This study aimed at investigating the methods used by teachers to assist the acquisition of numeracy skills by Standard 10 Geography learners. The problem of high failure rate in these skills was considered in terms of Perkins' (1992) minimum conditions for learning which, according to him, could assist and improve learner performance. These are : clear information, thoughtful practice, informative feedback and strong motivation. This investigation also draws upon Gallimore and Tharp' s (1991) means of assisting performance in the zone of proximal development, which include modeling, contingency management, feeding back, instructing, questioning and cognitive structuring. Data was collected by means of a number of lesson observations in three senior secondary schools in the Eastern Cape Province. This data was analysed in terms of whether or not teachers included Perkins' (1992) minimum conditions for learning in their methods of teaching and whether or not teachers used Gallimore and Tharp's (1991) means of assisting performance in their teaching activities.The overall result of the investigation indicated the overuse of the lecture method and the "recitation script" which denied learners opportunities to participate actively in the lesson. This research indicated, therefore, that the methods used by teachers in teaching Geography numeracy skills did not contribute towards the improvement of the learners' performance. A number of suggestions are made regarding initial and in-service teacher education and the encouragement of research by teachers into their own professional practice. / Thesis (M.Ed.)-University of Natal, Pietermartizbrug, 1998.

Numeracy skills are vital for a child with diabetes as they need to be able to manage their diabetes effectively, in order to protect one from the complications that come with diabetes. There have been numerous studies that illustrate the poor numeracy skills in children with diabetes. A numeracy intervention specifically related to diabetes was put into place to illustrate whether or not such an intervention is effective in improving a child’s diabetic numeracy ability, which will lead to the improvement of diabetes self-management in the future. A Quantitative quasi-experimental pre-test - post-test non equivalent control group design was conducted to explore the efficacy of an applied numeracy intervention in a South Africa type 1 diabetic child population. The study group comprised of 58 children with type 1 diabetes, each group consisted of 29 participants, and each participant in the experimental group was closely matched according to their level of formal education, grade, age and sex to a research participant in the control group. Both groups were measured before and after the intervention. The children were between the ages of 8 and 13. All participants were in formal education between Grades 3 and Grade 8. Results revealed that participants in both groups had lower ‘functional’ grades as compared to their ‘actual grade’ level which suggests that they performed below their expected grade level. Participants performed better in areas assessing basic mathematical skills than areas which assessed applied diabetes mathematical skills. The intervention was shown to be effective as analyses revealed that there was a highly significant difference (p<0.001) between the Pre and Post Test (applied mathematical sections) of the experimental group which took part in the intervention. This research is only the starting point for the assessment of the effectiveness of a numeracy component in diabetes related education in South Africa, and through this one would hope that more research in South Africa will be done in this area.

Quantitative literacy, or numeracy, has been discussed as an essential component of mathematics instruction. In recent years community colleges around the nation introduced a quantitative literacy alternative to the developmental algebra curriculum for students placed into remedial mathematics. The QL curriculum consists of problem situations that are meant to improve numeracy through a combination of collaborative work and a student-centered pedagogy. There is little research that investigates the enactment of that curriculum. Research in K-12 indicates that teachers’ beliefs influence the enactment of curriculum, but studies that connect instructional practices and faculty beliefs are scarce. This study employs a multiple qualitative case study approach to investigate the alignment between four community college instructors’ beliefs about teaching, learning, the nature of mathematics, and curriculum on their enacted practices in two different developmental mathematics courses at a large urban community college (UCC). One is a standard developmental algebra curriculum and the other curriculum is based on quantitative literacy. Data were collected through semi-structured interviews, classroom observations and field notes. The results indicate an alignment between the professed beliefs and enacted practices for all but one instructor in this study. The findings imply that curriculum plays a significant role when its intended design correlates with instructors’ belief systems. The study also discusses the differences in instructional practices across the quantitative literacy and elementary algebra curricula taught by the instructors in this study.

This thesis replicates and explores some of the recent findings by Robert Siegler regarding the development ofaddition skills in grade one children. Siegler states that children employ a number ofdifferent strategies to solve single digit addition problems, these strategies coexist and compete, and cognitive variability is an essential aspect of cognitive development. He also advocates the use ofthe microgenetic approach in order to explore cognitive development. Many of Siegler' s observations were replicated while the microgenetic approach produced valuable information. Consideration of Siegler's work resulted in two research questions being formulated, both concerning the actual selection of strategies. First, a prediction analysis was employed to test the hypothesis that children attempt to match the most appropriate strategy to the problem presented according to a principle ofleast effort (defined as the attempt to maximise benefit and minimise cost). The predictions were stipulated prior to the analysis and were based on the arithmetic development literature. It was predicted that children would tend to retrieve the answers to small problems and tie-problems or calculate the answer by counting on from the larger addend by the amount indicated by the small addend (which involves reversing the order of the addends when the first addend is the smaller of the two). The strategy selections (n=229) made by a sample of 12 grade one learners on 21 single digit addition problems were categorised and compared to the predictions. The prediction analysis reduced the expected error by 63%, supporting the least effort model of strategy choice. The result is statistically significant (2=10.231, p / Thesis (M.A.)-University of Natal, Pietermaritzburg, 2000.

This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.

The purpose of this study was to determine whether gifted pupils can master an enriched advanced level curriculum in mathematics using self-regulated learning strategies. A mathematics curriculum for class five primary school learners in Nigeria was developed for this study. An empirical study was conducted on primary five pupils who were seen to be significantly gifted in mathematics. The study employed the quantitative method of research, that is, the true experimental research. The pre-test, post-test control group design was used. Sixty gifted pupils who participated in a mathematics enrichment programme (MEP) were assigned into two groups of the control group and experimental group with thirty pupils forming each group. The control group was exposed to direct teaching (DT) while the experimental group used self-regulated learning (SRL) strategies. Four teachers served as facilitators in the MEP. The teaching and learning activities were carried out at a higher cognitive level as opposed to the regular curriculum, ensuring that the contents of the MEP were enriched and accelerated. Pupils in both the experimental group and the control group were administered a pre-test, problem-solving exercises, and post-test. These pupils also completed an attitudinal questionnaire to provide feedback about the MEP. The empirical results show that gifted pupils in primary five are capable of self-regulating their own learning through self-monitoring, self-evaluation, and self-reinforcement. The empirical results also show that there is a significant relationship between self-regulated learning, gifted learners, and an enriched advanced level differentiated curriculum as a realistic alternative to the present regular curriculum for gifted pupils in the mainstream of education. The findings further show that the lack of differentiation of instruction, lack of facilities such as libraries, media centres, and support materials contributes to low achievement of gifted pupils. Furthermore, the findings show that pupils were challenged and motivated with the MEP to the extent that they were engaged to think divergently and applied their metacognitive skills in finding solutions to mathematical problems. Therefore, the findings of this study could have significant implications for the future direction of gifted primary school education as well as teacher education. This study has made a significant contribution to the existing body of knowledge for implementing an enriched advanced level curriculum using SRL strategies for mathematically gifted pupils in the mainstream of primary school education.

M. Tech. Education / The intention of this study was to establish the use of the Annual National Assessment (ANA) results in improving learner performance in schools and to further establish the understanding and interpretation of the national assessment policy at school level and at circuit/district level in General Education and Training (GET) settings of Casteel schools, Bohlabela district. The literature supported the fact that available ANA results have identified certain challenges which require specific interventions to improve current skills in Literacy and Numeracy. Despite these concerns and the fact that the results do not achieve the set target of ensuring that 60 percent of learners achieve a pass mark of 50 percent, the results of the study indicated that the primary teachers, principals and circuit/district officials remained generally positive in their perception of turning the situation around.

Thesis (MEd)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This study explored the number sense of 47 final year primary school pre-service teachers in Namibia and was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests. The literature review revealed that learner performance is linked to teacher subject knowledge (Ball, 1990, Ma, 1999) and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics (Ball, 1990; Graven 2004). Number sense studies of pre-service teachers (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) have indicated that the development of number sense should be a focus of primary pre-service teacher education. The data in this mixed method research design were obtained from a Number Sense Questionnaire, a Written Computations Questionnaire and a Mental Calculations Questionnaire. These questionnaires were adapted from instruments developed by Professor Der-Ching Yang for 6th and 8th grade learners in Taiwan. Teacher confidence was measured by the McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Six randomly selected pre-service teachers were interviewed to determine their use of number-sensible strategies. The correlation analysis shows a strong relationship between number sense and mental calculations; between number sense and confidence in both the ability to do and the ability to teach mathematics and between mental and written calculations. The overall results of this study reveal that the final year primary pre-service teachers demonstrate limited number sense and possess very few of the indicators of number sense that were described by Kalchman, Moss and Case (2001). The findings expose a lack of conceptual understanding of the domain numbers and operations, particularly in the domain of rational numbers and the operations of multiplication and division. The pre-service teachers have little or no access to a variety of flexible number-sensible strategies to solve problems and calculate mentally. They lack the fluency in basic facts and procedures to perform written calculations efficiently and correctly. Unexpectedly, the analysis of the confidence survey shows that they are confident in both their ability to do mathematics and their ability to teach mathematics. It is recommended that mental calculations and computational estimation should become a focus of primary school mathematics education. Institutions responsible for teacher training should develop the number sense of pre-service teachers and research effective and long-term professional development programmes. The confidence and willingness of the teachers to learn can be used as an important resource. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die getalbegrip van 47 finale jaar primêre skool voordiens-onderwysers in Namibië en is gemotiveer deur die swak prestasie van die Namibiese primêre skool leerlinge in beide nasionale en internasionale gestandaardiseerde assesseringstoetse. Die literatuurstudie het aan die lig gebring dat leerlinge se prestasie gekoppel is aan onderwyservakkennis (Ball, 1990, Ma, 1999) en dat onderwysers se vertroue in hulle vermoë om wiskunde te doen en te onderrig, die manier waarop hulle onderrig en hul bereidwilligheid om wiskunde te leer beïnvloed (Ball, 1990, Graven 2004 ). Studies van voordiens primêre onderwysers se getalbegrip (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) toon dat die ontwikkeling van getalbegrip 'n fokus van primêre voordiensonderwyseropleiding behoort te wees. Die data in hierdie gemengde metode navorsing is verkry uit 'n Getalbegrip, 'n Skriftelike Berekeninge en 'n Hoofrekene Vraelys. Hierdie vraelyste is gebaseer op die instrumente wat ontwikkel is deur Professor Der-Ching Yang vir graad 6 en 8 leerlinge in Taiwan. Onderwyservertroue is gemeet deur die McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Ses ewekansig geselekteerde voordiens-onderwysers is ondervra om te bepaal watter sinvolle strategieë hulle gebruik om vrae oor getalbegrip te beantwoord. Die korrelasie-analise toon 'n sterk verband tussen getalbegrip en hoofrekene; tussen getalbegrip en vertroue in die vermoë om wiskunde te doen en te leer, en tussen vermoë om hoofrekene en skriftelike bewerkinge te doen. Die algehele resultate van hierdie studie dui daarop dat die finale jaar primêre voordiens-onderwysers oor beperkte getalbegrip en baie min van die aanwysers van getalbegrip wat deur Kalchman, Moss en Case (2001) beskryf is, beskik. Die bevindinge toon ‘n gebrek aan begrip van die domein van getalle en bewerkings, veral in die domein van rasionale getalle en die bewerkings vermenigvuldiging en deling. Die voordiens-onderwysers beskik oor min of geen soepel strategieë om probleme op te los en hoofrekene te doen nie. Hulle beskik nie oor die vlotheit in basiese feite en bewerkings om skriftelike berekeninge doeltreffend en korrek uit te voer nie. Die vertroue wat voordiens-onderwysers uitgespreek het in hulle vermoë om wiskunde te doen en onderrig staan in sterk teenstelling met hierdie bevindige. Dit word aanbeveel dat hoofrekene en skatting 'n fokus van primêre skool wiskunde-onderwys behoort te wees. Instansies gemoeid met onderwyseropleiding behoort die getalbegrip van voordiensonderwysers te onwikkel en navorsing te doen oor effektiewe en lang-termyn programme vir professionele ontwikkeling. Onderwysers se vertroue en bereidwilligheid om te leer kan as 'n belangrike hulpbron gebruik word.

National and international assessment results, research studies and reports point to South Africa as having educational challenges, specifically with mathematics, science and language. Addressing some of these issues is a key aim for the SANC project at Rhodes University, the context in which this study takes place. Working from a broad Vygotskian perspective of learning and development, this study had a dual focus and investigated how Grade 3 learners’ mathematical proficiency progressed (or not) whilst participating in after school maths clubs over the course of a year, and explored how the mediation offered in the clubs enabled or constrained the emergence of zones of proximal development (ZPD) and thus learning for the club learners. Methodologically, this study works within a largely qualitative, interpretive research paradigm and is designed using a longitudinal case study research strategy. Two after school maths clubs formed the empirical field. The study drew on a range of data collection methods to investigate the dual nature of the research questions for Grade 3 learners. Examples include adapted one-to-one mathematical proficiency interviews and paired task based interviews. The study highlighted the relationship between the multiple roles I played both within the research study and within the SANC project context and emphasises the influence and future implications for these various roles within the SANC project and beyond in terms of my own role as club mentor, for the future design of the SANC project maths club programme and for broader teacher and club facilitator development within and beyond the project. This study has offered insight into how mathematical proficiency may develop in Grade 3 South African learners and as such is an important contribution to the newly developing field of both numeracy and primary educational research in Southern Africa. Additionally, the research findings point to the clubs, as an example of an out-of-school time (OST) programme, providing potentially enabling spaces for both recovery and extension of mathematical proficiency in learners as these spaces are free from several contextual constraints that teachers face in their classrooms. Furthermore, it was found that learners showed development of their conceptual understanding, procedural fluency and adaptive reasoning as proposed by Kilpatrick, Swafford and Findell (2001). The use of various elements of the Maths Recovery (MR) programme (Wright, 2003) in the research process has highlighted various important contributions for broader research. For example, the need to investigate less time consuming approaches to both diagnostic assessment and learner mathematical profiling. Findings from this study support Meira and Lerman’s (2001, 2009) recently developed notion that catching attention is key to the creation or emergence of a ZPD. The study found that a combination of ‘attention catching’ and ‘tuning in’ enabled the creation (emergence) and sustainment of ZPDs in club learners. The study proposed the notion of tuning in where participants in a mathematical interaction continually adjust to each other in order to communicate mathematically. Furthermore, the study found that when attention is not caught or the participants are not tuned in, the learning activity may still be useful in assisting learners to consolidate their existing learning and / or build confidence and as such is particularly relevant to the South African context where fluency in calculating is weak (Hoadley, 2012; Schollar, 2008). This emergent notion of ‘flow’ additionally can play a supporting role in the emergence of a ZPD. The study also found that the manner in which the mediation was offered is important. The results show that the mathematical contributions learners make during interactions captured the mentors’ attention and resulted in mediation that was intentional but spontaneous, flexible, responsive and in-the-moment. This study makes theoretical and methodological contributions to various aspects of mathematics education research particularly with regard to how ZPDs emerge and are sustained and how mediation is offered to facilitate the emergence of ZPDs. Additionally, some aspects of the Learning Framework in Number (LFIN) as part of the Maths Recovery programme have been extended to work in a South African after school club context and to provide useful information for both learner progression over time and for planning of club activities. As such this study thus also contributes to the newly developing field of primary mathematics research in South Africa and to the body of research on primary after school learning programmes both locally and internationally.

Thesis (MEd) -- University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Learning and the development of numeracy in the foundation phase are regarded as highly important. In this critical period learners attain the fundamental knowledge that is needed for future learning and development. A serious problem within South African schools is that a great number of foundation phase learners show difficulties in numeracy. Various reasons can be provided for these difficulties, for example, learners do not receive good teaching, they hold negative attitudes towards numeracy, they encounter language barriers, and so forth. It is important that the learners’ difficulties in numeracy are attended to immediately and effectively, to be able to minimise the gaps between the learners’ functioning level and the level the learner is suppose to be on. The Western Cape Education Department (WCED) laid bare their concern with the current problem in numeracy when they launched the WCED Literacy and Numeracy Strategy 2006-2016. As part of this the Metropole North Education and Management Development Centre (EMDC) requested and implemented an intervention programme for grade 2 and grade 3 learners. Part of this problem is that many foundation phase educators lack the necessary knowledge to identify the learners with difficulties and especially to attend to these difficulties. The goal of this research study was to investigate the realization of an early intervention programme implemented over a limited period of time of ten weeks in grade 2 and grade 3 classrooms. The current study aimed at providing educators with resources to offer learning support to their disadvantaged learners within the Numeracy classroom. This study has implications for the way in which educators approach and teach numeracy, as well as for the type of learning support the educators provide their disadvantaged learners with. The intervention programme is based on a problem centered approach with constructivism as underlying epistemology. This approach views the educator as a facilitator who provides the learners with opportunities to be actively involved in the learning environment to construct knowledge. The importance of word problems and discussion within the Numeracy classroom are emphasized and it is necessary that the educator create the appropriate classroom atmosphere so that this approach can be implemented effectively. Learning is an active process and it is the responsibility of the educator to provide the learners with appropriate learning activities for learning and development to take place. The study made use of programme evaluation as research methodology. Programme evaluation refers to a research goal instead of specific research methods, because various methods can be used which may be quantitative or qualitative in nature. The gathering of data was done through classroom observations by the researcher, informal interviews with participating educators, questionnaires, and semi-structured interviews with the educators at the four schools the researcher monitored intensively during the implementation process of the intervention programme. The gathering of data was an ongoing process and the researcher analysed and interpreted the learners’ work at the end of the implementation process. The researcher checked this analysis by means of the literature review, transcripts and field notes. This formed the basis on which conclusions and recommendations could be made. The conclusions confirmed the importance of early intervention and the efficacy of the problem centered approach within the numeracy classroom. It also confirmed the disadvantages of the training model that was used, that is the Cascade model. With this study it was possible to determine that a ten week intervention programme was too short a period to observe meaningful improvements in learners. Therefore further research should be done on addressing learners’ difficulties and to train and support educators to provide learning support to their learners.