Thesis (M.Ed. (Education)) - Rhodes University, 2009. / A thesis submitted in partial fulfilment of the requirements for the degree of Master of Education.

The poor performance in mathematics of learners in schools in Namibia, especially in the grades where learners sit for the national examinations, has been a concern of everybody. Since independence, the Ministry of Education in collaboration with several donor agencies has been aware of the poor performance in mathematics in the country. Several international and local studies have been made in an effort to identify the problems that are hindering learners’ performance in mathematics in Namibia. The findings of some studies that were conducted in the country such as the Southern Africa Consortium Monitoring Education Quality (2004), the Presidential Commission on Education, Culture and Training (1999), and the Mathematics and Science Teachers Extension Program (2002) revealed that the inadequate proficiency of primary teachers in mathematics content could be responsible for learners’ poor performance in mathematics. This study, therefore, is aimed at investigating the mathematical proficiency of lower primary (LP) teachers in Namibia. The study used three instruments to collect data namely, a profile questionnaire – to collect teachers’ demographic data, a proficiency test – to test their proficiency level of mathematics using the content of Grade 4 and 5 learners’ mathematics syllabi and a semi-structured interview schedule – to get views about their own mathematics content knowledge, attitudes towards mathematics as well as problems that hinder effective teaching and learning of mathematics at LP phase. The study was conducted with 30 lower primary teachers from five primary and combined schools in the Ohangwena circuit of the Ohangwena region. The study found out that: (1) the mathematical proficiency of LP teachers is below the Grade 7 Mathematics content. Most teachers are not able to solve the content of mathematics at upper primary (UP) phase. (2) LP education is receiving very little support from the Ministry compared to other phases. (3) There are no workshops or training courses organised for LP teachers. They do not receive enough textbooks and materials, their classrooms are overcrowded and teachers cannot pay attention to individual learners. (4) There is a dire need for LP Head of Departments (HODs) who are specialised at LP; most HODs for LP at schools are not specialised in this area. When it comes to views about future content of mathematics that should be given to LP teachers in Namibia, respondents recommended that future LP teachers should have knowledge of mathematics up to at least Grade 10 but preferably up to Grade 12. They do not want to be restricted to LP mathematics, but would like to have a broader knowledge of mathematics content. This would make them more confident in solving their children’s problems in mathematics. Overall, participants recognised the value of mathematics and the role that it plays in society.

Thesis (PhD)--Stellenbosch University. / ENGLISH ABSTRACT: Education has always occupied a central role in the discipline of economics, featuring prominently in the theoretical constructs of the discipline and, more recently, in their empirical applications. While one can trace the origins of Human Capital theory all the way back to Adam Smith’s ‘The Wealth of Nations’, the two major advances in our understanding of education’s role in economic development transpired in the last 50 years. The first was half way through the 20th century with the work of work of Mincer (1958), Schultz (1961) and particularly that of Becker (1962) who formalized the idea of Human Capital. The second advance was at the turn of the 21st century when Hanushek and Kimko (and later Wößmann) incorporated measures of education quality into their models of economic growth. This latest strand of research serves as the point of departure for this thesis, placing education quality at the centre of the discussion. The thesis begins by focussing on the South African case and highlighting three broad issues that characterise education in the country: (1) the high levels of inequality that can be seen when comparing student performance by race, language, geographic location and socioeconomic status. New evidence is presented to show that South Africa does indeed have two public schooling systems, reiterating and confirming the findings of other South African scholars. (2) Using intra-survey benchmarks of student achievement, Chapter 2 develops a new method of quantifying learning deficits in mathematics by using three different datasets covering grades 3, 4, 5, 6 and 9. The learning gap between the poorest 60% of students and the wealthiest 20% of students is found to be approximately three grade-levels in grade 3 and grows to between four and five grade-levels by grade 9. (3) The focus then shifts to the complex issue of language and performance, which is addressed in Chapter 3. Here the aim is to exploit an unusual occurrence whereby a large group of South African students were tested twice, one month apart, on the same test in different languages. Using a simplified difference-in-difference methodology it becomes possible to identify the causal impact of writing a test in English when English is not a student’s home language. The final two chapters of the thesis widen the remit of analysis to include 11 countries in Sub-Saharan Africa, viz. Kenya, Lesotho, Malawi, Mozambique, Namibia, South Africa, Swaziland, Tanzania, Uganda, Zambia and Zimbabwe. Here the aim is to develop a composite measure of education access and education quality by combining household data (DHS) on grade completion and survey data (SACMEQ) on cognitive outcomes. The new measure, termed access-to-literacy and access-to-numeracy is reported for all countries and important sub-groups in Chapter 4. The method is then used in Chapter 5 to compare access-to-learning over a period of increased access to schooling (2000-2007). In all countries there was an improvement in access to literacy and numeracy, challenging the widely held perception that there is always an access-quality trade-off in education. In particular, girls and those in relatively poor households benefited most from this improvement in access to literacy and numeracy. The thesis ultimately concludes that if children are to realize their full potential, the expansion of physical access to schooling in the developing world must be accompanied by meaningful learning opportunities. The acquisition of knowledge, skills and values must be the central aim of educational expansion. / AFRIKAANSE OPSOMMING: Onderwys het nog altyd ʼn rol in ekonomie as vakgebied gespeel. Dit is verstaanbaar, want vaardighede en onderwys was nog altyd ʼn prominente deel van die teoretiese konstrukte en meer onlangs ook van empiriese toepassings in die dissipline. Terwyl die oorsprong van menslike-kapitaalteorie teruggevoer kan word na Adam Smith se Wealth of Nations, het die twee grootste deurbrake met die verstaan van onderwys se rol in ekonomiese ontwikkeling in die laaste vyftig jaar plaasgevind. Die werk van Mincer (1958), Schultz (1961) en veral Becker (1962), wat in die middel van die vorige eeu formele gestalte aan die begrip ‘menslike kapitaal’ gegee het, was die eerste deurbraak. Die tweede deurbraak was teen die eeuwending toe Hanushek en Kimko (en later Wößmann) maatstawwe van onderwysgehalte in hulle ekonomiese groeimodelle begin insluit het. Hierdie nuwe tak van die navorsing plaas onderwys vierkant in die sentrum en dien as vertrekpunt vir hierdie proefskrif. Die proefskrif begin deur aandag op drie breë kwessies te vestig wat kenmerkend is van onderwys in Suid-Afrika: (1) Die hoë vlakke van ongelykheid volgens ras, taal, geografiese gebied en sosio-ekonomiese status in studente se prestasie. (2) In hoofstuk 2 word ʼn nuwe metode aangebied om leeragterstrande kwantitatief te meet met behulp van norme van leerlingprestasie in skoolvlak-opnames vir grade 3, 4, 5, 6 en 9. Daar word bevind dat die leergaping tussen die armste 60% en die rykste 20% van studente in graad 3 ongeveer drie jaar is en teen graad 9 tot vier of vyf jaar aangroei. (3) Die fokus verskuif daarna na die verwikkelde kwessie van taal en skoolprestasie, wat in hoofstuk 3 bespreek word. Hier is die doel om die ongewone geval uit te buit waar ʼn groot groep Suid-Afrikaanse leerlinge binne die verloop van ʼn maand tweemaal dieselfde toets geskryf het, maar in twee verskillende tale. Met behulp van ʼn vereenvoudigde verskil-tussen-verskille-benadering is dit moontlik om te bepaal hoe groot die kousale effek is waar ʼn leerling wie se moedertaal nie Engels is nie die toets in Engels moes skryf. Die laaste twee hoofstukke van die proefskrif bevat ʼn wyer analise van elf lande in Sub-Sahara Afrika, naamlik Kenia, Lesotho, Malawi, Mosambiek, Namibia, Suid-Afrika, Swaziland, Tanzanië, Uganda, Zambië en Zimbabwe. Die doel is om ʼn saamgestelde maatstaf van onderwys-toegang en -gehalte te skep deur huishoudingsdata (DHS) oor graadvoltooiing en skoolopnamedata (SACMEQ) oor kognitiewe uitkomste te kombineer. Die nuwe maatstaf, genaamd ‘toegang-tot-geletterdheid’ en ‘toegang-tot-syfervaardigheid’, word in hoofstuk 4 vir al die lande en subgroepe opgestel. Die metode word dan in hoofstuk 5 gebruik om toegang-tot-leergeleenthede te vergelyk oor ʼn periode waartydens skooltoegang verbreed het (2000-2007). Daar was ʼn verbetering in toegang tot geletterdheid en syfervaardigheid in alle lande, teenstrydig met die wyd-gehuldigde siening dat daar altyd ʼn afruiling tussen toegang en gehalte van onderwys bestaan. In besonder word bevind dat meisies sowel as kinders uit arm huishoudings die meeste by die toename in toegang tot geletterdheid en syfervaardigheid gebaat het. Die gevolgtrekking is dat die vervulling van die potensiaal van kinders in die ontwikkelende wêreld vereis dat die verbreding van fisiese toegang tot skole met beduidende leergeleenthede gepaard moet gaan. Die aanleer van kennis, vaardighede en waardes moet die sentrale doel van die uitbreiding van onderwysgeleenthede wees.

L’objectif de ce travail est d’analyser les déterminants des inégalités de performances scolaires de 56 392 élèves en fin de cycle primaire dans 2 603 établissements scolaires situés dans 647 districts des 12 pays d’Afrique australe et orientale (Afrique du Sud, Botswana, Kenya, Lesotho, Malawi, Mozambique, Namibie, Ouganda, Swaziland, Tanzanie, Zambie et Zimbabwe) à partir de la troi-sième enquête de 2007 du Consortium de suivi de la qualité de l’éducation en Afrique orientale et australe (SACMEQ III). Le travail s’articule autour de trois chapitres. Il s’agit d’étudier, dans le premier chapitre, l’influence des caractéristiques individuelles de l’élève et de l’école sur les per-formances scolaires, ainsi que le rôle important des caractéristiques régionales. Dans le deuxième chapitre, nous cherchons à analyser comment l’inspection des établissements scolaires et leur ac-cessibilité par rapport au domicile des élèves agissent sur l’eÿcience scolaire. Le dernier chapitre propose d’étudier les facteurs socio-économiques et les conditions de scolarité déterminant les per-formances et les inégalités scolaires entre les filles et les garçons, compte tenu de leurs origines socio-économiques. Pour ce faire, nous avons utilisé di˙érentes approches économétriques, à savoir une modélisation multiniveau dans le premier chapitre, un modèle de frontière non paramétrique dans le chapitre deux et un modèle d’économétrie spatiale dans le chapitre trois. Les résultats montrent que les acquis des élèves, l’eÿcience des établissements et les inégalités scolaires entre les filles et les garçons sont très hétérogènes en Afrique australe et orientale. Les résultats révèlent que les élèves qui enregistrent des scores relativement élevés sont situés dans les régions urbaines riches et ayant accès aux moyens de transport. De profondes inégalités scolaires existent du fait de la carence de transports, d’infrastructures routières, éducatives et de santé particulièrement pour les districts situés en milieu rural et dans les quartiers pauvres des grandes villes. Il est également montré que les variables touchant les missions d’inspection des écoles, l’utilisation de la langue d’instruction à la maison et la sécurité dans le milieu scolaire jouent un rôle important dans la réussite des élèves. Les résultats obtenus permettent une meilleure compréhension du système sco-laire dans ces pays. / The objective of this work is to analyze the determinants of inequalities in the school performance of 56 392 pupils at the end of primary school in 2 603 schools located in 647 districts in 12 countries of Eastern and Southern Africa (Botswana, Kenya, Lesotho, Malawi, Mozambique, Namibia, Swa-ziland, Tanzania, Uganda, Zambia and Zimbabwe) based on the third 2007 Southern and Eastern Africa Consortium for Monitoring Educational Quality (SACMEQ III) survey. The work is struc-tured around three chapters. The first chapter studies the influence of individual characteristics of the student and the school on school performance, as well as the important role of regional characteristics. In the second chapter, we seek to analyze how the inspection of schools and their accessibility by students a˙ect the eÿciency of schools. The last chapter proposes to study the socio-economic factors and schooling conditions a˙ecting performance and inequalities in access between girls and boys, taking into account their socio-economic backgrounds. To do this, we used di˙erent econometric approaches, namely a multilevel model in the first chapter, a non-parametric frontier model in chapter two, and a spatial econometric model in chapter three. The results show that the achievements of pupils, the eÿciency of institutions and inequality in access to school between girls and boys are highly heterogeneous in Southern and Eastern Africa. The results also indicate that the students who registered relatively high scores are located in rich urban areas with access to the means of transportation. Moroever, deep inequalities in schooling exist due to deficiency of transportation, road infrastructure, educational and health conditions particularly in districts located in rural areas and in poor neighborhoods in large cities. We also show that the variables a˙ecting school inspection missions, the use of the teaching langage at home and security of the school environment play an important role in student success.

This thesis consists of three empirical studies. The first study, Rationales to Language-in-Education Policies in Postcolonial Africa: Towards a Holistic Approach, considers two issues. First, it explores the factors affecting the choice of an LiE policy in 35 African countries. The results show that the countries adopting a unilingual education system put different weights on the influential parameters than countries adopting a bilingual education system. Second, the study investigates how decision makers can ensure the optimal choice of language(s) of instruction by developing a non-cooperative game theoretic model with network externalities. The model shows that it is never optimal for two countries to become bilingual, or for the majority linguistic group to learn the language of the minority group, unless there is minimum cooperation to ensure an equitable redistribution of payoffs. The second study, The Role of Language in Learning Achievement: A Namibian Case Study, investigates the role played by home language and language proficiency on SACMEQ II mathematics scores of Namibian Grade-6 learners. HLM is used to partition the total variance in mathematics achievement into its within- and between-school components. Results show that although home language plays a limited role in explaining within- and between-school variations in mathematics achievement, language proficiency (proxied by reading scores) plays a significant role in the heterogeneity of results. Finally, the third study, Language Skills and Economic Returns, investigates the economic returns to language skills, assuming that language competencies constitute key components of human capital. It presents results from eight IALS countries. The study finds that in each country, skills in a second language are a significant factor that constrains wage opportunities positively.

Philosophiae Doctor - PhD / This thesis attempted to develop insight into why, contrary to expectation and predictions, learners in Rundu obtained better scores in a standardised English comprehension test than learners in Katima Mulilo, given that the conditions of teaching and learning were judged to be least favourable in Rundu. / South Africa

This thesis attempted to develop insight into why, contrary to expectation and predictions, learners in Rundu obtained better scores in a standardised English comprehension test than learners in Katima Mulilo, given that the conditions of teaching and learning were judged to be least favourable in Rundu.

This thesis attempted to develop insight into why, contrary to expectation and predictions, learners in Rundu obtained better scores in a standardised English comprehension test than learners in Katima Mulilo, given that the conditions of teaching and learning were judged to be least favourable in Rundu.

Thesis (MEcon)--University of Stellenbosch, 2006. / Education production function analysis is widely recognised as one important area of research that needs to inform education policymaking, specifically policy relating to the mix of funded inputs in a schooling system. Arriving at production functions is a complex task, and is fraught with methodological pitfalls. This thesis sets out to establish a framework for undertaking education production function analysis, and in discussing its various elements, including its pitfalls, recommendations for good practice are arrived at. The material analysed is of four types: texts on econometric theory; existing production function analyses; documentation relating to three dataintensive school monitoring programmes, namely Brazil’s SAEB, South Africa’s Systemic Evaluation and the international SACMEQ programme; and lastly data, relating mainly to South Africa, from the 2000 run of SACMEQ. The thesis is organised according what can be regarded as seven key analysis steps. These steps include a focus on the importance of a ‘mental model’, the relative benefits of the one-level regression model and the hierarchical linear model (HLM), and the formulation of actual production functions for South Africa based on the SACMEQ data, using both one-level and HLM models. Key conclusions are, firstly, that the HLM, though still under-developed, offers great analysis potential and, secondly, that production function analyses ought to be translated into budgetary terms in order for them to become fully meaningful to the policymaker.

Mathematics Education / M. Ed. (Mathematics Education)