Science and Technology Education

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An exploration of grade 11 mathematical literacy learner's engagement with start-unknown and result-unknown type problems set in a variety of real life contexts.
(2013) Mbonambi, Martin Sipho.; Bansilal, Sarah.
With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject might develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is taught and assessed, which influences the focus of ML in the classrooms. One of the differences between the respective subjects of Mathematics and Mathematical Literacy is that when it comes to the latter, there has been less emphasis on carrying out algebraic procedures, and a greater focus on working with contexts. However, algebraic skills can be advantageous even when solving problems set within contexts. One area, which surfaces the distinction between arithmetic and algebraic skills, is in the substitution and computation of a formula, as compared to the solution of equations. In this study, I focus on this distinction by examining Grade 11 ML learner skills in solving both result-unknown problems and start-unknown problems, where the former involves substituting and computing the result of a formula or equation for which the input is given. The latter involves re-arranging the equation or formula in order to solve for the input when the output is given. With this in mind, this study sets out to explore the strategies used by Grade 11 learners to solve result-unknown and start-unknown problems set in real life contexts. This is a qualitative study, carried out with three hundred and forty Grade 11 Mathematical Literacy learners from rural and urban school in North Durban. Data was gathered from a document analysis of 340 learners’ written responses to the research instrument, along with interviews with ten of these learners. There were four tasks in the research instrument, each of which had a result-unknown, a start-unknown and a reflection question. In the four tasks with the exception of Question 1.2.1 and 1.2.2 in tasks one, were set around a linear equation, while Question 1.2.1 and 1.2.2 involved a hyperbolic equation. Semi-structured interviews were conducted individually with ten learners and the audio recorded. The purpose of the interviews was to explore some of the factors that influenced their written responses. The findings revealed the solving of start-unknown questions to be a serious problem for learners. On average, the success rate at result-unknown questions was 75%, while it was 26% for start-unknown questions. For start-unknown questions based on linear equations only, the success rate was a mere 19 percent. Some strategies used by learners in responding to start-unknown questions included number grabbing, systematic guess and test, conjoining, symbol manipulation and working backwards. On average, over the four tasks based on linear equations, only nine percent of learners successfully used strategies based on algebraic skill. Most learners who obtained correct answers in the start-unknown questions used the guess and test strategy. Strategies identified in result-unknown questions included direct arithmetic strategy. The study recommends that for ML learners, teachers need to impress upon learners that the location of the formula in the question is not an indication that certain questions would be answered using the formula, because the formula is placed next to them. It also recommends that teachers create opportunities for learners to continue to practice the algebraic skills they learned in the GET band, particularly in the area of transforming and solving simple linear equations.
An exploration of mathematical literacy teachers' perceptions of, and performance in mathematical literacy tasks based on algebra.
(2010) Vilakazi, Aubrey Sifiso.; Bansilal, Sarah.
Mathematical Literacy (ML) has only recently been introduced to learners, and research in South Africa concerning learners’ conceptual understanding in ML is not widely available. However an important predictor of learners’ success or difficulties in concepts is the success or difficulties that in-service teachers experience themselves. It is therefore important for us as mathematics educators to identify areas in Mathematical Literacy that teachers are struggling to learn and apply. With this in mind, the study sets to explore teachers’ perceptions about, and performance in Mathematical Literacy tasks based on algebraic concepts. This study is located within the principles of the qualitative research case study approach. The combination of data collection techniques has allowed me to identify broad trends across the group as a whole as well as differences within the participants of the group itself. The participants of the study were a class of 17 students who were completing the ACEML programme at UKZN. Four sources of data were used. Firstly, data was generated from teachers’ reflections about certain tasks, the solution of which required the use of algebra. A second data collection instrument was an open-form questionnaire and the third instrument was two unstructured interviews with two teachers. The final instrument was the analysis of the teachers’ examination scripts. For this study, teachers from this group were classified along the lines of whether they were qualified to teach mathematics or not. The theoretical framework for the study was derived from the OECD/PISA (2003) cycle of mathematisation which specifies 5 aspects of mathematisation, together with the theory of reification. For the purpose of this research, a participant was considered as a “mathematics specialist” if s/he studied mathematics up to tertiary level, while a participant was considered as “non-mathematics teacher” if s/he studied mathematics only up to Grade 12 level. The findings reveal that although the teachers conveyed varying understandings of the ML curriculum, they believed that knowledge of basic algebra was necessary and adequate for them to deal with ML problems. Furthermore the teachers believed mathematical teaching experience contributes to improved problem solving in ML and that ‘practice and familiarity’ helped teachers improve their problem solving skills in ML. They also voiced a concern that the pace of the programme constituted a barrier to their success. Within the group, it was found that Mathematics specialist teachers performed better than the non-Mathematics teachers. All teachers found the mathematisation aspects of solving the mathematical problem and of reinterpreting the mathematical solution to make sense of the real-life problems, challenging, while the non-Mathematics teachers experienced problems with all five aspects of mathematisation. The findings of the study suggest that teachers need help in moving from lower levels to higher levels of mathematisation. Opportunities for mathematical modeling experiences need to be incorporated in the part-time in-service contact courses like ACEML. Further research is needed to inform education authorities about whether the use of teachers with only grade 12 mathematical knowledge to teach ML is advisable.
An exploration of the role of the advanced certificate in education on the professional development of mathematical literacy teachers.
(2012) Thembela, Thandimfundo Eugene.; Bansilal, Sarah.
Mathematical Literacy (ML) was introduced as a new subject in 2006, as an alternative to Mathematics for learners in Grade 10 to 12 in South African schools. The challenge of the shortage of Mathematics teachers (and hence Mathematical Literacy teachers), was exarcebated. Hence the KwaZulu Natal Department of Education (KZNDoE) jointly with the University of KwaZulu-Natal (UKZN) initiated a programme designed to re-skill teachers to teach this new subject. This study explores the professional development of such teachers as a result of their participation in the Advanced Certificate in Education (ACEML) course at UKZN. Their professional development is explored in terms of their content knowledge, a content specific pedagogy and their professional identity and beliefs. The study was informed by a naturalistic, interpretivist orientation. Two versions of semi-structured questionnaires were completed by a total of twenty-three teachers. The first version, called Questionnaire A, was completed by fifteen teachers while the second version, Questionnaire B, by eight teachers respectively. Later, semi-structured interviews with four of the teachers were conducted. Their previous academic records were also used as data sources. The key findings of the study revealed that all teachers interviewed perceived improvement in their content knowledge as a result of their participation in the programme. Examples of improvements in their content-specific pedagogies were their increased repertoire of teaching strategies, their increased confidence, their focus on learners‟ prior understanding and their ability to link their teaching to real life applications. Findings also indicate that many teachers developed strong identities as Mathematical literacy teachers. A shift in identity was also evident with some teachers switching over from previous specialisations to teaching only Mathematical Literacy. Many teachers also felt that the generic modules helped them gain a broader understanding of their role. Claims that Mathematics teachers who have not studied the ACEML cannot teach ML as successfully as those who have, were made by most teachers.
An exploration of the strategies used by grade 12 mathematical literacy learners when answering mathematical literacy examination questions based on a variety of real-life contexts.
(2011) Debba, Rajan.; Bansilal, Sarah.
With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject will develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is assessed which influences the focus of ML in the classrooms. With this in mind, this study set out to explore the ways in which a class of Grade 12 learners engaged with a preparatory examination designed and administered by the KZN Department of Education. This is a qualitative study carried out with seventy-three grade 12 mathematical literacy learners from an urban school in North Durban. The purpose of this research is to explore the learners’ engagement with the examination tasks, thereby identifying possible factors which influence learners’ success in these items. Data were gathered from a document analysis of the 2009 KZN Trial Examination question paper and marking memorandum; 73 learners’ written responses to the examination tasks, and interviews with ten of these learners. The purpose of the document analysis was to identify contexts in which learners performed well or poorly, as well as to assess the design of the instrument. Semi-structured interviews were conducted individually with ten learners and video recorded. The purpose of the interviews was to explore some of the factors which influenced their written responses. The findings revealed that the task design was problematic for learners in terms of the order of the questions and the placement of the crucial information necessary to answer the questions. Some tasks also contained errors. The complexity of the scenario in terms of the amount of information, the language used, and the presence of distracters further influenced the way in which learners responded to the task. Learners’ personal experience of the context also affected the way they interpreted and responded to the task. Factors that constrained learners’ success in the examination task included poor conceptual understanding, misconceptions and language-related misinterpretation. It was also found that learners did not consider it a priority to make sense of the context: they focused on identifying formulae or information that could be used to present answers with little concern about the reasonableness of their responses. Some strategies used by learners in responding to the task included number grabbing, guessing without checking, scanning for crucial information and assumption-making. The study recommends that provincial examination papers be subject to the same stringent moderation requirements of the national examinations. It also recommends that should diagrams be used, they must be relevant to the context and should not conflict with the subject matter. The use of contexts should cater for alternate answers and multiple approaches and the marking memorandum should be flexible to accommodate these multiple approaches. Care must be taken in the presentation and placement of crucial information, so that learners do not miss the information they need to answer the questions. When familiar contexts are being used, task designers should also consider whether learners’ everyday experiences may conflict with these scenarios.
Grade 9 learners experiences of the common tasks for assessment in mathematics literacy, mathematics and mathematical sciences.
(2008) Khan, Mumtaz Begum.; Bansilal, Sarah.
This was a qualitative study carried out with one Grade 9 MMLMS class. The purpose of the study was to explore the experiences of the learners with respect to the CTA that they completed for their summative assessment. The methods of data collection were classroom observation, document analysis and interviews. Data was gathered from 4 classroom observations, a document analysis of the 2005 CTA instrument, the detailed responses of 3 learners to the CTA as well as a focus group interview with the 3 learners. The document analysis was done against a framework of moderating criteria identified by the moderating board of the eTA. The 4 lessons were video taped while the researcher was a participant observer in the classroom. The transcription of the tapes, the field notes and observation schedules were analysed with the intention of providing answers to the main research question. Similarly the interviews were video taped, transcribed and then analysed to provide further insight into the research question. Finally the learners' responses to certain items were scrutinized for further details. The findings revealed that the task design, which relied on grounding each task within one context, was problematic for the learners. The learners struggled with the language used in the tasks and often could not pick out crucial information from all the details associated with the contextualization. The language of the tasks was set at a high level of readability, higher than the average Grade 9 level. Furthermore, the teacher's interventions often seemed to hinder rather than facilitate their understanding of the mathematics. The results of the study have implications for teachers (to be careful of how they mediate the tasks), curriculum developers (to take note of the criticisms levelled at assessment tasks set in real life contexts) and mathematics educators (to voice their concerns about national assessment instruments which may themselves not be valid indicators of what learners can and cannot do).
Grade twelve learners' understanding of the concept of derivative.
(2008) Pillay, Ellamma.; Bansilal, Sarah.
This was a qualitative study carried out with learners from a grade twelve Standard Grade mathematics class from a South Durban school in the province of KwaZulu-Natal, South Africa. The main purpose of this study was to explore learners‟ understanding of the concept of the derivative. The participants comprised one class of twenty seven learners who were enrolled for Standard Grade mathematics at grade twelve level. Learners‟ responses to May and August examinations were examined. The examination questions that were highlighted were those based on the concept of the derivative. Additionally semi-structured interviews were carried out with a smaller sample of four of the twenty seven learners to gauge their perceptions of the derivative. The learners‟ responses to the examination questions and semi-structured interviews were exhaustively analysed. Themes that ran across the data were identified and further categorised in a bid to provide answers to the main research question. It was found that most learners‟ difficulties with the test items were grounded in their difficulties with algebraic manipulation skills. A further finding was that learners overwhelmingly preferred working out items that involved applying the rules. Although the Higher and Standard grade system of assessing learners‟ mathematical abilities has been phased out, with the advent of the new curriculum, the findings of this study is still important for learners, teachers, curriculum developers and mathematics educators because calculus forms a large component of the new mathematics curriculum.
Learner errors and misconceptions in ratio and proportion : a case study of grade 9 learners from a rural KwaZulu-Natal school.
(2012) Mahlabela, Patisizwe Tennyson.; Bansilal, Sarah.
Proportionality is the content domain of mathematics that is rooted in ratio and proportion. It is believed to be vital for problem solving and reasoning, which are key cognitive domains of mathematics teaching and learning. Hence, ratio and proportion forms part of curricula for all countries. Studies carried out in different parts of the world found that while learners can do simple and routine manipulations of ratio and proportion, they struggle to solve problems that involve these concepts. Researchers apportion the blame for this to the strategies that learners use to solve the problems. Researchers found that learners use flawed strategies due to misconceptions that learners have on ratio and proportion. The purpose of the study is to explore learner errors and misconceptions on ratio and proportion. A test that comprised of questions that are appropriate to the National Curriculum Statement (NCS), for General Education and Training (GET) band, was used to collect data. Items in the instrument were selected and adapted from a tool used in Concepts in Secondary Mathematics and Science (CSMS) study. The participants in the study are 30 Grade 9 learners from a rural school in KwaZulu-Natal (KZN). The findings of the study are that learners have a limited knowledge and understanding of ratio and proportion, hence their performance in items on the topic is poor. A great proportion of the learners have serious misconceptions of ratio and proportion. They use incorrect strategies to solve problems on ratio and proportion that produce errors. The errors and misconceptions they exhibit are not different from those observed by similar studies conducted in other parts of the world. The study recommends a structured focus on ratio and proportion because the topic is fundamental to proportional reasoning. It recommends clarity for teacher trainers, textbook writers and teachers on what learners need to learn on ratio and proportion. It recommends serious exploration of errors and misconceptions on ratio and proportion, and a teaching approach that considers errors and misconceptions as opportunities for learning.
Learners' voices on assessment feedback : case studies based at a KwaZulu-Natal school.
(2007) Naidoo, Magieambal.; Bansilal, Sarah.; James, Angela Antoinette.
The introduction of an Outcomes Based approach to education in South Africa has drawn attention to the nature of assessment. This research study investigated learners' perceptions of educator feedback and aimed at investigating and understanding: learners' meanings of educator feedback, forms of feedback that learners consider effective, and why do they consider these feedback forms as effective? In this case study, journal writing and group interviewing were used as data collection instruments. The five participants were Grade: 9 learners from a secondary school in Phoenix, Durban. The participants engaged in seven units of journal entries each. Having read these journal entries, these five learners comprised the group that was interviewed. The group interviewing provided depth in the five case studies. The findings of this study revealed that learners have significant perceptions of 'educator feedback'. Their definitions of feedback conveyed a broader concept of educator feedback than I had expected. Through their definitions of feedback, learners' outlined their expectations of educator feedback. Learners also disclosed their preferences for some forms of feedback over others. Furthermore, they provided reasons for valuing certain forms of feedback. Their views on the significance of feedback related mostly to: enhancement of learning; correction of errors and avoiding the same errors in subsequent tasks Moreover, learners divulged their positive and negative experiences of educator feedback. Learners' positive experiences of feedback resulted from feedback that promoted learning through remediation of errors and feedback that was motivating. Learners' negative experiences were linked to forms of feedback that they considered as inadequate. These forms of feedback were as inadequate in that learners did not understand where they had gone wrong or why they were wrong. Feedback that had a negative effect on their emotions caused them embarrassment. Forms of feedback that encouraged competition were not valued. Learners raised concerns over the language of feedback (verbal and written) and also the use of red ink in written feedback. A further matter raised was that feedback should relate directly to the mathematics, rather than being personal.

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Browsing Science and Technology Education by Author "Bansilal, Sarah."