This study examined the use of the set, area, and linear models of fraction representation to enhance elementary students' conceptual understanding of fractions. Students' preferences regarding the set, area, and linear models of fractions during independent work was also investigated. This study took place in a 5th grade class consisting of 21 students in a suburban public elementary school. Students participated in classroom activities which required them to use manipulatives to represent fractions using the set, area, and linear models. Students also had experiences using the models to investigate equivalent fractions, compare fractions, and perform operations. Students maintained journals throughout the study, completed a pre and post assessment, participated in class discussions, and participated in individual interviews concerning their fraction model preference. Analysis of the data revealed an increase in conceptual understanding. The data concerning student preferences were inconsistent, as students' choices during independent work did not always reflect the preferences indicated in the interviews.

Abstract in English, Tswana and Northern Sotho / The study aimed to explore teachers’ mathematical knowledge in respect of teaching the concept of fractions to Grade 6 learners. To that end a qualitative study was done, using a case study design. Data were collected through the observation of, and interviews with, three teachers at three schools in the Capricorn South district. Rooted in the theory of constructivism, the study was supplemented by the conceptual framework of mathematical knowledge for teaching (MKT) (Ball et al., 2008) and Shulman’s (1986) notion of pedagogical knowledge for teaching (PCK). The key finding of this investigation revealed that, of the three teachers, two did not develop the concept of fractions for their learners, but merely followed the traditional method of teaching the concept by encouraging their learners to memorise rules without understanding. Only one teacher emphasised an understanding of mathematical concepts. The main observation which the researcher made, was that teachers require a great deal of knowledge and expertise, in carrying out the work of teaching subject matter related to fractions. / Maikaelelo a thutopatlisiso e ne e le go tlhotlhomisa kitso ya dipalo ya barutabana malebana le go ruta barutwana ba Mophato wa 6 mogopolo wa dikarolwana. Go fitlhelela seo, go dirilwe thutopatlisiso e e lebelelang mabaka, go dirisiwa thadiso ya thutopatlisiso ya dikgetsi. Go kokoantswe data ka go ela tlhoko le go nna le dipotsolotso le barutabana ba le bararo kwa dikolong tsa kgaolo ya Capricorn Borwa. Thutopatlisiso eno e e theilweng mo tioring ya kago ya kitso e ne e tshegeditswe ke letlhomeso la sediriswa sa tokololo sa kitso ya dipalo ya go ruta (MKT) (Ball et al. 2008) le mogopolo wa ga Shulman (1986) wa kitso e e kgethegileng ya go ruta (PCK). Phitlhelelo ya botlhokwa ya patlisiso eno e senotse gore mo barutabaneng ba le bararo, ba le babedi ga ba a tlhamela barutwana ba bona mogopolo wa dikarolwana, mme ba latetse fela mokgwa wa tlwaelo wa go ruta mogopolo ka go rotloetsa barutwana go tshwarelela melawana kwa ntle ga go tlhaloganya. Ke morutabana a le mongwe fela yo o gateletseng go tlhaloganngwa ga megopolo ya dipalo. Temogo e kgolo e e dirilweng ke mmatlisisi ke gore barutabana ba tlhoka kitso le boitseanape jo bogolo go tsweletsa tiro ya go ruta dithuto tse di amanang le dikarolwana. / Dinyakišišo di ikemišeditše go utolla tsebo ya dipalo ya baithuti mabapi le go ruta kgopolo ya dipalophatlo go baithuti ba Kreiti ya 6. Ka lebaka la se go dirilwe dinyakišišo tša boleng, go šomišwa tlhamo ya dinyakišišo tša seemo. Tshedimošo e kgobokeditšwe ka go lekodišiša, le go dira dipoledišano le, barutiši ba bararo ka dikolong tše tharo ka seleteng sa Borwa bja Capricorn. Ka ge di theilwe go teori ya gore baithuti ba itlhamela tsebo, dinyakišišo di tlaleleditšwe ke tlhako ya boikgopolelo ya tsebo ya dipalo go ruteng (MKT) (Ball le ba bangwe, 2008) le kgopolo ya Shulman (1986) ya tsebo ya diteng tša thuto (PCK). Kutollo ye bohlokwa ya dinyakišišo tše e utollotše gore, go barutiši ba bararo, ba babedi ga se ba ba le kgopolo ya dipalophatlo go baithuti ba bona, eupša fela ba no latela mokgwa wa setlwaedi wa go ruta kgopolo ye ya dipalophatlo ka go hlohleletša baithuti ba bona go tsenya melawana ye ka hlogong ka ntle le go e kwešiša. Ke fela morutiši o tee yo a gateletšego gore go swanetše go ba le kwešišo ya dikgopolo tša dipalo. Temogo e tee yeo monyakišiši a bilego le yona, ebile gore barutiši ba hloka tsebo ye kgolo le botsebi, go phethagatša mošomo wa go ruta diteng tša thuto tšeo di amanago le dipalophatlo. / Mathematics Education / M. Ed. (Mathematics Education)