe. Data sources included teachers' interviews, classroom observations, and analysis of documents such as teachers' lesson plans, Grade R curriculum for mathematics and course
Pythagoras, 2004
Various studies have shown that what teachers consider to be optimal ways of teaching mathematics is influenced by their beliefs about the nature of mathematics, and that it is advantageous to determine teachers' conceptions of the nature of mathematics before developing curriculum interventions. With the imminent introduction of Mathematical Literacy in the FET phase in South Africa this study provides a snapshot of beliefs of teachers in the Eastern Cape, South Africa. Various methods were employed to stimulate teachers to both reflect on their beliefs and to make them explicit. A questionnaire was administered to 339 in-service teachers in urban and rural areas of the Eastern Cape. A sample of ninetyfive of these teachers completed a second questionnaire based on videotapes of lessons recorded during the TIMSS (1995) study that they had viewed. These teachers also ranked their own teaching on a continuum ranging from traditional to constructivist approaches and provided explanations for their ranking. A further sub-sample of thirty-six teachers participated in individual interviews, which explored their perceptions of the nature of mathematics and their own teaching practice. In order to investigate whether these beliefs were mirrored in practice, four teachers were observed and videotaped in their classrooms. The data generated by this study suggest that the participating teachers' espoused beliefs of the nature of mathematics tended to be innovative, and correlated with innovative views of teaching and learning; however these views were often not reflected in their practice. The implications that the apparent inability of teachers to translate their beliefs into practice have for the introduction of a contextual, problem-based Mathematical Literacy curriculum for teachers is explored.
International Journal of Science and Technology Education Research
Mathematics and Science education is very important for any nation to realise meaningful economic development. Most studies looking at this important aspect of education focus on post primary to tertiary education leaving the primary level which is a foundation for those levels making the story incomplete. This study explored the dynamics of primary school teaching of Mathematics and Science with respect to the subject matter content knowledge for Mathematics and Science by the pre-service and in-service primary school teachers in Lesotho. The study assessed the Mathematics and Science subject content of 85 first-year pre-service teachers at the College of Education and 22 in-service as reflected in their scores in the national examinations at three levels: Primary School Leaving Education, Junior Certificate and Cambridge School Certificate. This was followed by a questionnaire to assess their views on subject specialisation as a remedy for poor performance. The results revealed that there are some teachers who have never passed Mathematics and Science at any level of education examined nationally, thus making it difficult and uncomfortable for these teachers to teach these subjects effectively as demonstrated by 14% of the in-service teachers. A large majority (77%) recommended the introduction of subject specialisation to commence at primary school level in order to improve Mathematics and Science performance.
Mathematical Knowledge for Teaching: How do Primary Pre-service Teachers in Malawi Understand it?
African Journal of Research in Mathematics, Science and Technology Education, 2020
While a consensus within the field exists that pre-service teachers need adequate knowledge and skills to become effective teachers in mathematics, less is known about how they understand the mathematical knowledge needed for teaching in elementary education. This paper explores how Malawian pre-service teachers understand the mathematical knowledge needed for teaching in primary schools. Written answers to a questionnaire survey, and data from six individual interviews collected at the beginning of the teacher-training programme will be presented. The analytical framework is based on the practicebased theory of mathematical knowledge for teaching, with a specific focus on the domains of the common, horizon and specialised content knowledge. The data revealed that, while taking theoretical courses, pre-service teaches develop only intuitive but complementary views of what is proposed by the theory, which is even the case with pre-service teachers with some prior teaching experience. Findings provide insights into the development of pre-service teachers' mathematical knowledge for teaching, and suggest that further research is needed on how pre-service teachers articulate their understanding of teaching in practice.
The relationship between teaching practices and students' achievement in mathematics in Lesotho
Research has found that teaching practices are a critical factor in promoting student achievement in mathematics and may therefore explain a substantial portion of the variance in student learning and achievement. The aim of this study was to assess the relationship between student achievement in mathematics and teachers' teaching practices in the Maseru District in Lesotho, Southern Africa. A self-report instrument -Mathematics Teaching Opinionate Scale (MaTOS) -was used to collect data from 40 Form C (Grade 10) mathematics teachers about their teaching practices. This paper outlines correlations found between specific teaching practices (formal presentation, teacher-guided discussion, group work and homework) and student achievement in mathematics. Possible implications of these correlations are discussed and recommendations for further research are put forward.
Lesotho Grade R teachers’ mathematical knowledge for teaching numeracy
South African Journal of Childhood Education
Background: It is important that mathematics teachers have a robust knowledge of the mathematics they teach. They need more than just knowledge of the content because they are expected to facilitate understanding of the content with their learners. This study focused on the knowledge of practising Grade R teachers from Lesotho.Aim: The purpose of this exploratory study was to explore practising Grade R teachers’ mathematical knowledge for the teaching of numeracy.Setting: The study was conducted with 48 practising Grade R teachers while they were enrolled in an in-service programme at a College of Education in Lesotho.Methods: Data was generated through the use of questionnaires. The questionnaire included items focusing on the four domains of knowledge, namely common content knowledge, special content knowledge, knowledge of content and students, and knowledge of content and teaching.Results: The findings revealed that some teachers were unable to carry out division problems accura...
Problems of Education in the 21st Century, 2019
This qualitative research reports the results of a short learning intervention programme conducted by South African National Roads Agency Limited (SANRAL) Chair in Science and Mathematics Education to enhance the mathematical knowledge of teachers in some South African schools. The short learning programme comprised the fostering of teachers’ mathematical knowledge and the formation of lesson study groups to apply the knowledge gained from the intervention programme in different schools in the country. The sample comprised 53 male and 72 female Mathematics teachers who were nominated from several school districts in the country. The participants were trained using Mathematical Knowledge for Teaching (MKT) which included the topics of probability/ratio and proportion (grades 1-9). The MKT consisted of these sets of expertise: Common Content Knowledge (CCK), Specialised Content Knowledge (SCK), Knowledge of Contents and Students (KCS), and Knowledge of Content and Teaching (KCT). The ...
Ready to teach? Reflections on a South African mathematics teacher education programme
In this paper, I interrogate the extent to which a current mathematics teacher education programme at University of KwaZulu-Natal prepares teachers to teach well in the regional context. In order to determine which aspects to consider in the analysis, I draw on studies of factors correlated to learner achievement in South African primary schools. First, this suggests that the consideration of context should play a strong part in our teacher education. Second, it indicates that teacher actions most strongly linked to learning – deep representations, feedback guiding learning and challenging learners on their level – only occur occasionally in KwaZulu-Natal schools, and with limited opportunity to develop mathematical proficiency. The question I raise is to what extent we prepare teachers to teach in this way, and with awareness of the context. Third, I briefly consider what other, perhaps overlooked, competencies our teachers need. In the light of Bernstein’s recognition of the centrality of evaluation in the pedagogic device, I have analysed the exam papers in the programme. My analysis utilises a pragmatically compiled bag of tools. First, I distinguish between the knowledge categories in our programme: contextual knowledge, curriculum knowledge, content knowledge, pedagogic content knowledge, and general pedagogical knowledge. Next, I explore the extent to which specialised knowledge is foregrounded in our programme, drawing on Maton’s distinction between a knowledge and a knower legitimisation code. Third, by distinguishing the semantic gravity of the course content, I aim to identify how theoretical or decontextualised knowledge is linked to the practice of mathematics teaching. This enables me to consider the extent to which the programmes favour cumulative or segmented learning. My findings indicate that the programme is strongly founded in a knowledge code, and that it covers all of the five aforementioned knowledge domains, but it needs further exploration how well these are linked within and across courses, thus providing cumulative learning. Teaching for deep representations is strongly reflected in the exam papers, both in the content knowledge and the pedagogical content knowledge components, but there is virtually no indication that providing appropriate challenges to learners is important. While students are tested on their recognition and realisation of assessing learners’ level of understanding, this is not utilised in teaching students to provide appropriate feedback, nor is it used to inform the design of activities which can cater for a classroom with learners of mixed ability or varying levels of current understanding. Furthermore, there is no assessment of the teachers’ preparedness to teach for adaptive reasoning. In that respect, the programme appears not to prepare the students adequately for quality teaching. I discuss whether this knowledge mix and what is not taught can be seen as having an implicit student in mind, thus limiting access to relevant teacher competencies for some students.
Mediterranean Journal of Social Sciences, 2013
This paper presents a theoretical framework comprising components of teacher knowledge that can render effective learner understanding of mathematical and science concepts. Twelve mathematics teachers at the secondary school level were selected from both countries on the basis of their school consistent good performance for at least three years. The study adopted a qualitative research method. The data on the teachers' PCK were collected through lesson observations, questionnaires, interviews, video recordings, teachers' written reports, and document analyses. An iterative coding and categorisation were used to identify the emerging theme of the study. The result of the study shows that the emerging theme that form the framework can inform mathematics and science instruction to balance the ternary relationship between curriculum content, learners and teacher quality in terms of pedagogical practice. The framework was found promising in either study but a more conclusive evidence will be given after a planned longitudinal study.
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In this article, we propose a rubric for assessing the teacher’s provision of opportunities to develop mathematical proficiency in classrooms. The rubric is applied to data from 30 video recordings of mathematics lessons taught in Grade 6 in one district of KwaZulu-Natal. The results suggest that opportunities to develop procedural fluency are common, but generally of a low quality; that opportunities to develop conceptual understanding are present in about half the lessons, but also are not of a high quality, and that overall opportunities to develop mathematical proficiency are limited, because learners are not engaging in adaptive reasoning, hardly have any opportunities to develop a productive disposition, and seldom are given the opportunity to engage in problem-solving which could develop their strategic competence.