According to research, problem solving is one of mathematics most important content, since teaching problem solving helps students to develop a deeper understanding of mathematics. At the same time, research shows that through history and even today, the majority of mathematics education consists of students working individually with information in the textbook that deals with methodology. This means that students are taught to develop their procedural skills, thus not being able to develop their problem solving skills and deeper understanding of mathematics. The purpose of this study was therefore to investigate the extent to which different textbooks for grade three deal with problem solving as well as the strategies and perspectives on problem solving that are identifiable in the textbooks. To find answers to my purpose, a study component analysis has been carried out on textbooks published in the following years: 1979, 1984, 2005, 2006 and 2012. The results show that textbooks handle problem solving in different ways but that similarities can also be identified. All books contain problem solving tasks that can be solved through different strategies, but the perspective of problem solving differs between the textbooks. The relationship between textbook and syllabus varies among the textbooks, which proves the importance of the teacher being able to influence the pupils' learning opportunities when selecting textbooks. / Enligt forskning är problemlösning ett av matematikens viktigaste innehåll, då undervisning av problemlösning utvecklar en djupare förståelse för matematik hos eleverna. Samtidigt visar forskning att genom historien och även idag består majoriteten av matematikundervisningen av att eleverna arbetar enskilt med uppgifter i läroboken som behandlar metodinlärning. Detta innebär att eleverna undervisas till att utveckla sin procedurförmåga och därmed inte får möjlighet att utveckla sin problemlösningsförmåga och djupare förståelse för matematik. Syftet med den här undersökningen var därför att undersöka i vilken utsträckning olika läroböcker för årskurs 3 behandlar problemlösning samt vilka strategier och perspektiv på problemlösning som är identifierbara i läroböckerna. För att söka svar på mitt syfte har en läroboksanalys genomförts på läroböcker som utgivits följande år: 1979, 1984, 2005, 2006 samt 2012. Resultatet visar att läroböckerna behandlar problemlösning på olika sätt men att likheter dessutom går att identifiera. Samtliga böcker innehåller problemlösningsuppgifter som kan lösas genom olika strategier, men perspektiven på problemlösning skiljer sig mellan läroböckerna. Relationen mellan lärobok och kursplan varierar bland läroböckerna, vilket bevisar vikten av att läraren kan påverka elevernas möjligheter till lärande vid val av lärobok.

Denna studie ämnar undersöka på vilka sätt läromedlet Singma är utformat för att utveckla elevers problemlösningsförmåga. Studien syftar också till att undersöka lärares generella upplevelse och uttryckta användning av Singma samt av hur lärarna beskriver att läromedlet ger dem förutsättningar att utveckla elevers problemlösningsförmåga. Studien utgörs av en läromedelsanalys av Singma och en teoretisk tematisk analys av lärares upplevelser av läromedlet. Resultatet av läromedelsanalysen ger slutsatsen att Singma skulle kunna anses vara utformat på ett sätt som möjliggör utvecklandet av elevers problemlösningsförmåga. Resultatet av den tematiska analysen belyser flera olika faktorer som påverkar lärares upplevelse av Singma samt möjligheter och utmaningar med läromedlet. Slutsatsen av den tematiska analysen visar på vikten av utbildning om läromedlet samt att lärare och elever behöver ompröva sin syn på matematikundervisning vid arbete med Singma.

Denna kvantitativa forskningsrapport inriktar sig på hur elever uppfattar sin egen matematiska förmåga, vilken grad av tilltro eleverna har till sin förmåga och hur de presterar i matematikämnet med särskilt fokus på metod- och problemlösningsuppgifter. Den litteratur som ligger till grund för studien baseras på vad det innebär att tro på sin egen förmåga, förmågan att kunna värdera sig själv och sin förmåga samt matematikuppgifters betydelse för skapandet av självuppfattning och tilltro till den egna förmågan. Den forskningsmetod som används för att kunna besvara studiens frågeställningar är av kvantitativ karaktär och består av ett självskattningsformulär där syftet är att synliggöra elevernas grad av tilltro till den egna matematiska förmågan samt ett tillhörande matematiktest där eleverna löser metod- och problemlösningsuppgifter. Lösningsfrekvensen av de olika uppgiftstyperna analyseras i relation till elevernas grad av tilltro. Studien genomsyras av ett socialpsykologiskt perspektiv och resultatet teoretiseras genom att utgå från den socialpsykologiska teorin om själveffektivitet samt symbolisk interaktionism. För att analysera sambanden har materialet även analyserats ur ett statistiskt perspektiv genom analysverktyget SPSS. Resultatet av studien visar att det verkar finnas ett samband mellan elevernas grad av tilltro till sin matematiska förmåga och hur de presterar i både metod- och problemlösningsuppgifter. / This quantitative study focuses on how students perceive their own mathematical ability, what degree of confidence students have in their ability and how they perform in mathematical tasks that focuses on method and problem solving ability. The literature underlying the study is based on the importance of believing in your own ability, the ability to assess yourself and your ability, and the importance of mathematics to maintain and create opportunity to develop self-perception and confidence in your own ability. The research method used to answer the questions of the study is of a quantitative nature and consists of a self-assessment form that aims to visualize the students' degree of confidence in their own mathematical ability and a mathematics test where students solve method and problem solving tasks. The dissolution rate of the different types of tasks is analyzed in relation to the students' degree of confidence. The study is pervaded by a social psychological perspective and the result is theorized by starting from the social psychological theory of self-efficacy as well as symbolic interactionism. To analyze the relationships, the material has also been analyzed from a statistical perspective, using the SPSS analyzing tool. The result of the study shows that there seems to be a connection between the students' degree of confidence in their mathematical ability and how they perform in both method and problem solving tasks.

Plusieurs organismes ont besoin d’information à propos de la valeur des alternatives afin de prendre la meilleure décision dans plusieurs contextes importants tels que l’approvisionnement, le choix d’un habitat ou d’un partenaire de reproduction. L’utilisation d’information sociale qui provient des congénères est généralement considérée comme avantageuse, dans la mesure où elle est peu couteuse à acquérir. Cependant, elle peut s’avérer néfaste lorsque celle-ci est incorrecte, désuète ou émise par un émetteur malhonnête dans le but de duper. Ainsi, deux questions cruciales se posent lorsque qu’un organisme a accès à de l’information sociale : quand copier ? et qui copier ? Parmi plusieurs autres facteurs, les capacités cognitives des individus pourraient affecter leur probabilité de copier et d’être copié. Spécifiquement, un individu ayant de bonnes capacités d’apprentissage serait plus certain de son information personnelle et devrait de ce fait moins utiliser l’information sociale qu’un individu moins performant. Les démonstrateurs ayant de meilleures aptitudes (en termes par exemple de capacité à résoudre de nouveaux problèmes) devraient également être considérés comme plus fiables et, de ce fait, être copiés préférentiellement. Afin de tester ces deux hypothèses, nous avons effectué une expérience avec des diamants mandarins (Taenyopigia guttata), dans laquelle les sujets pouvaient copier le choix de 2 démonstrateurs qui leur procuraient tous les deux une information sociale contradictoire à leur information personnelle mais différaient dans leur capacité à résoudre un problème. Les sujets étaient par la suite testés dans une tâche d’apprentissage associatif. À l’encontre de nos hypothèses, les individus plus performants dans la tâche d’apprentissage n’ont pas utilisé l’information sociale moins souvent que ceux qui ont eu besoin d’un grand nombre d’essais pour atteindre le critère d’apprentissage. Par contre, nous avons trouvé que les sujets qui avaient une préférence plus marquée utilisaient moins l’information sociale que ceux qui avaient fait un choix plus aléatoire. De plus, les individus qui ont utilisé l’information sociale ont copié plus fréquemment le choix du démonstrateur qui avait été observée en train de réussir une tâche de résolution de problème plutôt que celui qui avait échoué. Ainsi notre étude démontre que les diamants mandarins évaluent la pertinence de l’information personnelle et social en considérant leur niveau d’incertitude et les performances cognitives des démonstrateurs dans une tâche de résolution de problème. / Animals frequently rely on others’ choice to decide with whom to mate or what to eat. Because social information use may lead to maladaptive decisions, individuals should not rely on social information unconditionally. In particular, reliance on social information should be more frequent when uncertainty about how to behave is high, and hence in individuals with poor learning abilities. When individuals who are copied provide contradictory social information, social learners should also preferentially copy the decisions of the most reliable model, and so, for instance, better-performing models in cognitive tasks. Here we conducted an experiment with zebra finches (Taeniopygia guttata) on which we measured (i) the preference for three colored feeders before and after they had received conflicting information from two models that respectively succeeded or failed to resolve a novel problem and (ii) the performance on an associative learning task. We found no evidence that individuals that were quicker to learn a new association relied less on social information compared to slower learners. Yet, the birds who exhibited a stronger initial preference used social information to a lesser extent compared to those who showed a less pronounced preference. Furthermore, we found that individuals copied more frequently the choice of the problem-solver over the non-solver model. Thus, our findings demonstrate that zebra finches weight personal and social information based on their level of uncertainty and the models’ performance in cognitive tasks.

Johan Adam Heyns is probably the most productive and noteworthy Afrikaans theologian of the twentieth century, born in South Africa. He was a real pioneer in his field. It is a well known fact that the kingdom of God played a vital role in all of his work. In fact, he used it as a systematic-theological category, which flows like a perennial river of opportunity, consistently through all of his writings. It gave him the opportunity to be consistent in both his systematic theology and in his ethics. Heyns used the kingdom of God as a systematic-theological category to show clearly how man and God can be co-workers in this world in a dialogical relationship. This relationship, of which God is the initiator, are characterised by the covenant between God, the Father-King, and man, the obedient child-servant. He also used the opportunity to integrate his love for philosophy with his love for theology. This integration opened up a wide spectrum of thoughts, ideas and meanings which he could scientifically analyze, explore, connect and merge together systematically. His contact with Stoker and their shared Calvinistic worldview as well as their shared Afrikaans culture and Christian religion, together with the influence of amongst others Du Toit and Snyman, Oberholzer, Vollenhoven, Barth, Brunner and Berkouwer, laid the foundation for his frame of reference. Unfortunately there was philosophical flooding from time to time, because it caused him to fill the kingdom of God with philosophical concepts which allowed him to think of the kingdom of God as an ontological cosmic-universal entity. His philosophical background and connection also leads to some inadequate speculations in his theology and especially in his eschatology. Inadmissibly he didn’t always use the Bible appropriately, although his doctrine of Scripture and hermeneutics were satisfactory. Heyns could have explored the important part which prayer must play in theology more thoroughly. But he did pioneer’s work in Dogmatics and Ethics in Afrikaans and as an ecumenist and church leader, which we must really appreciate. Lastly his philosophical modus operandi also had a positive side. It helped him to differentiate between important theological concepts. Heyns distinguished between the rule of God and the kingdom of God, as well as between the realisation of the kingdom of God and the eschatological fulfilment of God’s kingdom. These differentiations were tested on some theological problems, including the question whether the kingdom of God is really an ontological entity, the Theodicy problem and the “Nah-erwartung” problem. It was found that these differentiations, when used consistently, have valuable theological problem solving abilities. Although Heyns perhaps didn’t realise this, and he weren’t consistent in the use of these differentiations, he must be credited for identifying and clarifying them. / Thesis (PhD)--University of Pretoria, 2010. / Dogmatics and Christian Ethics / unrestricted

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.

Accounting transactions are becoming more complex, and more extensive accounting guidance is provided on a continuous basis in the accounting standards. In addition, accounting guidance changes often and additional guidance is added to the standards regularly. In view of this immense amount of accounting knowledge that an accountant can be expected to have, exacerbated by often multifaceted structures in accounting problems, it can be challenging and onerous to solve certain accounting problems. The premise of this study is that accounting problems can also be solved in a less complex manner with reference to the foundational accounting concepts included in the Conceptual Framework for Financial Reporting (CF). The solution to the accounting problem using the CF should result in a similar answer had the detailed, complex accounting guidance been consulted. This is based on the understanding that the detailed guidance is consistent with the CF and that the CF is not underdeveloped. In the experience of the author of this dissertation, however, the CF is rarely used to consider the accounting treatment of specific transactions and the first point of reference is usually the detailed, specific guidance. In order to impart a practice of incorporating the CF in problem-solving, the study in this dissertation is underpinned by educational philosophies rooted mainly in constructivism, and specifically in Ausubel’s subsumption theory. Applied to accounting education, this theory suggests a frameworkbased approach whereby educators first instil a detailed knowledge of the CF in an Accounting course and thereafter present details of specific accounting transactions by building and crossreferencing to the foundational concepts in the CF. In addition, the paradigm in Accounting courses should also incorporate problems and experiments through which students can construct their own knowledge, rather than being passive recipients of an educator’s teaching style. Recent literature on framework-based teaching suggests that such an approach is beneficial as it enhances lifelong learning. This study reported on a framework-based approach incorporated in an Accounting course and aimed to determine students’ ability to solve complex accounting problems by referring only to the CF, as well as to determine the factors that could influence their ability to solve the problems and the preferred problem-solving approach of students in facing future accounting problems. In order to address the broad aim of this study, it was divided into two sections, each to identify and analyse a different aspect of accounting problem-solving that incorporated the CF. The study in this dissertation focused mainly on an interpretive research paradigm. The first project had the primary objective of determining whether students have the ability to solve complex accounting problems by using only the CF and determining which factors could influence their ability. This was established by analysing the content and results of an assignment administered to third-year Accounting students at a South African university in which students were required to solve problems using only the CF. The second project had the objective of determining the preferred future approach students will take in solving accounting problems after they have been exposed to a framework-based assignment. This was established through qualitative measures and augmented by a questionnaire to analyse the students’ perceptions. The contributions of this dissertation are manifold and include, but are not limited to, the realisation that a conceptual approach to accounting education is beneficial in Accounting courses. The results in this study indicate that the ability of students to solve complex accounting problems by referring only to the CF may depend on the complexity of the scenario and the students’ familiarity with the problem. In addition, after being exposed to a framework-based assignment, students may tend to prefer a mixed approach in solving accounting problems, which entails a combination of the concepts in the CF and specific accounting guidance governing a particular transaction. The author also believes that this study makes a practical contribution by providing an actual framework-based assignment which can be used or adapted by other Accounting educators to use in similar courses, or to help them develop similar assignments or case studies or to replicate the study. From an educational perspective, it is recommended that Accounting educators incorporate an emphasis on the CF in their teaching approach. As students are exposed to opportunities to exercise their judgement using the concepts included in the CF, they will gain experience in this and be able to exercise better judgement in future. Each time a student is exposed to a problem requiring to be solved using the CF, or is required to make necessary judgements with regard to the CF, it will lead to the creation of new knowledge which the student can constantly link and cross-reference to existing knowledge and experiences. It also appears that, when students are exposed to problem-solving using the CF, it may lead to accountants adopting a more balanced approach by considering more CF constructs in solving future accounting problems. Although the study in this dissertation was conducted at only one university, its implications are by no means limited to this institution. Extrapolation of results cannot be attempted due to the nature of the research design, but the results in this study are valuable and enhance accounting education literature in better understanding students’ problem-solving abilities and their preferred problemsolving approach. The research is therefore valuable to any Accounting educator, as well as the institutional bodies guiding accounting education and its syllabi. It is hoped also that some of the findings will inspire other educational institutions to promote a framework-based approach in an innovative manner. / MCom (Accountancy), North-West University, Potchefstroom Campus, 2015

Accounting transactions are becoming more complex, and more extensive accounting guidance is provided on a continuous basis in the accounting standards. In addition, accounting guidance changes often and additional guidance is added to the standards regularly. In view of this immense amount of accounting knowledge that an accountant can be expected to have, exacerbated by often multifaceted structures in accounting problems, it can be challenging and onerous to solve certain accounting problems. The premise of this study is that accounting problems can also be solved in a less complex manner with reference to the foundational accounting concepts included in the Conceptual Framework for Financial Reporting (CF). The solution to the accounting problem using the CF should result in a similar answer had the detailed, complex accounting guidance been consulted. This is based on the understanding that the detailed guidance is consistent with the CF and that the CF is not underdeveloped. In the experience of the author of this dissertation, however, the CF is rarely used to consider the accounting treatment of specific transactions and the first point of reference is usually the detailed, specific guidance. In order to impart a practice of incorporating the CF in problem-solving, the study in this dissertation is underpinned by educational philosophies rooted mainly in constructivism, and specifically in Ausubel’s subsumption theory. Applied to accounting education, this theory suggests a frameworkbased approach whereby educators first instil a detailed knowledge of the CF in an Accounting course and thereafter present details of specific accounting transactions by building and crossreferencing to the foundational concepts in the CF. In addition, the paradigm in Accounting courses should also incorporate problems and experiments through which students can construct their own knowledge, rather than being passive recipients of an educator’s teaching style. Recent literature on framework-based teaching suggests that such an approach is beneficial as it enhances lifelong learning. This study reported on a framework-based approach incorporated in an Accounting course and aimed to determine students’ ability to solve complex accounting problems by referring only to the CF, as well as to determine the factors that could influence their ability to solve the problems and the preferred problem-solving approach of students in facing future accounting problems. In order to address the broad aim of this study, it was divided into two sections, each to identify and analyse a different aspect of accounting problem-solving that incorporated the CF. The study in this dissertation focused mainly on an interpretive research paradigm. The first project had the primary objective of determining whether students have the ability to solve complex accounting problems by using only the CF and determining which factors could influence their ability. This was established by analysing the content and results of an assignment administered to third-year Accounting students at a South African university in which students were required to solve problems using only the CF. The second project had the objective of determining the preferred future approach students will take in solving accounting problems after they have been exposed to a framework-based assignment. This was established through qualitative measures and augmented by a questionnaire to analyse the students’ perceptions. The contributions of this dissertation are manifold and include, but are not limited to, the realisation that a conceptual approach to accounting education is beneficial in Accounting courses. The results in this study indicate that the ability of students to solve complex accounting problems by referring only to the CF may depend on the complexity of the scenario and the students’ familiarity with the problem. In addition, after being exposed to a framework-based assignment, students may tend to prefer a mixed approach in solving accounting problems, which entails a combination of the concepts in the CF and specific accounting guidance governing a particular transaction. The author also believes that this study makes a practical contribution by providing an actual framework-based assignment which can be used or adapted by other Accounting educators to use in similar courses, or to help them develop similar assignments or case studies or to replicate the study. From an educational perspective, it is recommended that Accounting educators incorporate an emphasis on the CF in their teaching approach. As students are exposed to opportunities to exercise their judgement using the concepts included in the CF, they will gain experience in this and be able to exercise better judgement in future. Each time a student is exposed to a problem requiring to be solved using the CF, or is required to make necessary judgements with regard to the CF, it will lead to the creation of new knowledge which the student can constantly link and cross-reference to existing knowledge and experiences. It also appears that, when students are exposed to problem-solving using the CF, it may lead to accountants adopting a more balanced approach by considering more CF constructs in solving future accounting problems. Although the study in this dissertation was conducted at only one university, its implications are by no means limited to this institution. Extrapolation of results cannot be attempted due to the nature of the research design, but the results in this study are valuable and enhance accounting education literature in better understanding students’ problem-solving abilities and their preferred problemsolving approach. The research is therefore valuable to any Accounting educator, as well as the institutional bodies guiding accounting education and its syllabi. It is hoped also that some of the findings will inspire other educational institutions to promote a framework-based approach in an innovative manner. / MCom (Accountancy), North-West University, Potchefstroom Campus, 2015

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)

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)