Thesis (MMus (Music))--University of Stellenbosch, 2009. / This study represents a contribution to the subject-didactical review of three prominent compositions for the violin by three prominent South African composers, namely the Sonata on African Motives by Stefans Grové (1985), Luamerava by Hendrik Hofmeyr (2000) and the Concerto for violin and orchestra by Allan Stephenson (2007). The three composers are discussed with reference to biographical detail and broad compositional style, while the works are reviewed according to musicological aspects as well as violin specific didactical aspects. To avoid too much repetition, a chapter concerning technical issues and practice methods pertaining to all three works was added. In the Sonata on African Motives, Stefans Grové merges his “old” compositional style, in this work loosely represented by a lack of tonality and metre, as well as complicated use of rhythm, with his “new” African voice (1984-). The African voice, represented by a melody he overheard a black roadworker sing, ties the work together. The sonata consists of five movements, with the first and fourth movements, and the third and fifth movements linked through content. This work presents challenging ensemble playing, rhythmic detail, diverse timbre changes in the violin part, as well as pitch difficulty due to unusual intervals without tonal context. Hendrik Hofmeyr‟s Luamerava was commissioned by SAMRO for the overseas scholarship. The title refers to the last of the mythical Children of the Lost Star who lived in the Cariba gorge on the banks of the Zambezi river (according to Mutwa‟s description of the oral culture of the people of that region). The piece, like the Grové, is thus linked to Africa. The work was composed for solo violin, Hofmeyr makes the most of the lyrical and sonorous qualities of the instrument. Compared to the other two works studied, Luamerava presents the most advanced technical challenges, with extensive doublestopping being the main challenge. Allan Stephenson‟s Concerto differs significantly from the other two works studied in the sense that it is instantly appealing to the general music lover, mainly because of his use of easy flowing melodies. The concerto has, as is tradition, three movements. Although the work contains ample technical challenges, it is obvious that it was composed by a string player – both the extensive running passages and double stopping are quite possible to play once good fingerings have been found. In the discussion of these works, attempts at solving specific technical problems are made.

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)