The study substantiates common strategies and theories regarding the teaching of sight-reading. The literature study done on sight-reading at the keyboard consists of opinions and recommendations resulting from empirical findings of well-known piano pedagogues. Seven beginner courses were analysed in order to assess their presentation of a well-structured development of piano sight-reading against the opinions and recommendations of well-known piano pedagogues and authors in this field as well as the personal experience of the researcher. During this process it was discovered that insufficient attention was paid to the development of the association between a note symbol and its corresponding key on the piano. However no attention was paid to the act of playing while reading ahead. The researcher compiled additional progressive exercises for the 7 to 9 year old beginner, to address the above-mentioned discrepancies. The exercises and their individual purposes are clearly explained with instructions regarding their performance. / Hierdie studie bevestig algemene strategieë en teorieë aangaande die ontwikkeling van vaardighede om musieknotasie te lees en te speel. Die literatuur wat in hierdie studie bestudeer is, handel oor opinies en aanbevelings van vooraanstaande klavierpedagoë wat voortspruit uit die resultate van hulle empiriese navorsing. Sewe aanvangskursusse is ontleed en die aktiwiteite en metodes waarvolgens vaardighede onderrig word om musieknotasie te leer lees en speel, is gemeet aan die aanbevelings van vooraanstaande klavierpedagoë, navorsers op die gebied, asook die navorser se eie ervaring met die boeke. Gedurende die studie is daar ontdek dat daar meesal nie aandag geskenk word aan die ontwikkeling van 'n assosiasie tussen 'n toonhoogtesimbool en ooreenstemmende klawer op die klavier nie en glad nie aan die proses van vooruitlees nie. Om hierdie tekortkominge te oorkom het die navorser 'n stel aanvullende en progressiewe oefeninge saamgestel wat maklik genoeg uitvoerbaar is vir die 7- tot 9-jarige beginner. Duidelike beskrywings van die oefeninge, elkeen se spesifieke doel, en aanwysings vir effektiewe uitvoering daarvan word verskaf. / Art History, Visual Arts & Music / M.A. (Musicology)

Text in English with abstracts in English, Afrikaans and isiZulu / The formalisation of first-order logic and axiomatic set theory in the first half of the 20th century—along with the advent of the digital computer—paved the way for the development of automated theorem proving. In the 1950s, the automation of proof developed from proving elementary geometric problems and finding direct proofs for problems in Principia Mathematica by means of simple, human-oriented rules of inference. A major advance in the field of automated theorem proving occurred in 1965, with the formulation of the resolution inference mechanism. Today, powerful Satisfiability Modulo Theories (SMT) provers combine SAT solvers with sophisticated knowledge from various problem domains to prove increasingly complex theorems. The combinatorial explosion of the search space is viewed as one of the major challenges to progress in the field of automated theorem proving. Pioneers from the 1950s and 1960s have already identified the need for heuristics to guide the proof search effort. Despite theoretical advances in automated reasoning and technological advances in computing, the size of the search space remains problematic when increasingly complex proofs are attempted. Today, heuristics are still useful and necessary to discharge complex proof obligations. In 2000, a number of heuristics was developed to aid the resolution-based prover OTTER in finding proofs for set-theoretic problems. The applicability of these heuristics to next-generation theorem provers were evaluated in 2009. The provers Vampire and Gandalf required respectively 90% and 80% of the applicable OTTER heuristics. This dissertation investigates the applicability of the OTTER heuristics to theorem proving in the hybrid theorem proving environment Rodin—a system modelling tool suite for the Event-B formal method. We show that only 2 of the 10 applicable OTTER heuristics were useful when discharging proof obligations in Rodin. Even though we argue that the OTTER heuristics were largely ineffective when applied to Rodin proofs, heuristics were still needed when proof obligations could not be discharged automatically. Therefore, we propose a number of our own heuristics targeted at theorem proving in the Rodin tool suite. / Die formalisering van eerste-orde-logika en aksiomatiese versamelingsteorie in die eerste helfte van die 20ste eeu, tesame met die koms van die digitale rekenaar, het die weg vir die ontwikkeling van geoutomatiseerde bewysvoering gebaan. Die outomatisering van bewysvoering het in die 1950’s ontwikkel vanuit die bewys van elementêre meetkundige probleme en die opspoor van direkte bewyse vir probleme in Principia Mathematica deur middel van eenvoudige, mensgerigte inferensiereëls. Vooruitgang is in 1965 op die gebied van geoutomatiseerde bewysvoering gemaak toe die resolusie-inferensie-meganisme geformuleer is. Deesdae kombineer kragtige Satisfiability Modulo Theories (SMT) bewysvoerders SAT-oplossers met gesofistikeerde kennis vanuit verskeie probleemdomeine om steeds meer komplekse stellings te bewys. Die kombinatoriese ontploffing van die soekruimte kan beskou word as een van die grootste uitdagings vir verdere vooruitgang in die veld van geoutomatiseerde bewysvoering. Baanbrekers uit die 1950’s en 1960’s het reeds bepaal dat daar ’n behoefte is aan heuristieke om die soektog na bewyse te rig. Ten spyte van die teoretiese vooruitgang in outomatiese bewysvoering en die tegnologiese vooruitgang in die rekenaarbedryf, is die grootte van die soekruimte steeds problematies wanneer toenemend komplekse bewyse aangepak word. Teenswoordig is heuristieke steeds nuttig en noodsaaklik om komplekse bewysverpligtinge uit te voer. In 2000 is ’n aantal heuristieke ontwikkel om die resolusie-gebaseerde bewysvoerder OTTER te help om bewyse vir versamelingsteoretiese probleme te vind. Die toepaslikheid van hierdie heuristieke vir die volgende generasie bewysvoerders is in 2009 geëvalueer. Die bewysvoerders Vampire en Gandalf het onderskeidelik 90% en 80% van die toepaslike OTTER-heuristieke nodig gehad. Hierdie verhandeling ondersoek die toepaslikheid van die OTTER-heuristieke op bewysvoering in die hibriede bewysvoeringsomgewing Rodin—’n stelselmodelleringsuite vir die formele Event-B-metode. Ons toon dat slegs 2 van die 10 toepaslike OTTER-heuristieke van nut was vir die uitvoering van bewysverpligtinge in Rodin. Ons voer aan dat die OTTER-heuristieke grotendeels ondoeltreffend was toe dit op Rodin-bewyse toegepas is. Desnieteenstaande is heuristieke steeds nodig as bewysverpligtinge nie outomaties uitgevoer kon word nie. Daarom stel ons ’n aantal van ons eie heuristieke voor wat in die Rodin-suite aangewend kan word. / Ukwenziwa semthethweni kwe-first-order logic kanye ne-axiomatic set theory ngesigamu sokuqala sekhulunyaka lama-20—kanye nokufika kwekhompyutha esebenza ngobuxhakaxhaka bedijithali—kwavula indlela ebheke ekuthuthukisweni kwenqubo-kusebenza yokufakazela amathiyoremu ngekhomyutha. Ngeminyaka yawo-1950, ukuqinisekiswa kobufakazi kwasuselwa ekufakazelweni kwezinkinga zejiyomethri eziyisisekelo kanye nasekutholakaleni kobufakazi-ngqo bezinkinga eziphathelene ne-Principia Mathematica ngokuthi kusetshenziswe imithetho yokuqagula-sakucabangela elula, egxile kubantu. Impumelelo enkulu emkhakheni wokufakazela amathiyoremu ngekhompyutha yenzeka ngowe-1965, ngokwenziwa semthethweni kwe-resolution inference mechanism. Namuhla, abafakazeli abanohlonze bamathiyori abizwa nge-Satisfiability Modulo Theories (SMT) bahlanganisa ama-SAT solvers nolwazi lobungcweti oluvela kwizizinda zezinkinga ezihlukahlukene ukuze bakwazi ukufakazela amathiyoremu okungelula neze ukuwafakazela. Ukukhula ngesivinini kobunzima nobunkimbinkimbi benkinga esizindeni esithile kubonwa njengenye yezinselelo ezinkulu okudingeka ukuthi zixazululwe ukuze kube nenqubekela phambili ekufakazelweni kwamathiyoremu ngekhompyutha. Amavulandlela eminyaka yawo-1950 nawo-1960 asesihlonzile kakade isidingo sokuthi amahuristikhi (heuristics) kube yiwona ahola umzamo wokuthola ubufakazi. Nakuba ikhona impumelelo esiyenziwe kumathiyori ezokucabangela okujulile kusetshenziswa amakhompyutha kanye nempumelelo yobuchwepheshe bamakhompyutha, usayizi wesizinda usalokhu uyinkinga uma kwenziwa imizamo yokuthola ubufakazi obuyinkimbinkimbi futhi obunobunzima obukhudlwana. Namuhla imbala, amahuristikhi asewuziso futhi ayadingeka ekufezekiseni izibopho zobufakazi obuyinkimbinkimbi. Ngowezi-2000, kwathuthukiswa amahuristikhi amaningana impela ukuze kulekelelwe uhlelo-kusebenza olungumfakazeli osekelwe phezu kwesixazululo, olubizwa nge-OTTER, ekutholeni ubufakazi bama-set-theoretic problems. Ukusebenziseka kwalawa mahuristikhi kwizinhlelo-kusebenza ezingabafakazeli bamathiyoremu besimanjemanje kwahlolwa ngowezi-2009. Uhlelo-kusebenza olungumfakazeli, olubizwa nge-Vampire kanye nalolo olubizwa nge-Gandalf zadinga ama-90% kanye nama-80%, ngokulandelana kwazo, maqondana nama-OTTER heuristics afanelekile. Lolu cwaningo luphenya futhi lucubungule ukusebenziseka kwama-OTTER heuristics ekufakazelweni kwamathiyoremu esimweni esiyinhlanganisela sokufakazela amathiyoremu esibizwa nge-Rodin—okuyi-system modelling tool suite eqondene ne-Event-B formal method. Kulolu cwaningo siyabonisa ukuthi mabili kuphela kwayi-10 ama-OTTER heuristics aba wusizo ngenkathi kufezekiswa isibopho sobufakazi ku-Rodin. Nakuba sibeka umbono wokuthi esikhathini esiningi ama-OTTER heuristics awazange abe wusizo uma esetshenziswa kuma-Rodin proofs, amahuristikhi asadingeka ezimweni lapho izibopho zobufakazi zingazenzekelanga ngokwazo ngokulawulwa yizinhlelo-kusebenza zekhompyutha. Ngakho-ke, siphakamisa amahuristikhi ethu amaningana angasetshenziswa ekufakazeleni amathiyoremu ku-Rodin tool suite. / School of Computing / M. Sc. (Computer Science)

The study substantiates common strategies and theories regarding the teaching of sight-reading. The literature study done on sight-reading at the keyboard consists of opinions and recommendations resulting from empirical findings of well-known piano pedagogues. Seven beginner courses were analysed in order to assess their presentation of a well-structured development of piano sight-reading against the opinions and recommendations of well-known piano pedagogues and authors in this field as well as the personal experience of the researcher. During this process it was discovered that insufficient attention was paid to the development of the association between a note symbol and its corresponding key on the piano. However no attention was paid to the act of playing while reading ahead. The researcher compiled additional progressive exercises for the 7 to 9 year old beginner, to address the above-mentioned discrepancies. The exercises and their individual purposes are clearly explained with instructions regarding their performance. / Hierdie studie bevestig algemene strategieë en teorieë aangaande die ontwikkeling van vaardighede om musieknotasie te lees en te speel. Die literatuur wat in hierdie studie bestudeer is, handel oor opinies en aanbevelings van vooraanstaande klavierpedagoë wat voortspruit uit die resultate van hulle empiriese navorsing. Sewe aanvangskursusse is ontleed en die aktiwiteite en metodes waarvolgens vaardighede onderrig word om musieknotasie te leer lees en speel, is gemeet aan die aanbevelings van vooraanstaande klavierpedagoë, navorsers op die gebied, asook die navorser se eie ervaring met die boeke. Gedurende die studie is daar ontdek dat daar meesal nie aandag geskenk word aan die ontwikkeling van 'n assosiasie tussen 'n toonhoogtesimbool en ooreenstemmende klawer op die klavier nie en glad nie aan die proses van vooruitlees nie. Om hierdie tekortkominge te oorkom het die navorser 'n stel aanvullende en progressiewe oefeninge saamgestel wat maklik genoeg uitvoerbaar is vir die 7- tot 9-jarige beginner. Duidelike beskrywings van die oefeninge, elkeen se spesifieke doel, en aanwysings vir effektiewe uitvoering daarvan word verskaf. / Art History, Visual Arts and Music / M.A. (Musicology)

Frans Vredenrijk Engelenburg (1863-1938) played a major role in the development and expansion of Afrikaans and the Afrikaans academic culture - especially in the northern part of South Africa. As a Dutch intellectual, lawyer and journalist in the nineteenth century South African Republic (Transvaal), he in particular played an important role as advisor and opinion maker from the 1890s onward. One of his biggest achievements was the key role that he played in the establishment of De Zuid Afrikaanse Akademie voor Taal, Letteren en Kunst in 1909. This study is the first part of a more comprehensive biographical project on the life of Engelenburg and the role he fulfilled in the history of the Akademie and South Africa until the thirties of the twentieth century. Since the 1600s the Engelenburg family has played a prominent role in the community where they lived. Aside from the high positions they had held for centuries before, they had in the fourth and again in the sixth generation married into noble families. This contributed to their important position in the community. Due to circumstances Engelenburg was not raised in the Engelenburg milieu. A family break in 1836 was the cause that Engelenburg's father, as a baby, was spirited away from this family milieu. Engelenburg received an extraordinarily good schooling. The solid intellectual foundation already laid then, to a large extent determined the course of his life. He was at the Stedelijk Gymnasium Arnhem when he met Marie Koopmans-De Wet (1834-1906), an aunt by marriage who lived in Cape Town, when on a visit to Europe. She was his soul mate and acted as a mentor and advisor to Engelenburg. The friendship strengthened with the years. He already at school had the desire to visit South Africa one day. His parents' divorce when he was still a student at the University of Leyden, steered his life in a very different direction than what he had foreseen for himself. The divorce was to a large extent the reason that, although he had studied law, he discarded the notion of a career in law after only a year. His decision to follow a career in journalism affected the rest of his life. The Transvaal War (1880-1881) meant that the Dutch developed an admiration for the Transvaalers for the determination and courage they displayed in their attempts to defeat the British army. President Paul Kruger's call shortly after the war that the Transvaal needed young Dutchmen further encouraged Engelenburg to come to South Africa. Previously Engelenburg had for a year worked for Fred Hogendorp at the Dagblad van Suidholland en s’Gravenhage in The Hague. Circumstances abruptly changed when Hogendorp suddenly became insane. During the same time, the owner of De Volksstem newspaper in Pretoria had committed suicide and Engelenburg seized the work opportunity. Within a matter of three months, he arrived in the Transvaal. Within a month after his arrival he was appointed chief editor of De Volksstem. He had studied the Transvaal situation thoroughly and by means of the newspaper and through tireless efforts, he contributed to improving the farming community’s cultural literacy. The education situation in the Transvaal enjoyed his constant attention. After the Anglo-Boer War (ABW) (1899-1902), he continued to work towards improving the education system in the Transvaal. He early on became involved in the Transvaal University College (later University of Pretoria). Before the ABW he did everything possible to promote the Dutch language to the Boer people. However, after the war he realised that Afrikaans had a rightful place, and he, in addition to Dutch, became a champion for the Afrikaans language. The battle between the proponents of Dutch and Afrikaans respectively, increased after the ABW. To achieve unity of action between the two groups, De Zuid Afrikaanse Akademie voor Taal, Letteren and Kunst was founded in 1909. Behind the scenes Engelenburg was one of the major driving forces to assist with the founding of the organisation. As a board member and later as chairman, he gave impetus to the Akademie. In 2009 the organisation celebrated its centenary. This is an important milestone, especially seen in the light of the current political climate in South Africa. The Akademie can now be regarded as a monument to Engelenburg as the fruit of his labour and perseverance during the first three decades of the Akademie’s existence. / Thesis (M.A. (History))--North-West University, Vaal Triangle Campus, 2010.

Frans Vredenrijk Engelenburg (1863-1938) played a major role in the development and expansion of Afrikaans and the Afrikaans academic culture - especially in the northern part of South Africa. As a Dutch intellectual, lawyer and journalist in the nineteenth century South African Republic (Transvaal), he in particular played an important role as advisor and opinion maker from the 1890s onward. One of his biggest achievements was the key role that he played in the establishment of De Zuid Afrikaanse Akademie voor Taal, Letteren en Kunst in 1909. This study is the first part of a more comprehensive biographical project on the life of Engelenburg and the role he fulfilled in the history of the Akademie and South Africa until the thirties of the twentieth century. Since the 1600s the Engelenburg family has played a prominent role in the community where they lived. Aside from the high positions they had held for centuries before, they had in the fourth and again in the sixth generation married into noble families. This contributed to their important position in the community. Due to circumstances Engelenburg was not raised in the Engelenburg milieu. A family break in 1836 was the cause that Engelenburg's father, as a baby, was spirited away from this family milieu. Engelenburg received an extraordinarily good schooling. The solid intellectual foundation already laid then, to a large extent determined the course of his life. He was at the Stedelijk Gymnasium Arnhem when he met Marie Koopmans-De Wet (1834-1906), an aunt by marriage who lived in Cape Town, when on a visit to Europe. She was his soul mate and acted as a mentor and advisor to Engelenburg. The friendship strengthened with the years. He already at school had the desire to visit South Africa one day. His parents' divorce when he was still a student at the University of Leyden, steered his life in a very different direction than what he had foreseen for himself. The divorce was to a large extent the reason that, although he had studied law, he discarded the notion of a career in law after only a year. His decision to follow a career in journalism affected the rest of his life. The Transvaal War (1880-1881) meant that the Dutch developed an admiration for the Transvaalers for the determination and courage they displayed in their attempts to defeat the British army. President Paul Kruger's call shortly after the war that the Transvaal needed young Dutchmen further encouraged Engelenburg to come to South Africa. Previously Engelenburg had for a year worked for Fred Hogendorp at the Dagblad van Suidholland en s’Gravenhage in The Hague. Circumstances abruptly changed when Hogendorp suddenly became insane. During the same time, the owner of De Volksstem newspaper in Pretoria had committed suicide and Engelenburg seized the work opportunity. Within a matter of three months, he arrived in the Transvaal. Within a month after his arrival he was appointed chief editor of De Volksstem. He had studied the Transvaal situation thoroughly and by means of the newspaper and through tireless efforts, he contributed to improving the farming community’s cultural literacy. The education situation in the Transvaal enjoyed his constant attention. After the Anglo-Boer War (ABW) (1899-1902), he continued to work towards improving the education system in the Transvaal. He early on became involved in the Transvaal University College (later University of Pretoria). Before the ABW he did everything possible to promote the Dutch language to the Boer people. However, after the war he realised that Afrikaans had a rightful place, and he, in addition to Dutch, became a champion for the Afrikaans language. The battle between the proponents of Dutch and Afrikaans respectively, increased after the ABW. To achieve unity of action between the two groups, De Zuid Afrikaanse Akademie voor Taal, Letteren and Kunst was founded in 1909. Behind the scenes Engelenburg was one of the major driving forces to assist with the founding of the organisation. As a board member and later as chairman, he gave impetus to the Akademie. In 2009 the organisation celebrated its centenary. This is an important milestone, especially seen in the light of the current political climate in South Africa. The Akademie can now be regarded as a monument to Engelenburg as the fruit of his labour and perseverance during the first three decades of the Akademie’s existence. / Thesis (M.A. (History))--North-West University, Vaal Triangle Campus, 2010.

This study, which explores the challenges of everyday English language words in learning physical sciences in Gauteng-East townships secondary schools highlights the difficulties that learners encounter in learning and developing scientific concepts and vocabulary. The study was conducted in four township secondary schools. A questionnaire consisting of 25 multiple choice items, as well as a semi-structured interview were used to collect data for this study. Descriptive statistics was used to analyse quantitative data while qualitative protocol was used to analyse qualitative data. The overall percentage mean scores of correct responses in the questionnaire for schools W, X, Y and Z were 47.2%, 56.9%, 55.2% and 57.2% respectively, which indicated that participants in the study have limited knowledge of everyday English words, when used in a science context. There was no significant gender discrepancy in terms of performance. In-depth analysis of the results revealed that the underlying difficulties were as a result of participants’ relative levels of proficiency in the English language, lack of precision in the use of this language, misreading, and confusion in terms of the use of words. Furthermore, the results were consistent with earlier findings from other countries as reported by various authors. The findings will contribute to knowledge about effective classroom instruction and teacher education from the perspective of language in science. / Kulolu cwaningo, kuhlolwa izinselelo zokusebenzisa amagama asetshenziswa nsuku zonke welimi lwesiNgisi ekufundeni iSayensi ezikoleni zezinga lesibili, emalokishini wabantu abaNsundu empumalanga neGauteng. Kuvezwa ubunzima obuhlangabezana nezingane zesikole ekufundeni nokuthuthukisa umqondo weSayensi nesilulumagama. Uphenyo lwenziwe ezikoleni ezine zasemalokishini. Imibuzo yayiquketwe izinhla ezingamashumi amabili nanhlanu lapho obuzwayo ezikhethela impendulo ekuyiyo, kanye nesinga nhlolokhono yasetshenziwa ukuthola ulwazi oluningi mayelana nalolu phenyo. Izibalo ezichazayo zisetshenziswe ukuhlola ubuningi, kanye nobuqotho kulandelwa umgudu wocwaningo wolwazi olutholakele. Kuvelile emva kophenyo ukuthi izimpendulo ezishaye emhlolweni ngokwamaphesenti kuzikole W,X.Y kanye no Z ngu 47%, 56,9%, 55.2%, kanye 57.2% ngokulandelana kwazo. Lokhu kubonisa ukuthi, abantwana banolwazi oluncane kakhulu ekusebenziseni amagama wesiNgisi asentsheziswa nsukuzonke ukufunda iSayensi. Kubuye kwatholakala futhi nokuthi awukho umehluko ohlukanisa ngobulili babafundi ophawulekayo ngokusebenza kwamagama esiNgisi. Kuphinde kuvele futhi ngokuhlaziya okunzulu, ukuthi kukhona ukwentuleka kwekhono elimini lesiNgisi, nokuthi abafundi abakwazi ukusebenzisa amagama ngendlela eqondile, babuye bafunde ekungeyikho, kanye nokudideka uma besebenzisa amagama. Okunye futhi okuvelayo, yikuthi lemiphumela ihambisana ncamashi neminye imiphumela evela kwamanye amazwe njengoba kubikwe abalobi abahlukene. Lokhu okuvelayo kuzosiza ukulungisa ukufunda kanye nokuqeqesha othisha, mayelana nukufundisa iSayensi ngolwimi lwesiNgisi. / Hierdie studie, wat die uitdagings van alledaagse Engelstalige woorde in die leer van Fisiese Wetenskappe in sekondêre skole in informele woonbuurte in Gauteng-Oos verken, beklemtoon die uitdagings wat leerders teëkom in die leer en ontwikkeling van wetenskaplike begrippe en taalgebruik. Die studie is uitgevoer in vier sekondêre skole in informele woonbuurte. ‘n Vraelys bestaande uit 25 veelvuldige-keuse items, tesame met ‘n gedeeltelike-gestruktueerde onderhoudskedule, is gebruik om data in te versamel vir hierdie studie. Beskrywende statistiek is gebruik om kwantitatiewe data te ontleed, terwyl kwalitatiewe protokol aangewend is om kwalitatiewe data te ontleed. Die algehele persentasie gemiddeldes van korrekte response op die vraelys vir skole W, X, Y en Z was 47.2%, 56.9%, 55.2% en 57.2% onderskeidelik, wat aangedui het dat die deelnemers aan die studie beperkte kennis gehad het van alledaagse Engelstalige woorde om in ‘n wetenskaplike konteks te gebruik. Geen noemenswaardige geslagsongelykheid in terme van prestasie is bevind nie. Indiepte ontleding van die bevindinge toon dat die onderliggende uitdagings die resultaat van deelnemers se relatiewe vlakke van taalvaardigheid in Engels, ‘n gebrek aan presiesie in die gebruik van die taal, gebrekkige leesvaardigheid en verwarring rondom die gebruik van woorde weerspiëel. Die resultate was verder in lyn met vroeëre bevindinge van ander lande, soos deur verskeie outeurs gerapporteer. Die bevindinge sal bydra tot kennis rondom effektiewe klasonderrig en onderwysersopleiding uit die oogpunt van wetenskaplike taalgebruik. / Science and Technology Education / M. Ed. (Natural Science Education)