Browsing by Author "Hobden, Sally Diane."

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The beliefs of preservice teachers about mathematics teaching and learning.
(1999) Hobden, Sally Diane.; Boughey, John.; Searle, Ruth Lesley.
Preservice teachers have had a twelve year "apprenticeship of observation" in the practice of teaching and as a consequence have internalised a set of beliefs about Mathematics teaching and learning. These beliefs are usually implicit but nevertheless influence the teaching practice of the preservice teachers to the extent that they "teach as they were taught." A preservice Mathematics Education course, falling as it does between the prospective teachers' experiences as scholars, and their future teaching experience provides an ideal opportunity for preservice teachers to review their personal beliefs prior to carrying them over to teaching practice. In order to facilitate this review, a series of activities was designed as part of a Mathematics Education course for preservice secondary phase Mathematics teachers. These activities provided opportunities for student teachers to examine their beliefs, to discuss and write about these beliefs, to read about the beliefs of others, and finally to decide whether they wished to retain or modify their personal beliefs. Data on the personal theories of the preservice teachers was obtained from the written responses to various critical incidents, from metaphors for the teaching and learning of Mathematics drawn and described by the preservice teachers, and from interviews with selected participants. These theories were classified into qualitatively different categories. After completing several developmental activities and a five week period of classroom teaching, the preservice teachers were invited to reconsider their personal theories and amend their metaphors. This provided evidence of reflection and development in their thinking. It is contended that the personal theories of preservice teachers are not only reflected in their classroom practice but also function as barriers to impede acceptance of novel ideas and innovations. The findings of this study contribute to the understanding of the thinking of preservice teachers and inform the development of a curriculum for the Mathematics Education component of a Professional Studies course.
A description of mathematical proficiency in number skills of grade ten learners in both the mathematics and mathematics literacy cohorts at a north Durban school.
(2008) Moodley, Vivendren Govindarajaloo.; Hobden, Sally Diane.
The main objective of this study was to determine the progress made in the development of mathematical proficiency, in the domain of number skills, by learners in the two cohorts (namely: Mathematics and Mathematical Literacy) during Grade ten. The research was conducted at Temple Valley Secondary School, which is situated at Verulam, north of Durban in KwaZulu-Natal. Furthermore, this research study was questionnaire-based employing basic descriptive statistics as well as qualitative analyses. Data was collected through numeracy (number) skill tests, a questionnaire and focus group interview responses of grade ten mathematics learners. A total of two skill tests were administered and 3 focused group interviews were conducted with six grade ten learners each. The first test and first attitudinal questionnaire was administered in May 2006 when learners had branched off into the two paths of mathematics. Thereafter, a second test and second attitudinal questionnaire was administered, during October 2006; when learners had completed most of the school year. The October-test was followed by the focus group interviews. A convenient sample was used in selecting the learners for this research study and a purposeful sampling technique was used for the focus group interviews. All grade ten learners at Temple Valley Secondary School were selected as the sample. The results showed that the mathematics learners slightly outperformed the mathematical literacy learners in the development of mathematical proficiency for number skills. The findings from this research could inform: Teachers of grade ten learners with an interest in improving the mathematical proficiency, in number skills, of learners and; curriculum developers and materials development specialists who prepare mathematical material for grade ten classrooms. The results showed that none of the grade ten learners, from either cohort, were mathematically proficient in May or October. From the study, it was noted that the female grade ten learners generally outperformed their male counterparts. The focus group interviews revealed that learners had a positive attitude to the learning of the subject mathematics, despite the poor test results of this study.
An exploration of the use of selected concrete teaching and learning materials in developing mathematics proficiency in fractions in three grade 7 classes in the Pinetown District.
(2013) Nyathi, Welcome Siyabonga.; Hobden, Sally Diane.
This study was motivated by my concern about the poor performance of primary school learners in the area of fractions. Fraction concepts should be well established by Grade 7 but I had found that they were problematic and wished to deepen conceptual understanding by the use of concrete teaching and learning materials such as, Cuisenaire rods, number lines, fraction circles, fraction strips and beans. The key research questions were: Can selected concrete teaching and learning materials help in developing proficiency in fractions in Grade 7 learners? Which pedagogical practices and strategies are helpful in developing mathematics proficiency in fractions? The research methodology can be described as action research. A set of activities developed by the Rational Number Project (RNP) in 2006 was used to teach a two week programme on basic fraction concepts to three successive Grade 7 classes. After the first two completed two week cycles, the learner work was studied, input from colleagues was sought and then after reflection, the next cycle was begun, implementing the lessons learnt. The data corpus includes biographical details of each of the learners, their final Grade 7 Mathematics and English marks, achievement on a fractions test, the completed activities and focus group interview transcripts. The theoretical framework of the RNP is based on the idea of multi-representations and in particular the translation model proposed by Lesh, one of the project researchers. In this study, the notion of mathematical proficiency is also used to analyse the different aspects of learning demonstrated by the learners. It was found that the achievements of the third cohort of learners were higher in the final test thus indicating that perhaps the improved teaching had an effect. Analysis of the learner work indicates that while the learners can speak correctly about the fraction ideas, and even draw correct pictures, they struggle to use the mathematical symbols correctly.
Exploring Zimbabwean students' approaches to investigations in advanced level Chemistry.
(2017) Chirikure, Tamirirofa.; Hobden, Paul Anthony.; Hobden, Sally Diane.
Abstract available in PDF file.
Mathematical attitudes and achievement strategies of successful mathematics learners.
(2011) Naidoo, Indarani.; Hobden, Sally Diane.
Too often, discussions about Mathematics express feelings of anguish and despair; and, indeed Mathematics results in general in South Africa can be described as dismal. The Department of Education (DoE) reported that in the 2010 National Senior Certificate examinations, 52.6% of learners obtained less than 30% in Mathematics and 69.1% of learners obtained less than 40% (DoE, 2010). This implies that a very small percentage of grade 12 learners would be eligible to further their studies in the fields of Mathematics and science at tertiary level, resulting in a depletion of science and Mathematics-oriented professionals. This study explored the mathematical attitudes and achievement strategies of successful Mathematics learners to overcome the factors that might impede achievement. This study has the potential to improve practice because the findings of the study and recommendations are made implicit in the discussion. In particular this study sought to investigate the following issues: (a) What are secondary school learners' attitudes towards Mathematics? (b) In what ways are these attitudes linked to factors to which the learners attribute their achievement in Mathematics? (c) What strategies do successful Mathematics learners use to overcome the factors that they identify as impeding their performance in Mathematics? This research involved a case study approach. The study solicited both quantitative and qualitative data from the participants. The participants comprised 95 Grade 10, 11 and 12 Mathematics learners. The Fennema-Sherman Mathematics Attitude Scales (FSMAS) questionnaire was used to collect data from participants. The data was analysed using Attribution Theory and Achievement Theory. Two learners, who obtained more than 60% in the 2011 half-year Mathematics examination, from grades 10, 11 and 12 respectively, constituted the focus group. The focus group interview enhanced the study by clarifying the responses to the questionnaire and providing answers to the second and third research questions. The findings of the research include the following: teachers play an important role in shaping learners’ attitudes toward Mathematics; learners are anxious when asked to solve mathematical problems; parents are very encouraging of their children learning Mathematics; the importance of Mathematics for future careers exerted a significant effect on mathematical achievement; and finally the various strategies that learners employ that positively impact on their achievement in mathematics include mastery experience, motivation, private tuition and peer group teaching-learning. The final section of this dissertation discusses the implications of this study for practising Mathematics teachers and suggestions for further research in the area of affect.
Mathematics for future engineers : a study of teaching and learning mathematics in an engineering curriculum.
(2014) Moodley, Mogasuri.; Hobden, Sally Diane.
This is a study of teaching and learning in the first mathematics module for engineering students at a South African university. The theoretical framing of the study is derived from multiple analytical tools: Bernstein’s theory of the Pedagogic Device; the construct of beliefs and Bloom’s revised taxonomy. As such this study draws on Bernstein’s concepts of recontextualisation, singulars and regions and classification and framing to describe the three message systems (content, pedagogy and assessments). The beliefs framework identifies the teaching styles used by lecturers while Bloom’s revised taxonomy provides the analytical tool to evaluate the quality of the final examination questions. This study took a pragmatist stance which privileged a mixed methods approach to data collection. The first research question sought to determine the role of mathematics in engineering. To fully understand the role of mathematics in engineering, document analysis was used to analyse the international (Washington Accord) and national (ECSA) professional body documents and the institutional requirements and interviews were conducted with academic staff in the department of mathematics and the school of engineering. The literature showed that mathematics is a key component in engineering education and in engineering practice. It also foregrounded the ongoing debate about whether it is sufficient for engineers to know the practical application of mathematics or whether knowledge of mathematics in all its abstraction is required. The second and third research questions looked at how teaching and learning is approached and reasons why it is approached in those ways. Data were generated from the documents stated above, observation of lectures as well as tutorials and interviews with relevant academic staff and students. An analysis of the Washington Accord and ECSA documents fell within the Official Recontextualising Field and showed the influence of the external bodies on the recontextualisation of the ME curriculum. The textbook and head of school (MSC), constituted the Pedagogic Recontextualising Field (PRF), and were found to influence the framing over selection, sequencing, pacing and evaluative criteria. It was also established that there was further recontextualisation at the level of the classroom (by lecturers). In effect, the recontextualisation resulted in the exclusion of proofs and theoretical underpinning of the mathematics taught. The module showed strong classification of content on the interdisciplinary, intradisciplinary and interdiscursive level while framing over selection, sequencing, pacing and evaluative criteria were strong. The regionalization of the ME module resulted in it being a site of conflict and struggle over ownership of the pedagogic device. Despite differences in beliefs about mathematics, the teaching styles of lecturers were similar in that they demonstrated an algorithmic, assessment-oriented approach to teaching. The analysis revealed that lecturers viewed mathematics in terms of application and as a tool to solve engineering problems. Analysis of the final examination questions showed that it fell within the cognitive domain of Apply in Blooms’ revised taxonomy. A closer inspection of the final examination questions and those of the mock examination showed a close correlation between the two indicating that the conceptual demand was not as high as initially established. Despite the strong alignment between lectures, tutorials and assessments, many students were unsuccessful in passing the module. The thesis concludes with a discussion of the implications of the findings and suggests recommendations for the improvement of teaching and learning mathematics to future engineers and for further research.
Maths anxiety and communication apprehension as barriers to learning mathematics.
(2011) Moodley, Savathrie.; Hobden, Sally Diane.
As learners progress through the educational system their interest in mathematics diminishes. Although mathematics is designed to challenge learners, it has produced a high number of failures. Mathematics is most often measured by speed and accuracy of learners’ computation with little emphasis on problem solving and pattern finding. Whilst there are not many opportunities for learners to work on rich mathematical tasks that require divergent thinking as well. Such an approach limits the use of creativity in the classroom and reduces mathematics to a set of skills to master and rules to memorise. In doing so, causes many learners to become anxious and apprehensive. Thus their curiosity and enthusiasm for mathematics disappear, as they get older. Keeping learners interested and engaged in mathematics by recognising and valuing their mathematical creativity may reverse this negative tendency. 97 learners from Riverview High School took part in the study. Three different instruments were used to collect data: Mathematics Anxiety Scale (MAS), Personal Report of Communication Apprehension (PRCA-24) and a focus group interview. The MAS questionnaire was used to measure the level of mathematics anxiety experienced by the learners. The PRCA-24 questionnaire is a self-report measure of communication apprehension. The underlying factors were established that were influential in determining the levels of maths anxiety and communication apprehension in individual learners. The results of the study suggest that learner’ ability and attitude played an important role that would lead to the large failure rate in mathematics. Analysis and interpretation of the findings lead to the following conclusions being reached: (a) perceptions of mathematics as being a difficult subject (b) learners negative attitude in mathematics (c) fear for the subject, (d) learners self-efficacy beliefs in mathematics, (e) peer behaviour and (f) teacher behaviour. The research study findings suggest that learner’ ability and attitude played an important role. These attitudes contribute directly to the existence of maths anxiety and communication apprehension in learners which impacts on their academic performance. The results of the study suggest that learners experience varying levels of maths anxiety and communication apprehension that impacts on their performance in Mathematics, which are barriers to learning mathematics.
Perceptions of the notion of mathematical literacy as a competence and as a subject.
(2007) Madongo, Phineas Sponsor.; Hobden, Sally Diane.
Given the controversy surrounding the theoretical concept of mathematical literacy within mathematics education community around the world and, in particular, its introduction as a new subject of study in the South Africa’s FET curriculum as part of a social transformation process, it seemed necessary and appropriate that a study of this nature had to be undertaken. Thus the study explored perceptions of the notion of ‘mathematical literacy’ as a competence and as a subject of study. It focused on a group of first-year in-service teachers who were part-time students in the faculty of education at Edgewood Campus in the University of KwaZulu-Natal, as well as the documentary analysis of some of the South African curriculum policy documents. The guiding research questions for this study were: (a) what understandings or notions of mathematical literacy are evident in the South African curriculum documents? (b) What are mathematics educators’ perceptions of the competencies of a mathematically literate person? (c) What are their perceptions of, beliefs and views, and initial experiences about mathematical literacy as a subject of study? (d) How do these perceptions and/or understandings play out in the implementation of the new Mathematical Literacy curriculum? In an attempt to answer these questions, I began by, first, exploring the wider theoretical perspectives (both locally and internationally) in extant literature within the domain of mathematics education, and which underpins the debate about mathematical literacy and its related terms as well as informing the recent curriculum change, particularly in South Africa. In the process I discussed the different connotations that were used to describe mathematical literacy and its related terms, as well as the arguments in favour of and against its introduction as a subject of study. Secondly, I explored teachers’ understandings of the concept of mathematical literacy both as a competence and as a subject of study in relation to the NCS documents, as well as the problems associated with its implementation and the importance of understanding the interplay between content and context used for its development. It is argued, however, that re-framing of ‘mathematical literacy’ as a subject of study rather than a competence proves to be problematic in terms of the distinction that could be drawn between epistemology and pedagogy. Finally I have discussed the implications which the findings of this study have for policy and practice, and for further research. Data on the understandings and teachers’ perceptions about mathematical literacy as a competence and a subject of study were obtained using both qualitative and quantitative styles of research as a mixed-mode approach. The major findings of this study are that (1) teachers generally perceived mathematical literacy as a subject of study (2) the South African curriculum documents portray ML as a subject, and therefore framed as such; (3) teachers generally consider a person mathematically literate if that person could do basic arithmetical calculations in everyday life (4) from the international perspective, there are variations on the interpretation of ML, and finally (5) the study has revealed that teachers had difficulties pertaining to their own pedagogical content knowledge of the new subject. Based on these findings it can be concluded that there is need for a sustained monitoring of the implementation process, reviewing of policy documents, and professional development of teachers involved with the teaching of mathematical literacy.
Readiness of learners to study space, shape and measurement in mathematical literacy : case studies at two Durban schools.
(2006) Pillay, Krubagaran Subramoney.; Hobden, Sally Diane.
This dissertation reports case studies conducted at two secondary schools in Durban. With the introduction of the Further Education and Training (FET) curriculum in 2006, learners who terminate their study of Mathematics at the end of grade nine will have to study Mathematical Literacy, an applications-based mathematics course. In South Africa the Mathematics results at the grade twelve exit examination are generally poor and learners are known to underachieve in the field of geometry. This study was aimed at determining the readiness of learners in studying geometry under the Learning Outcome, Space, Shape and Measurement in the Mathematical Literacy curriculum. Questionnaires were administered to grade nine learners who had elected not to study, or were excluded from studying, Mathematics from grade ten onwards. Data was sought to determine what factors influence the decision to discontinue mathematics, and to gauge attitudes to the study of mathematics. Learners were given a test to measure geometry skills and knowledge that they ought to have acquired by the end of the senior phase in geometry. Data was also obtained from focus group interviews with both of learners and educators. This study indicates that learners do not continue mathematics because of the difficulties they experience. Furthermore they do not have the requisite skills and knowledge in Space, Shape and Measurement to cope with the Mathematical Literacy curriculum. Nevertheless, the attitudes of learners to the study of this new subject are positive. It is suggested that educators need to conduct baseline assessments to determine learners' abilities so as to plan appropriate revision measures before continuing with the teaching of Mathematical Literacy.
Towards successful mathematical literacy learning - a study of preservice teacher education module.
(2007) Hobden, Sally Diane.; Mitchell, Claudia Arlene.; North, Delia Elizabeth.
The purpose of this study was to extend our knowledge about mathematical literacy learning with the focus on a foundational preservice teacher education module required for prospective teachers. The construct of mathematical proficiency provided a framework for understanding how successful learning depends on a multiplicity of competences, and in particular to highlight the pivotal role of a productive disposition towards mathematics in becoming mathematically literate. The main questions that guided the study were as follows: What is the nature and strength of the productive disposition strand of mathematical proficiency evident in preservice teachers entering a Mathematical Literacy module and how does this productive disposition change over the course of the module? and What pedagogical practices and learning behaviours best enable preservice teachers to achieve mathematical literacy? The study was undertaken as two overlapping case studies, the first describing the preservice teachers at the onset of their studies in the Mathematical Literacy for Educators module, and in the second, a three part story-telling case study of the unfolding of the module over three years from 2003 to 2005. The mathematics autobiographies of 254 preservice teachers and the data obtained from a premodule questionnaire and introductory class activities contributed to the first case study which was summarised in the form of three fictional letters. Written reflections, final module evaluations and the insights of my co-workers contributed to the second case study which documented the successes and struggles of the preservice teachers as the module unfolded each year. Complementary mixed methods techniques were used to analyse the multiple sources of data and to weave strong ropes of evidence to support the findings. Statistical analysis pointed to themes which were supported or tempered by qualitative evidence reported in the voices of the preservice teachers themselves. The analysis revealed that many of the preservice teachers entering the Mathematical Literacy for Educators module had found their school experience of mathematics to be dispiriting and consequently had developed negative dispositions towards the subject. The change in this disposition depended on their success in the module and the empathy shown by the lecturer. Helpful pedagogical practices were found to be those that supported language difficulties in learning mathematics, assisted in organising learning, remediated for poor schooling background in mathematics and took account of the diversity amongst the students. I argue that many of the lessons learned and insights gained from teaching the Mathematical Literacy for Educators module are relevant to the expanding number of mathematics courses required as part of humanities programmes. In addition, they can inform practices at school level and in both in mathematics and mathematical literacy teacher education.