Sarah Bansilal

Teacher training for mathematical literacy: A case study taking the past into the future

With the advent of the Minimum Requirements for Teacher Education Qualifications policy (MRTEQ), higher education institutions (HEIs) are rethinking curricula for teacher training in order to enable entree for in-service teachers to reskill, retrain and have access to higher qualifications. In the field of mathematical literacy (ML), most teacher training has been offered via government-funded Advanced Certificate in Education (ACE) qualifications, which have now largely been phased out. In this article we examine two ACE ML programmes offered in KwaZulu-Natal (KZN) in order to present some lessons that have been learnt. We put forward some elements that we consider to be essential for training ML teachers and also raise concerns about future training of ML teachers.

Teachers' understanding of inflation: developing a crystalline concept

ABSTRACT Inflation rates are often reported in the media and interpreted differently by various people. The purpose of the study was to explore mathematical literacy teachers’ written responses to questions based on the concept of percentage increase and inflation. The participants were a group of 59 in-service South African teachers who were enrolled on a course to help them to teach the subject mathematical literacy. The findings show that 95% of the teachers could carry out a percentage increase calculation without any difficulties, but only 37% could correctly work out a two-step calculation using the inflation rate figures. Across all the items, there were only eight teachers (14%) who showed evidence of engagement with all the contextual constraints embedded in the inflation concept. Teachers exhibited poor covariational reasoning with respect to the changes in the inflation rates and changes in the price of goods. The study suggests that opportunities for the development of covariational reasoning should be promoted.

Exploring the notion of Mathematical Literacy teacher knowledge

The introduction in South Africa of the subject Mathematical Literacy was an innovative response to the low levels of numeracy amongst adults. No other country has developed a subject with such an exclusive focus and this raises challenges for ML teacher educators to design a suitable curriculum to train ML teachers. In this paper I first propose a contextual attributes model of ML. Contextual attributes such as contextual signifiers, language, rules and visual mediators are identified and it is argued that ML learners require opportunities that facilitate engagement with these attributes in order to participate in the domains and make informed decisions. I then explore some implications of this model for the conceptualisation of ML knowledge for teaching.

An Exploration of the Assessment and Feedback Practices in a Practical Teaching Intervention for In-service Teachers

Abstract There is much concern in South Africa about the quality of teaching in our schools, and many teacher development programmes have introduced a classroom support component where in-service teachers are assessed on their teaching practice skills. However, limited research related to the support and assessment functions of such interventions has been published. The qualitative study reported in this paper focused on the feedback reports given to 249 rural mathematics and science teachers as part of the assessment of their teaching practices. The teachers from the South African province of KwaZulu-Natal (KZN) were enrolled on a teacher development programme. The purpose of the study was to explore the nature of the feedback reports that were provided and to assess the value of allocating assessment scores to the teachers. The data were broken down into 1 028 feedback units that were used to generate open codes. These codes were refined into six main categories. The findings reveal that the written comments covered a range of issues related to teacher professional development. However, the majority of the comments did not provide rich opportunities for reflection. It was also found that the scores lay within a narrow range and did not work well in differentiating between a range of competencies. It is recommended that the feedback role of the university tutor should receive more attention than that of the evaluative function of the classroom support visits.

Teacher Professional Development Programmes in MST for Developing Contexts.

ABSTRACT Since 1994, the democratic South African government has introduced change in all spheres of South African life in a bid to address some challenges such as the redundant, racialised curriculum, the poor results achieved by learners in Grade 12, and the fact that few black matriculants were entering science based careers. A key feature of these poor results was the large group of teachers who were inadequately ‘trained’ during the apartheid era: trained, that is, to teach for subservience and not for critical thinking. Current actions to address this crisis are being undertaken in a collaborative relationship between the Department of Education and Higher Education Institutions. Current initiatives in the professional development of Mathematics, Science and Technology teachers at a South African university are explored. The purpose of this article is to explore the challenges of designing an MST professional development programme in a developing context. The discussion is elaborated with reference to MST programmes run by one particular university. The rationale, foundational principles, model of delivery, programme structure and assessment for the specialisations within the teacher professional development programmes at the university are described. The discussion foregrounds the role of teachers as professionals, the role of context and of content knowledge, as well as the role of pedagogic content knowledge in the professional development of teachers.

Arriving at the starting point? Exploring a teacher's use of circular reasoning in a mathematics classroom

Abstract The problem of poor content knowledge of mathematics teachers in South Africa has been so widely reported that such reports provoke little reaction. My study was set around the following question: How does a teacher with poor mathematics knowledge teach mathematics for understanding? The participant in the study was a teacher who was mediating an assessment task with a Grade 9 mathematics class. Data was generated from five classroom observations, as well as interviews with the teacher and students. The purpose of the study was to explore the ways in which her mathematics knowledge impacted on classroom interactions. It was found that because of the teachers poor understanding of the concepts of ratio and number, she missed some key ideas and presented explanations that were convoluted and which involved circular reasoning. The analysis also revealed that the teachers development was hampered by the stressful working conditions. The study recommends that school and education management teams sh...

Tracing the impact: A case of a professional development programme in Mathematical Literacy

Abstract The introduction of the subject Mathematical Literacy (ML) as part of the education reform process, led to the development of many large scale in-service programmes designed to train practising teachers to teach the new subject. The purpose of the study is to examine the challenges associated with providing in-service training for teachers of ML, by focusing on one district. We present a case study of one programme that was offered by two different universities in three large-scale funded cohorts in the province of KwaZulu-Natal (KZN). Data for the study was generated by student records, questionnaires and follow up surveys with each school in the district. By considering the success rate as the number of actual qualified teachers in relation to the number that was needed, we quantified the rate at 13%. Some of the factors which were responsible for this low rate are related to the processes of recruitment and selection of the appropriate teachers for the programme; the low pass rate as well as the deployment and management of the graduates at the end of the programme. It is recommended that future large scale teacher training initiatives be jointly managed by the universities and the education authorities, to ensure higher rates of success.

How much freedom does a teacher have in designing a learning event when adhering to assessment prescription

Abstract This article captures a mathematics teachers understanding and practice of a new national curriculum specification for assessment. This is an externally mandated summative assessment programme in South African public schools at the Grade 9 level. The study is set in the context of an under-resourced classroom with a large number of learners from disadvantaged backgrounds who have serious problems with fundamental mathematical concepts. The theoretical framework for the study draws upon the philosophy of critical realism. Data for the case study were generated from seven lesson observations, two interviews with the teacher and a focus group interview with a group of learners from the class. The article concludes with the argument that there are contradictory stipulations emanating from the policy that proved to be irreconcilable in the teachers classroom setting and practice.

The experiences of first-year students in mathematics in using an e-learning platform at a university of technology

Abstract Universities of technology in South Africa have been trying to provide effective and flexible learning experiences to cater for the influx of students enrolling in the institutions who come from diverse educational backgrounds. One of the challenges arising from their diverse educational backgrounds is their poor background in the use of technologies for teaching and learning. The teaching of mathematics, particularly, is made more difficult because of the large number of students who have many misconceptions as a result of problems from the basic education that they were part of, for a period of 12 years. Consequently, a number of them do not make it to the mainstream education system due to poor performance in first-year mathematics. The purpose of the study on which this article reports was to determine the impact that an e-learning platform could have on mathematics first-year students when used as a supplement to the traditional methods of teaching. The study utilised quantitative and qualitative methods, with the qualitative data being used to interpret and make sense of the quantitative data. Participants were 35 first-year students in the Department of Civil Engineering at a university of technology. Data were generated from questionnaires and focus group interviews. It was found that the actual use of the system is dependent not only on student behavioural intention to use the system, but external factors also contribute negatively to the actual system use. Some external factors that were identified include poor Internet connectivity, insufficient computers and an inflexible timetable. The study recommends that universities of technology should take greater care in designing their academic calendars, so that it alleviates instead of tighten the constraints under which students work.

Dealing with the Abstraction of Vector Space Concepts

University mathematics students often find the content of linear algebra difficult because of the abstract and highly theoretical nature of the subject as well as the formal logic required to carry out proofs. This chapter explores some specific difficulties experienced by students when negotiating vector space and subspace concepts. Seventy-three in-service mathematics teachers’ responses to two items testing the ability to prove that a given set is not a subspace and that a given set is a subspace of a vector space were studied in detail. Follow-up interviews on the written work were conducted to identify the participants’ ways of understanding. The action–process–object–schema (APOS) theory was used to unpack the structure of the concepts. Findings reveal that the teachers struggled with the vector sub-space concepts mainly because of prior non-encapsulation of prerequisite concepts of sets and binary operations and difficulties with understanding the role of counter-examples in showing that a set is not a vector subspace.