This master's thesis deals with unusual applications tasks and problem tasks in teaching mathematics at the upper primary school as well as with their solving strategies. The whole work is build around an analysis of pupils' solutions of selected problem tasks. It was found that solving the tasks caused considerable troubles to a significant part of the pupils. The final part of the thesis contains a collection of problem tasks along with their solutions that is focused on teaching heuristic problem solving strategies and based on the analysis results.

This mixed methods research design, which was modelled on the constructivist view of schooling, sets out to investigate the effect of developing mathematical problem solving skills of grade 8 learners on their performance and achievement in mathematics. To develop the mathematical problem solving skills of the experimental group, a problem-centred teaching and learning environment was created in which problem posing and solving were the key didactic mathematical activity. The effect of the intervention programme on the experimental group was compared with the control group by assessing learners’ problem solving processes, mathematical problem solving skills, reasoning and cognitive processes, performance and achievement in mathematics. Data were obtained through questionnaires, a mathematical problem solving skills inventory, direct participant observation and questioning, semi-structured interviews, learner journals, mathematical tasks, written work, pre- and post- multiple-choice and word-problem tests. Data analysis was largely done through descriptive analysis and the findings assisted the researcher to make recommendations and suggest areas that could require possible further research. / Mathematics Education / M. Ed. (Mathematical Education)

Text in Afrikaans / Summary in English and Afrikaans / This study analyses the adolescent's peer pressure and the handling thereofby the adolescent, the parents, teachers and educational psychologist. The literature confirms that peer pressure is a multidimensional phenomenon. Certain factors such as the parent's behavioural- and cognitive functioning, the adolescent's social competence and susceptibility to peer pressure influence his compliance to peer pressure. Processes such as identification, internalization, modelling and coercion are involved in this compliance. The implementation of a mentor system and suggested program at school and the teaching of social-, decisionmaking, problemsolving- and selfassertiveness skills will help the adolescent to use peer pressure positively. The educational psychologist can support the adolescent and parents through individual, family and group therapy. / Hierdie studie handel oor die ontleding van portuurgroepdruk by die adolessent en die hantering daarvan deur die adolessent self, die ouers, onderwysers en opvoedkundige sielkundige. Die literatuur bevestig dat portuurgroepdruk 'n komplekse fenomeen met verskeie dimensies is. Verskeie faktore soos die ouers se gedrags- en kognitiewe funksionering, die adolessent se sosiale bekwaamheid en sy vatbaarheid vir portuurgroepdruk bei:nvloed sy toegewing aan portuurgroepdruk. Prosesse soos identifikasie, internalisasie, modellering en dwang is by die toegewing aan portuurgroepdruk betrokke. 'n Voorgestelde program vir die skool, die implementering van 'n portuurmentorprogram en die onderrig van sosiale-, besluitnemings-, probleemoplossings- en selfgeldingsvaardighede kan die adolessent help om portuurgroepdruk te gebruik. Die opvoedkundige sielkundige kan die ouer en adolessent deur individuele-, gesins- en groepterapie bystaan. / Educational Studies / M. Education (Guidance)

Students’ performances in mathematics in an Open Distant Learning setting have not always been impressive. An exploratory study into the problem solving skills of the University of South Africa students in the Calculus module MAT112 is being conducted using past examinations scripts between 2006 and 2009. The study re-assesses the work done in the end-of-year Calculus examinations, by both looking at the distribution of marks awarded and assigning new scores based on an assessment rubric adapted for the problem at hand. Further assessment of qualitative dimensions that is important for problem solving in Calculus is developed from the data obtained from the assessment rubric. Using factor analysis, a hesitation factor, transfer-of-knowledge factor as well as ingenuity factor, are identified in successful Calculus problem solving. The study proposes two conceptual models; the first is to guide students in solving Calculus problems while the second one is meant to assist lecturers in the assessment of students of Calculus. / Science and Technology Education / M. Ed. (Technology Education)

The aim of this study was to investigate the effect of context-based problem solving instruction (CBPSI) on the problem solving performance of Grade 10 learners, who performed poorly in mathematics. A cognitive load theory (CLT) was used to frame the study. In addition, CLT was used to: 1) facilitate the interpretation and explanation of participants‟ problem solving performance; and, 2) influence the design of CBPSI to hone participants‟ problem solving skills. The study was conducted in the Gauteng province of South Africa and involved a two-week intervention program in each of the nine participating high schools. Participants consisted of 783 learners and four Grade 10 mathematics teachers. A non-equivalent control group design was employed, consisting of a pre- and post- measure. In addition, classroom observations and semi-structured interviews were conducted with teachers and learners. Teachers employed conventional problem solving instructions in four control schools while the researcher implemented CBPSI in five experimental schools. Instruction in experimental schools entailed several worked-out context-based problem solving examples given to participants in worksheets. The main aspects of CBPSI embraced elements of the effects of self-explanation and split-attention, as advocated by CLT. Due to the design of CBPSI participants in experimental schools became familiar with the basic context-based problem solving tasks that were presented to them through the worked-out example samples. In turn, the associated cognitive load of problem solving tasks was gradually reduced. The principal instrument for data collection was a standardized Functional Mathematics Achievement Test. The pre-test determined participants‟ initial problem solving status before intervention. A post-test was given at the end of intervention to benchmark change in the functionality of CBPSI over a two-week period. Using one-way analysis of covariance (ANCOVA), Analysis of Variance (ANOVA), and other statistical techniques the study found that participants in experimental schools performed significantly better than participants in control schools on certain aspects of problem solving performance. In addition, semi-structured interviews and classroom observations revealed that participants rated CBPSI highly. On the whole, the study showed that CBPSI is an effective instructional tool to enhance the problem solving performance of Grade 10 mathematics learners. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)

The purpose of the study was to investigate grade 11 learners’ problem solving skills and conceptual reasoning on concepts in stoichiometry. Two theoretical frameworks were used in this study namely, cognitive load theory (CLT) and typology of curriculum representation (levels of curriculum alignment). The explanatory sequential mixed method research design were applied where 410 physical sciences learners in their intact classes and eleven of their teachers participated in the study. The participants completed purposefully designed research instruments consisting of an achievement test (LAT), a teacher and a learner questionnaire (TSQ and LCQ), and a teacher lesson plan on stoichiometry-related concepts (TLP). Other instruments used include a semi-structured interview schedule (LIS), classroom observation schedule (COS) and learner work books (LWB). The study was underpinned by five research questions. Pearson correlations showed that the justifications given by learners for choosing right or wrong objective options were not due to chance and suggested a learner choosing the right objective option has the right conceptual reasoning. Findings indicate that there is a positive correlation between problem-solving skills and conceptual reasoning where conceptual reasoning statistically predicted learners’ problem-solving skills using Regression. Problem solving is an important cognitive activity in everyday and professional contexts. Therefore, it requires teachers to know where to focus their teaching and how to assess learners’ work to avoid unnecessary overloading of the working memory of learners which might affect their performance. Conceptual reasoning and problem-solving errors were made during the problem solving, for example, learners could not apply mole ratio, they were unable to do change of subject and they interchanged the meanings of chemical terms such as mole, molecule, atoms and mass. In terms of possible reasons for the errors, and how it linked to the way learners were taught, the curriculum levels were considered. Findings indicate that there is a mismatch between what is expected in stoichiometry from the CAPS curriculum termed intended curriculum and the implemented curriculum which includes teacher lesson plans, classroom observations and learner workbooks. The classroom observations schedule was designed in line with the teacher lesson plan. There were topics planned in the lessons that were not found in the learner workbooks. The analysis of the content of learners’ workbooks for topics treated under stoichiometry, revealed that 75.7% of concepts were being taught while 24.3% were not. The analysis showed that learners experienced difficulties with calculating the concept of limiting reactant. There is a mismatch between implemented and attained curriculum as well. In the TSQ, teachers indicated that the errors were due to misconceptions, misunderstanding, carelessness and misinterpretation. These were found during marking of the learner achievement test. In conclusion, this study did not find a direct link between the way the learners were taught and the errors they committed during problem solving based on the implemented (TLP, LWB and COS) and attained curriculum (LAT, LCQ, LIS and DoBE report) / Science and Technology Education / Ph. D. (Mathematics, Science and Technology Education)

With the realization that traditional instructional approach has not yielded satisfactory results, quasi-experimental and descriptive research designs were employed to investigate whether the application of constructivist instructional approach in the learning of stationary points in differential calculus by Grade 12 learners in South Africa would improve conceptual learning. Three Gauteng high schools of 204 Grade 12 learners constituted the research fields – one served as the control group while the other two represented the experimental group. Being a mixed-method research, quantitative data were gathered through pre-test and post-test while qualitative data were collected from classroom observations. Both inferential and descriptive statistical methods of data collection and analysis were used. The results obtained indicate that the experimental group demonstrated a better understanding of the concept of stationary points than the control group. / Mathematics Education / M. Sc. (Mathematics Education)

Problem-based learning (PBL) is an active teaching strategy that could be implemented in the South African educational system to assist in developing problem-solving skills, critical thinking skills, collaborative skills, self-directed learning and intrinsic motivation in students. Even though it is not easy to drift from a teacher-centred strategy to a student-centred strategy, but this drift is supposed to be a paradigm drift for the nation. ‘Physics is difficult’ has been the anthem of students in South African high schools. This has led to lower pass rates in physics and as a result low physics career person in society. Physics students in high schools need to be exposed to the PBL strategy since the PBL strategy focuses on real-life problems to develop problem-solving skills, critical thinking skills and self-directed learning in students which are the skills needed for concept formation in Physical Science. Basically, the education of Physical Science students focused on the ability to acquire skills to solve real-life problems. This study focuses on exploring the experiences of high school physics teachers at Entsikeni cluster, South African, when implementing problem-based learning (PBL) in their physics classrooms. The study uses the mixed-method approach where three different research instruments were used to collect quantitative and qualitative data sequentially. Questionnaires, RTOP and interview protocol were employed. The findings of the study indicate that teachers project positive attitudes toward the PBL strategy but may probably not continue to use it because it requires more time than that which is allocated in the Curriculum Assessment and Policy Statement (CAPS) Physical Science document and as a result may not be able to finish their ATP on time. Teachers are teaching physics with no specialization in physics, which probably could lead to poor, pass rates in Physical Science. Teachers were inexperienced in teaching physics in the FET and could probably affect students’ academic performance. It is recommended they apply the PBL strategy to correct the negative effect of their inexperience on students’ performance. It is evident that if inexperienced trained teachers apply an instructional strategy based on research, they tend to develop students' performance as compared to applying the traditional instructional strategy. / Science and Technology Education / M. Sc. (Physics Education)