Student performance on the recently implemented Provincial Mathematics 10 examination concerns mathematics teachers. Using results from the Foundation Skills Assessment (FSA) to implement a strategy for students' improvement as well as properly placing students into the correct curriculum pathway may be an effective way for improving student success. Students who participated in the 2001/2002 FSA may have also participated in the 2004/2005 provincial mathematics 10 examination. Using regression analysis, three separate models were created for students writing the Principles of Mathematics 10 examination (n = 27 292, R2 = 0.320), Essentials of Mathematics 10 examination (n = 5 052, R2 = 0.169), and Applications of Mathematics 10 examination (n = 2 662. R2 = 0.231). The independent variables included Item Response Theory Scaled scores for the Numeracy and Reading Subtests of the FSA, gender, aboriginal status, English as a second language status, and school size. As well, hierarchical linear model (HLM) was implemented as an exploration to compare the coefficients with the regression analysis. In all three cases the coefficients of the HLM were similar to the linear regression. Disciminant analysis also predicted student placement in the three pathways at 61% accuracy using FSA results and other independent variables.

"2006" / Thesis (PhD)--Macquarie University, Australian Centre for Educational Studies, Institute of Higher Education Research and Development, 2007. / Bibliography: p. 167-173. / Introduction -- Experience and expression -- Becoming a professional -- Study design -- Graduates' experiences: a narrative -- Reflections on communication -- Examples of texts -- Reflections on learning and teaching -- Reflections and implications. / The aim of this study is to inform curriculum change in the mathematical sciences at university level. This study examines the transition to professional work after gaining a degree in the mathematical sciences. Communication is used as the basis for the analysis of the transition because of the importance of language choices in work situations. These experiences form part of the capabilities that become part of a person's potential to work as a professional. I found a subtle form of power and, of the opposite, lack of power due to communication skills. It is not as obvious as in, say, politics but it is just as critical to graduates and to the mathematical sciences. -- There were 18 participants in the study who were graduates within five years of graduation with majors in the mathematical sciences. In-depth interviews were analysed using phenomenography and examples of text from the workplace were analysed using discourse analysis. Descriptions of the process of gaining employment and the use of mathematical discourse have been reported in the thesis using narrative style with extensive quotes from the participants. -- The research shows that graduates had three qualitatively different conceptions of mathematical discourse when communicating with a non-mathematical audience: jargon, concepts/thinking and strength. All participants modified their use of technical terms when communicating with non-mathematicians. Those who held the jargon conception tried to simplify the language in order to explain the mathematics to their audience. Those who held the concepts/thinking conception believed that the way of thinking or the ideas were too difficult to communicate and instead their intention with mathematical discourse was to inspire or sell their ability to work with the mathematics. The strength conception considers the ethical responsibility to communicate the consequences of mathematical decisions. Not one of the participants believed that they had been taught communication skills as part of their degree. -- Participants gained a 'mathematical identity' from their studies and acquiring a degree gave them confidence and a range of problem-solving skills. Recommendations are made about changes in university curriculum to ensure that graduates are empowered to make a high-quality transition to the workplace and be in a position to use their mathematical skills. Mathematical skills are necessary but not sufficient for a successful transition to the workplace. Without the ability to communicate, graduates are unable to release the strength of their knowledge. / Mode of access: World Wide Web. / xi, 195 p. ill

Through a qualitative case study approach this research investigated the nature of three Grade 4 learners’ mathematical learning dispositions. It further explored how these dispositions evolve within the context of their participation in a weekly after school mathematics club over time. Of particular significance the research drew on the dispositional frameworks of Kilpatrick, Swafford and Findell’s (2001) and Carr & Claxton (2002) and pointed to ways in which these framework can be usefully brought together to provide a richer picture of learning dispositions. Kilpatrick, Swafford and Findell’s (2001) framework of mathematical proficiency involves five interrelated strands of which productive disposition is the fifth strand and largely underresearched (Graven, 2012). This strand is defined as ‘the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (Kilpatrick, Swafford and Findell, 2001, p. 131). Carr & Claxton (2002) similarly argue for the importance of learning dispositions and point to the importance of resilience, playfulness and resourcefulness as three key indicators. The research outlines findings of the three case study learners in terms of data obtained from a questionnaire and interview about students’ learning dispositions. The interview asked learners various questions including for example, complete the sentence ‘Maths is…’, describe an effective learner of mathematics and say what you do if you don’t know an answer. The instrument was first administered orally and learners were asked to write their answers (in May 2012) and a year later it was administered as an interview by the club facilitator (in May 2013). While there is the limitation of comparison due to the different ways in which learners responded in 2012 (written) and 2013 (oral) the shifting nature of responses in certain respects provides some indication of shifts towards increasingly productive dispositions. Additionally the research analysed detailed transcripts of video recordings of several club sessions over a five-month period. Findings suggest ways of extending dispositional frameworks and that learners have restricted dispositions particularly in terms of sense making and resourcefulness across time. The findings also suggest shifts in dispositions over time especially in terms of seeing steady effort as paying off.

From Introduction: As the headmaster of a large co-educational High School in East London, I have to counsel Standard 7 pupils at the end of each year with regard to their subject choices for the Senior Secondary phase. In consultation with the teacher-psychologists and the Standard 7 teachers, one has to make decisions with regard to subjects which could have far-reaching effects on the pupil. Year after year the greatest discussion and most difficult decisions concern whether or not to continue with mathematics. At the end of the Standard 7 year, the pupil is faced with a choice of subjects, one of which is usually mathematics. Depending on the school, this choice is often wide and the average Standard 7 pupil can, in spite of careful counselling and advice, still be bewildered and confused. One of the best methods of objectively predicting pupil performance is through the use of various standardised tests. Although some norm-based tests exist, very few schools apply these tests to help predict mathematics performance in the Senior Secondary Course. To aid the pupil in deciding whether or not mathematics should be taken in Standards 8, 9 and 10 it would be extremely useful if there were some guide or predictor on which this decision could be based, as it is generally accepted amongst teachers that mathematics can be a stumbling block in the Cape Senior Certificate, particularly by the weaker candidate. If it could be shown that the Standard 7 year-end mathematics mark could be used to help predict whether :- •the pupil would be likely to pass or fail mathematics in the Cape Senior Certificate; •what symbol the pupil would obtain; a decision as to whether or not he should continue with the subject could be made at this stage, and, depending on his Standard 7 mark, what the likely consequences of this decision would be. In the United Kingdom in particular, the use of A-level examination results have been used as predictors in subsequent educational courses and this has been the subject of fairly extensive research during the 1970's. The extent to which O-level examination results are predictive of A-level achievement has, however, received very little attention. The situation in South Africa is very similar and very little, if any, work has been done in assessing the effectiveness of using school marks in the lower standards of high school to predict marks in the upper standards. It is difficult to suggest a reason for this as such work would be of inestimable value in providing information for use in the counselling and selection of subjects for pupils embarking on the Senior Secondary Course.

This study reports on an investigation into the manner in which mathematical symbols influence learners’ understanding of mathematical concepts. The study was conducted in Greater Sekhukhune and Capricorn districts of Limpopo Province, South Africa. Multistage sampling (for the district), simple random sampling (for the schools), purposive sampling (for the teachers) and stratified random sampling with proportional allocation (for the learners) were used. The study was conducted in six schools randomly selected from rural, semi-urban and urban settings. A sample of 565 FET learners and 15 FET band mathematics teachers participated in the study. This study is guided by four interrelated constructivist theories: symbol sense, algebraic insight, APOS and procept theories. The research instruments for the study consist of questionnaires and interviews. A mixed method approach that was predominantly qualitative was employed. An analysis of learners’ difficulties with mathematical symbols produced three (3) clusters. The main cluster consists of 236 (41.6%) learners who indicate that they experience severe challenges with mathematical symbols compared to 108 (19.1%) learners who indicated that they could confidently handle and manipulate mathematical symbols with understanding. Six (6) categories of challenges with mathematical symbols emerged from learners’ encounters with mathematical symbols: reading mathematical text and symbols, prior knowledge, time allocated for mathematical classes and activities, lack of symbol sense and problem contexts and pedagogical approaches to mathematical symbolisation. Two sets of theme classes related to learners’ difficulties with mathematical symbols and instructional strategies emerged. Learners lack symbol sense for mathematical concepts and algebraic insight for problem solving. Learners stick to procedurally driven symbols at the expense of conceptual and contextual understanding. From a pedagogical perspective teachers indicated that they face the following difficulties when teaching: the challenge of introducing unfamiliar notation in a new topic; reading, writing and verbalising symbols; signifier and signified connections; and teaching both symbolisation and conceptual understanding simultaneously. The study recommends teachers to use strategies such as informed choice of subject matter and a pedagogical approach in which concepts are understood before they are symbolised. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education)

M.Ed. (Subject Didactics) / It is important that allowances be made for the Mathematics gifted pupil, who is seen as the problem solver of the future. Mathematics gifted pupils, on the average, use half their time to work thoroughly through the average syllabus and achieve 90% plus. The average subject teacher does not always have the necessary time for the gifted pupil. He is thus left to his own devices. The lack of facilities, sufficient qualified teachers, support from like-minded people, stimulating opportunities, resource centres and other stimulating factors add further to the pupils' frustrations. Enrichment of syllabi is seen as one of the most prominent provisional possibilities for the gifted child. The reason for this is found in the fact that the gifted child does not constitute even 5% of the population. They are kept mainly in the mainstream and are in no way identified as a group for any type of special educational need, like acceleration. Enrichment by means of educational computer programmes does not need individual teaching or a faster pace, but an adjustment in the activities within the classroom. Teaching, with the aid of computers, offers an educational aid which offers the opportunity for more effective provision for the gifted child ...

Matriculation pass rates in South Africa, especially in Mathematics, have been poor. The literature and personal experience suggests that a problem with homework may be a factor in this. In order to discover how Port Elizabeth learners from ex-DET schools perceived and experienced Mathematics homework, and the nature of such homework, ten case studies of Grade 11 learners were done. While conducting and analyzing the case studies, a pattern emerged from the findings, which together with some new questions, needed to be explored on a larger sample population. In order to do this and to be able to generalize the findings, four follow-up studies in the form of surveys on Mathematics homework were conducted at nine schools. These studies involved a learner questionnaire, a teacher questionnaire, the timing of learners as they did set Mathematical problems and the analysis of common errors made by the learners while doing the problems. The findings revealed that learners received too little homework too infrequently and did it inefficiently and ineffectively. The learners worked too slowly, did not complete the homework, left out the difficult problems and made numerous unnecessary mistakes. However, most of the learners claimed to have enough time available to do their homework and spent approximately one hour on Mathematics homework when it had been assigned. Many of the misconceptions and the resultant errors originated from work that should have been well covered in previous grades. However, parts of the syllabi were omitted in previous grades and completion of the syllabus and homework was only seriously considered in Grade 12. Some implications of the findings for educational practice and further research are discussed.

This thesis describes an intervention using the Mathematics Recovery programme in a South African context with a small sample of Grade 4 learners. The study uses a qualitative case study approach. The data collection included video recorded one-to-one oral interviews with the learners. I used the Learning Framework in Number (LFIN) developed by Wright, Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention interview data and to determine their levels of multiplicative reasoning. The analysis showed the positive impact of the Mathematics Recovery programme on the improvement of multiplicative reasoning. The study contributes to the use of Mathematics Recovery programmes in South Africa from both a teacher and teacher educator perspective.

This research report focuses on an investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms in the Grahamstown region, South Africa. Boredom seems to be strongly evident in our classrooms. Quantitative data was derived from an initial survey questionnaire while semi-structured interviews were used to elicit qualitative data. The data from the survey was analysed quantitatively using descriptive statistics. The quantitative data was categorised according to the structure of the survey. The data was represented in bar graphs and then discussed accordingly. In the final narrative I infused extracts from the interviews with my quantitative analysis. The qualitative data was analysed and coded according to different categories and themes that emerged through repeated engagement with the interview transcripts. The findings revealed that boredom is a common problem in the 8 Grade 10 Mathematics schools in the Grahamstown region and this finding answered my first research question. To answer my second research question, the results showed that learners were bored due to many factors, such as; lack of understanding, repetition and the teacher’s actions and many more. My findings align with what is highlighted by Nett, Goetz, & Hall. (2011) that many learners from particularly the senior secondary schools frequently report episodes of boredom. The study recommends that teachers make their teaching more interesting, much use of concrete teaching materials and make mathematics tasks to be relevant and real.

My involvement with mathematics education amongst township educators and learners over the past seven years has highlighted the absence of sustained meaning and meaning making of mathematical concepts. It appears though that this instrumental rather than relational understanding of FET mathematics is not unique to township learners but is encountered amongst learners of all socio-economic classes and is representative of many FET mathematics learners. Given that the language of learning and teaching is a major contributory factor in the South African education system, it appears that the language of mathematics itself is a greater exacerbating factor for many learners of mathematics. The exclusive algorithmic approach to classroom mathematics further seems to alienate many learners from the essence of the meaning of mathematical tasks. This research undertakes to determine whether metateaching and metalearning as forerunners to metacognition facilitates the acquisition of the sustained meaning of mathematical concepts. Metateaching and metalearning refer to the acute and deliberate awareness by educator and learner as to what constitutes concepts. Teaching and learning therefore presupposes the deconstruction of concepts into its subsumed derivative roots. It also assumes an awareness of the tacit degrees of abstraction that characterise tasks and the content of tasks. This in turn has implications for the educator's adopted sequence of topics for instruction. Metacognition implies awareness on the part of the learner (and educator) as to how material is learned and a further awareness as to how that learning can be sustained. Whether we ascribe meaningful learning to radical or social constructivism, or to associationist didactive approaches, or a combination of these, we are making assumptions about how learners acquire and sustain mathematical meaning because mathematics is, by and large a symbolic language often devoid of affective connotation. Furthermore our assessments of learners' tasks amount to clinical corrections of austere formulae wrapped in algorithmic procedures which manifest nothing of a learner's experience of mathematics or the deeper understanding (or misunderstandings) which characterise a learning and/or assessment episode. To this end the research design of this interpretive case study requires learners to expound in textual accounts their thoughts as they describe the evolution of a mathematical process as they approach a solution and eventually interpret it. The textual account exposes the concept definition for what it really is in a learner's understanding of it and it is the expressiveness of language that indicates whether the understanding of a learner is approaching the concept image. The textual accounts vary in richness in terms of mathematical register and this in turn reflects the conceptual depth. The mechanism which seems to promote the conversion from concept definition to concept image is the graphical representation of the mathematical task or procedure, possibly because of its greater concreteness as opposed to the abstraction of its algebraic form.