Development of High School Mathematics Teachers

Abstract

The study will describe professional development intervention strategy on teaching and learning for high school mathematics teachers and how the use of NDR will influence teachers' professional practices. The focus of the study will be to encourage teachers to use NDR for their lesson preparation. The study will employ concurrent triangulation mixed research design to assess the possible impact of NDR on the performance of mathematics in high school. Teacher and learner performance data will be collected on participating teachers, controlled teachers, and their learners during the study period. This professional development intervention will have an impact on teachers' lesson preparation, instruction, and approaches as well as the performance of their learners.

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Keywords: Error analysis, National Diagnostic Report; Professional Development

Introduction and Background

The release of the 2015 Trends in International Mathematics and Science Study (TIMSS) reports for grades five and nine has provoked once more another storm of debates as South Africans grapple with the reasons behind the perceived poor learners' performances in mathematics and science. TIMSS is an assessment of the mathematics and science knowledge of fourth and eighth grades learners from selected countries around the world. In a simple language, South Africa's mathematics achievement at grade five is 45th out of 48 countries (a position shared with Morocco and Saudi Arabia) (TIMSS, 2015). According to the report, the low performance of South African learners for mathematics at grade five and nine (and science at grade nine) is linked to the factors at home, school, and community environments. Generally, the learners at independent schools performed exceptionally well followed by fee-paying public schools. The worst affected learners are those from no-fee public schools.

This study will focus on high school mathematics teachers' professional development with the use of annual grade 12 error analysis provided in the National Diagnostic Report in South Africa. The focus of the study is to investigate what are some of the practices of the teachers in the different environments that contribute to high performing results in mathematics. The National Diagnostic Report (NDR) is a report that gives an in-depth analysis of National Senior Certificate candidates' performance; question by question analysis of learners' responses as well as possible misconceptions and errors.

The current low-achievement of grade 12 learners in Mathematics calls for effective change, which requires a commitment to developing necessary turn-around strategies to support such change. These may include necessary resources, indispensable knowledge, skills, and the ability to identify difficulties within schools that can affect the changes.

McNeill, GonzalezHoward, KatshSinger, and Loper (2016) indicate that factors that influence in mathematics teaching are that teachers lack subject knowledge, science-specific curricular expertise, and confidence to teach. They further indicate that large classes and lack of access to trained classroom assistance might be another factor that hinders the success of teaching mathematics in schools. According to Idris (2011), inadequate subject matter knowledge and understanding of mathematics may lead to teachers' inability to appreciate the learning problems faced by learners or to design questions and activities that can probe learners' understanding. Hill, Blunk, Charalambous, Lewis, Phelps, and Sleep (2008) also advocate for the need of mathematics teachers to demonstrate mathematical knowledge for teaching (MKT) and strong Mathematical Quality Instruction (MQI). Mathematics knowledge for teaching includes two facets: the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. The latter emphasise that Mathematics teachers need to know how to present mathematical problems, have knowledge of the subject matter and good knowledge about the learners' difficulties, misconceptions and the ways they construct their knowledge. All these are vital for effective teaching and learning (ibid).

The researcher expects that subject-based diagnostic analysis will be institutionalised within the pedagogical practice not only at national level but also at provincial, district and school levels. The researcher hopes that every Grade 12 teacher and subject advisor on a yearly basis will see the NDR as a key resource that will be utilised effectively. The NDR presents an evaluation of learner performance in the selected subjects by highlighting the areas of weakness in each of the subjects and articulating the remedial measures to be adopted at the school level to improve performance in these subjects. The findings and recommendations are based on qualitative data that is drawn from the subject reports compiled by the chief markers, internal moderators and subject specialists post the marking process. Quantitative data gathered from the analysis of 900 randomly selected scripts per subject, per province were also used to analyse learner performance on a per question basis (NDR, 2018). As a result, the NDR provides teachers, subject advisors, curriculum planners and curriculum implementers with an overview of learner performance in each of the key subjects. The NDR in each subject, commences by presenting comparative data on the performance trends observed over a four-year period in the subject, and then provides an overview of learner performance in the Subject and this is followed by a detailed diagnostic analysis per question in the respective question papers in each subject. Common errors, misinterpretations, and misconceptions identified during marking and suggestions for improvement are provided. The poor quality of answers provided by some candidates in certain subjects continues to suggest gaps in the scope of content coverage, teaching methodology and content knowledge of some of the teachers in South Africa.

Identified gaps and progress in the report should determine the extent to which further interventions are necessary for the next academic year. This also suggests that continued reference to previous Diagnostic Reports is essential since the areas of weakness identified in past years may still be applicable in particular cases; It is these recurrent areas of weakness that must become the baseline for intervention by the subject advisory services in the next academic year.

The purpose of the study is to explore the use of error analysis feedback in the National Diagnostic Report as a professional developmental tool to enable Mathematics teachers to better adjust their instructional strategies to help students improve their National Senior Certificate (NSC) examination results in Mathematics. The continuous high performance of some high school mathematics teachers versus low- performing teachers in the same subject calls for a study on practices of the teachers in our schools. Teaching is a very complex and demanding profession and at the same time extremely challenging (Levenberg, 2014). The error analysis in the NDR highlights weaknesses in learner responses in the different subjects. Uncovering misconceptions or error patterns in the learner responses can directly inform instructional practice (Makonye, 2016).

Error analysis is the study of errors in learners' work with a view to looking for possible explanations for these errors (Herholdt& Sapire, 2014). Priyani and Ekawati (2018) also described error analysis as a way of analysing errors in learners' work with a view of finding explanations for those errors. It is a multifaceted activity involving analysis of correct, partially correct and incorrect processes and possible remediating strategies. An interesting question may be asked: Do Mathematics teachers in high-performing schools make use of the error analysis in the National Diagnostic Reportto provide targeted instructions to correct such errors? Or could it be that Mathematics teachers in ever-low performing schools never make any effort to identify the patterns of errors or mistakes and reasons that their students make in their activities. Research in mathematics education has shown that a focus on errors, as evidence of mathematical thinking on the part of learners, helps teachers to understand learner thinking, to adjust the ways they engage with learners in the classroom situation, as well as to revise their teaching approach (Adler, 2017; Baumert, et al., 2010; Luneta & Makonye, 2010).

Furthermore, recent studies on misconception and errors in mathematics education have also led to the need to interrogate error analysis at professional development level of mathematics teachers. GeorgeWalker and Keeffe (2010:20) argue, "Recognition of the need to change the way in which mathematics is taught and learned is international in scope". Research evidence from other countries indicates that professional preparation of teachers is significantly related to students' achievement (National Mathematics Advisory Panel, 2008). Additionally, the recent reports of the international TEDS-M (2008) study also have it that rigorous mathematics instruction in schools and demanding programs in the preparation by the university teachers in countries like Taiwan and Singapore accounts for their teachers having better knowledge of mathematics and its teaching. Based on the research done in South Africa, Bantwini (2009:178) says that despite the reforms in place, most teachers lack adequate pedagogical content knowledge, lesson planning and are deficient in the use of various instructional approaches and assessment approaches. Therefore, it is crucial to address the issues identified because of their direct and severe impact on teacher quality and performance and eventually on learners' science learning.

The study will seek to determine the possible rel...