The purpose of this study was to explore solution strategies that can enhance the achievement of low-performing Grade 12 learners in the following mathematical aspects: finding the general term of a quadratic sequence, factorising third degree polynomials, determining the centre and radius of a circle, and calculating the angle between two lines. A convenience sample of twenty-five low-performing Grade 12 learners from a secondary school in Capricorn District of Limpopo Province participated in the study which adopted a repeated-measures research design. Learners were exposed to multiple solution strategies and data were collected using achievement tests. Findings indicated significant differences in learners‟ average scores due to the solution strategies used. In determining the general term of a quadratic sequence, learners‟ scores were significantly higher when they used formula and the table method than with the method of residues and solving simultaneous equations. Synthetic division made learners to achieve better scores than long division and equating coefficients in factorising third degree polynomials. The use of formulae to find the centre and radius of a circle made learners to have better achievement scores than completing the square. In calculating the angle between two lines learners‟ scores were better using formula and the cosine rule than using theorems. It was concluded that exposing low-performing Grade 12 learners to multiple solution strategies would enhance their achievement in the mathematical aspects explored in the study. Some of the solution strategies that made learners to achieve better results were not in the prescribed mathematics textbooks. The study therefore recommends that mathematics teaching should not be textbook-driven and that low-performing Grade 12 learners should not be regarded as beyond redemption. / Mathematics Education / M.Sc. (Mathematics, Science and Technology 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))

Syftet med studien var att undersöka hur lärare i årskurs F-3 undervisar problemlösning i matematik för att främja elevers problemlösningsförmåga. Denna kvalitativa studie avgränsas till sex lärare som undervisar i årskurserna F-3 som är verksamma på skolor i Mellansverige. Studiens empiri är baserat på lärarnas återgivningar om hur de planerar och genomför sin undervisning i problemlösning i matematik. Resultatet visade att samtliga lärare kopplar problemlösning till vardagliga sammanhang där undervisningen bör ha variation för att eleverna ska utvecklas och uppnå problemlösningsförmågan. När det kom till lärarnas planering av undervisningen utgår lärarna från de tre didaktiska områdena syfte, metod och innehåll där alla tre områdena behöver vara välplanerade och strukturerade. Problemlösningsuppgifterna kan variera och innehålla både öppna och slutna frågor, med ett respektive fler svarsalternativ. Ord, begrepp, strategier och representationsformer är även viktiga områden som läraren behöver betona samt undervisa om. Resultatet visade även att samarbete och diskussioner utgör två avgörande och betydelsefulla arbetsformer för att eleverna ska få möjlighet att utveckla problemlösningsförmågan. Slutsatsen med studien är att lärarens planering och genomförande i problemlösning utgör en väsentlig roll för att eleverna ska kunna utveckla problemlösningsförmågan. Det är lika viktigt att undervisa om strategier och representationsformer som att arbeta genom samarbete och diskussioner med klasskompisar och lärare om olika elevlösningar och svar. / The purpose of this study was to investigate how primary school teachers in preschool class to year 3 teach about problem-solving in mathematics to further support students' problem-solving ability. This qualitative study is limited to six teachers who teach preschool class to year 3 who are active in schools in the central parts of Sweden. The empirical study is based on the teachers' representations of how they plan and carry out their teaching of problem solving in mathematics. The results showed that all teachers link problem solving to everyday contexts where teaching should have variety for students to develop and achieve problem solving ability. When it came to teachers' planning of teaching, they are based on the three didactic areas of purpose, method, and content, where all three areas need to be well-planned and structured. The problem-solving tasks can vary and contain both open and closed questions, with one or more answer alternatives. Words, concepts, strategies, and forms of representation are also important areas that the teacher needs to emphasize and teach about. The results also showed that collaboration and discussions constitute two crucial and important working methods for the students to have the opportunity to develop problem-solving ability. The conclusion of the study is that the teacher's planning and implementation in problem-solving constitutes an essential role for the students to be able to develop problem- solving ability. It is just as important to teach about strategies and forms of representation as to work through collaboration and discussions with classmates and teachers about different student solutions and answers.