published_or_final_version / Linguistics / Master / Master of Arts

This study used Polya’s problem-solving model to map the level of development of the algebraic problem solving skills of Grade 12 learners from the Oshana Region in Northern Namibia. Deficiencies in problem solving skills among students in Namibian tertiary institutions have highlighted a possible knowledge gap between the Grade 12 and tertiary mathematics curricula (Fatokun, Hugo & Ajibola, 2009; Miranda, 2010). It is against this background that this study investigated the problem solving skills of Grade 12 learners in an attempt to understand the difficulties encountered by the Grade 12 learners in the problem solving process. Although there has been a great deal of effort made to improve student problem solving throughout the educational system, there is no standard way of evaluating written problem solving that is valid, reliable and easy to use (Docktor & Heller, 2009). The study designed and employed a computer aided algebraic problem solving assessment (CAAPSA) tool to map the algebraic problem solving skills of a sample of 210 Grade 12 learners during the 2010 academic year. The assessment framework of the learners’ problem solving skills was based on the Trends in International Mathematics and Science Study (TIMSS), Schoenfeld’s (1992) theory of metacognition and Polya’s (1957) problem solving model. The study followed a mixed methods triangulation design, in which both quantitative and qualitative data were collected and analysed simultaneously. The data collection instruments involved a knowledge base diagnostic test, an algebraic problem solving achievement test, an item analysis matrix for evaluating alignment of examination content to curriculum assessment objectives, a purposively selected sample of learners’ solution snippets, learner questionnaire and task-based learner interviews. The study found that 83.8% of the learners were at or below TIMSS level 2 (low) of algebraic problem solving skills. There was a moderate correlation between the achievement in the knowledge base and algebraic problem solving test (Pearson r = 0.5). There was however a high correlation between the learners’ achievement in the algebraic problem solving test and achievement in the final Namibia Senior Secondary Certificate (NSSC) examination of 2010 (Pearson r = 0.7). Most learners encountered difficulties in Polya’s first step, which focuses on the reading and understanding of the problem. The algebraic strategy was the most successfully employed solution strategy. / Mathematics Education / M. Sc. (Mathematics, Science and Technology Education (Mathematics Education))

This study used Polya’s problem-solving model to map the level of development of the algebraic problem solving skills of Grade 12 learners from the Oshana Region in Northern Namibia. Deficiencies in problem solving skills among students in Namibian tertiary institutions have highlighted a possible knowledge gap between the Grade 12 and tertiary mathematics curricula (Fatokun, Hugo & Ajibola, 2009; Miranda, 2010). It is against this background that this study investigated the problem solving skills of Grade 12 learners in an attempt to understand the difficulties encountered by the Grade 12 learners in the problem solving process. Although there has been a great deal of effort made to improve student problem solving throughout the educational system, there is no standard way of evaluating written problem solving that is valid, reliable and easy to use (Docktor & Heller, 2009). The study designed and employed a computer aided algebraic problem solving assessment (CAAPSA) tool to map the algebraic problem solving skills of a sample of 210 Grade 12 learners during the 2010 academic year. The assessment framework of the learners’ problem solving skills was based on the Trends in International Mathematics and Science Study (TIMSS), Schoenfeld’s (1992) theory of metacognition and Polya’s (1957) problem solving model. The study followed a mixed methods triangulation design, in which both quantitative and qualitative data were collected and analysed simultaneously. The data collection instruments involved a knowledge base diagnostic test, an algebraic problem solving achievement test, an item analysis matrix for evaluating alignment of examination content to curriculum assessment objectives, a purposively selected sample of learners’ solution snippets, learner questionnaire and task-based learner interviews. The study found that 83.8% of the learners were at or below TIMSS level 2 (low) of algebraic problem solving skills. There was a moderate correlation between the achievement in the knowledge base and algebraic problem solving test (Pearson r = 0.5). There was however a high correlation between the learners’ achievement in the algebraic problem solving test and achievement in the final Namibia Senior Secondary Certificate (NSSC) examination of 2010 (Pearson r = 0.7). Most learners encountered difficulties in Polya’s first step, which focuses on the reading and understanding of the problem. The algebraic strategy was the most successfully employed solution strategy. / Mathematics Education / M. Sc. (Mathematics, Science and Technology Education (Mathematics Education))

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This study investigated the problem-solving skills of Grade 12 learners in probability. A total of 490 Grade 12 learners from seven schools, categorised under four quintiles (socioeconomic factors) were purposefully selected for the study. The mixed method research methodology was employed in the study. Bloom’s taxonomy and the aspects of probability enshrined in the Mathematics Curriculum and Assessment Policy Statement (CAPS) document of 2011 were used as a framework of analysis. A cognitive test developed by the researcher was used as an instrument to collect data from learners. The instrument used for data collection passed the test of validity and reliability. Quantitative data collected was analysed using descriptive and inferential statistics and qualitative data collected from learners was analysed by performing a content analysis of learners’ scripts. The study found that the learners in this study were more proficient in the use of Venn diagrams as an aid in solving probability problems than in using tree diagrams and contingency tables as aids in solving these problems. Results of the study also showed that with the exception of Bloom's taxonomy synthesis level, learners in Quintile 4 (fee-paying schools) had statistically significant (P-value < 0.05) higher achievement scores than learners in Quintiles 1 to 3, (i.e. non-fee-paying schools) at the levels of knowledge, comprehension, application, analysis and evaluation of Bloom’s taxonomy. Contrary to expectations, it was revealed that the achievement of the learners in probability in this study decreased from Quintile 1 to Quintile 3 in all but the synthesis level of Bloom's taxonomy. Based on these findings, the study argued that the quintile ranking of schools in South Africa may be a useful but not a perfect means of categorisation to help improve learner achievement. Furthermore, learners in the study demonstrated three main error types, namely computational error, procedural error and structural error. Based on the findings of the study it was recommended that regular content-specific professional development be given to all teachers, especially on newly introduced topics, to enhance effective teaching and learning. / Mathematics Education / Ph. D. (Mathematics, Science and Technology Education)

Practical work plays an important role in the teaching and learning of science. This study was conducted to determine whether the methods and practices employed by physics teachers in Zimbabwe as required by the Zimbabwe School Examination Council (Zimsec) ‘A’ Level Physics Syllabus (9188) on the assessment of practical work skills assist the students in developing other crucial practical skills like manipulation, observational, planning and designing apart from presentation and analysis skills. The convergent parallel mixed methods approach of Creswell (2014) was used to collect, present and analyse data. Quantitative data were collected using the structured observation schedule to get assessment marks for a student using both methods of indirect assessment of practical work skills (IAPS) and direct assessment of practical work skills DAPS for the same practical work activity. Qualitative data were obtained from interviews with the physics teachers and Focus Group Discussion (FGD) with the ‘A’ level physics students. Pearson’s correlation coefficient (r) of the percentage rating of marks obtained by the student as observed during practical work sessions compared to the obtained mark from the submitted practical work report for the same practical work activity was calculated and found to be 0.135 with a Pvalue of 0.432. Both the narrative approach (Creswell, 2007) and conservation analyses (Gray, 2011) were used to present and analyse data from focus group discussions with ‘A’ level physics students and interviews with the physics teachers. The major finding from the analysis of quantitative data was that there was no association between the grades obtained by the student from DAPS as compared to IAPS for the same practical work activity as the value of r was found to be very low. This implied that passing practical work through the assessment of practical work report did not necessarily mean that the student could have mastered the basic skills of manipulation, designing, observation and planning. The views of physics teachers and students who participated in the study were that, the current method of practical work assessment used by Zimsec is not relevant in encouraging students to develop a variety of practical work skills as students concentrated on mastering presentation and analysis skills in order to pass practical work examinations. The study recommends that an alternative model of practical work assessment that integrates both DAPS and IAPS should be used to ensure valid and reliable assessment of practical work skills of ‘A’ level physics students. / Curriculum and Instructional Studies / D. Ed. (Didactics)

Abstracts in English, Sotho and Zulu / Waste generation is a global problem encountered by many nations. In recent years, population growth, booming urbanisation, an increase in economic activities and rise of communities’ living standards have significantly escalated household waste generation which has been a cause for concern. Waste production in households and schools imposes serious concern on the environment. To curb further depletion of environmental resources, sustainable consumption and household waste management practices and systems cannot be over emphasised. Therefore, the aim of the study was to explore the views of secondary school teachers’ views with regard to learners’ awareness of household waste management in Newcastle, South Africa. This study, following a qualitative approach, adopted a case study design to explore secondary teachers’ views on learners’ awareness on household waste management in the Newcastle municipality, in the Amajuba District, South Africa. By using semi- structured interviews, non-participatory observation and documents analysis, data were collected from three secondary schools and nine teachers, teaching Natural Sciences, Social Sciences and Life Orientation in Grade 8. The findings revealed that teachers understand the importance and benefits of household waste management although misconceptions of household waste management still prevailed. A challenge that emerged showed that teachers lack training to successfully integrate household waste management in their subjects. Their failure to identify household waste management themes in their CAPS subjects was sufficient evidence for the urgency of in-service training of teachers to assist them in integrating environmental education (EE) themes such as household waste management in their subjects. Although teachers experienced several challenges regarding implementing the theme of household waste management in their subjects, they considered the benefits outweighed the challenges. / Tlhahiso ya ditshila ke bothata bo aparetseng dinaha tse ngata. Dilemong tsa morao tjena, kgolo ya baahi, ho eketseha ha ditoropo, ho eketseha ha mesebetsi ya moruo, le ho phahama ha maemo a bophelo a baahi ho ekeditse tlhahiso ya ditshila tsa malapa ka mokgwa o bonahalang, e leng seo e leng sesosa sa ho tshwenyeha. Tlhahiso ya ditshila malapeng le dikolong e baka mathata a tebileng tikolohong. Ho thibela ho qepha ho eketsehileng ha mehlodi ya tikoloho, tshebediso e tsitsitseng le ditlwaelo tsa taolo ya ditshila tsa malapeng le ditsamaiso ho hloka ho elwa hloko ka tsela e kgethehileng. Kahoo, sepheo sa phuputso e ne e le ho hlahloba maikutlo a matitjhere a dikolo tse mahareng mabapi le tlhokomediso ya baithuti ka taolo ya ditshila tsa malapa Newcastle, Afrika Borwa. Phuputso, ka ho sebedisa mokgwa wa boleng, e amohetse moralo wa phuputso e ikgethileng ho hlahloba maikutlo a matitjhere a dikolo tse bohareng hodima tlhokomediso ya baithuti mabapi le taolo ya ditshila tsa malapa mmasepaleng wa Newcastle, Seterekeng sa Amajuba, Afrika Borwa. Ka ho sebedisa dipuisano tse hlophisitsweng hantle, tlhahlobo e sa kenyelletseng bonkakarolo le manollo ya ditokomane, datha e ile ya bokellwa ho tswa dikolong tse tharo tse bohareng le ho matitjhere a robong, a rutang Saense ya Tlhaho, Saense ya Phedisano le Thuto ya Bophelo bakeng sa baithuti ba Sehlopha sa 8. Diphetho di senotse hore matitjhere a utlwisisa bohlokwa le melemo ya taolo ya ditshila tsa malapa le hoja maikutlo a fosahetseng mabapi le taolo ya ditshila tsa malapa a ntse a atile. Phephetso e ileng ya hlaha e bontsha hore matitjhere a haellwa ke kwetliso ya ho kenyelletsa ka katleho taolo ya ditshila tsa malapa dithutong tsa bona. Ho hloleha ho kgetholla dihlooho tsa taolo ya ditshila tsa malapa dithutong tsa bona tsa CAPS e ne e le bopaki bo lekaneng ba ho potlaka ha kwetliso ya matitjhere a tshebetsong ho ba thusa ho kenyelletsa dihlooho tsa thuto ya tikoloho (EE) jwalo ka taolo ya ditshila tsa malapa dithutong tsa bona. Leha ele hore matitjhere a ile a ba le diphephetso mabapi le ho kenyelletsa dihlooho tsa taolo ya ditshila tsa malapa dithutong tsa bona, ba ile ba utlwa hore melemo e feta diphephetso. / Ukukhiqizeka kukadoti kuyinkinga ehlangabezana nezizwe eziningi emhlabeni. Eminyakeni esanda kudlula, ukukhula kwenani labantu, ukukhula kwamadolobha, ukukhula kwemisebenzi yamabhizinisi kanye nokukhuphuka kwezinga lempilo yabantu yikho okuye kwadala ukuthi imizi ikhiqize izinga eliphezulu likadoti/lenkukuma, okuyinkinga ebekade ivele isikhona. Ukukhiqizeka kukadoti emakhaya kanye nasezikoleni kudala izinkinga ezibi kakhulu endaweni. Ukuqeda ukumoshakala/ukuguga kwemithombo yezendawo okuqhubekela phambili, kusobala ukuthi kudingeka izindlela ezisimelele zokugaywa kukadothi kanye nezindlela zokulawula kukadothi kanti konke lokhu kuyiqiniso elingenakuphikiswa. Ngakho-ke, inhloso yocwaningo kwakuwukuphenya imibono yabafundisi bezikole zamabanga aphakeme mayelana nokuxwayisa uhlelo lokulawulwa kukadoti endaweni yase Newcastle, eNingizimu Afrika. Lolu cwaningo ngokulandela indlela yocwaningo eyencike kwingxoxo, luye lwalandela idizayini yocwaningo lotho ukuphenya imibono yabafundisi bamabanga aphakeme mayelana nokuxwayiswa kwabafundi ngokulawulwa kukadoti emakhaya ngaphansi kukamasipaladi waseNewcastle, ongaphansi kwesiFunda saseMajuba, eNingizimu Afrika. Idatha iye yaqoqwa ngokusebenzisa inhlolovo embaxambili, kwahlaziywa indlela yokuziphatha futhi kwahlaziywa imibhalo, kanti le datha iqoqwe ezikoleni zamabanga aphakeme ezintathu kanye nakubafundisi abayisishiyagalolunye, okungabafundisi abafundisa izifundo phecelezi Natural Sciences, Social Sciences kanye neLife Orientation yabafundi bakaGreyidi 8. Ulwazi olutholakele luveze ukuthi abafundisi bazwisisa ukubaluleka kanye nezinzuzo zohlelo lokulawulwa kukadoti, yize kusekhona ukudideka/ukungazwisisani mayelana nohlelo lokulawula ukuphatha kukadoti. Inselelo ebonakele, ikhombise ukuthi abafundisi baswela ukuqeqeshwa ukuze bakwazi ukuzwisisa kahle uhlelo lokulawulwa kukadoti kwizifundo zabo. Ukwehluleka kwabo ukwehlukanisa izindikimba zokulawulwa kukadoti emakhaya ezifundweni zabo zeCAPS kuye kwaba wubufakazi obanele besidingo esisheshayo sokuqeqeshwa kwabafundisi abasemsebenzini ukubanceda ukuba bakwazi ukuhlanganisa izindikimba zezifundo zezendawo environmental education (EE) ezinjengokulawulwa kukadoti ezifundweni zabo.Yize abafundisi behlangabezana nezinselele ezimbalwa mayelana nokusebenzisa indikimba yokulawulwa kukadoti ezifundweni zabo, baye babona ukuthi izinzuzo zalokhu zedlula izinselele. / Curriculum and Instructional Studies / M. Ed. (Environmental Education Curriculum)