The purpose of this study is to find out teachers view on manipulatives as a way to concretize a certain mathematical content and to highlight knowledge and experiences within the range of using manipulatives to concretize. By answering the questions below different approaches a teacher may have towards the manipulatives and how that may impact on student’s learning will also be discussed in comparison to mainly traditional and socially constructive theories of learning. What is the teachers view on manipulatives as a way to concretize? What purpose do they have when using manipulatives? According to the teachers, what does it mean to concretize a certain mathematical content? According to the teachers, what connection is there between manipulatives and concretizing? Through interviews and observations conclusions can be made that the teachers are in general positive towards using manipulatives as a way to concretize a certain mathematical content although the definition of what a manipulative is differ somewhat between the teachers. The teachers working with manipulatives do it in a well thought out fashion but more research is needed to furthermore define the purpose of using manipulatives. Few countries spend so much time concretizing and working with manipulatives as Sweden do, but still Sweden score below the OECD-average on the mathematical PISA-tests. You make ask yourself if this then is the right way to go to enhance student’s mathematical knowledge.

The aim of this study is to examine how inductive and deductive concreteization as a didactic method in mathematics teaching can promote the development of knowledge and learning among students. It is also of interest to hear a number of interviewed teachers perceptions about inductive and deductive concretization as a method in mathematics teaching. The examination is for grades 1-3. Theories dealt with in the study are learning promoting theories such as concretization, proximal development zone, conceptualization and creative reasoning.The study's questions will therefore examine:· How can inductive and deductive concretization as a didactic method in mathematics teaching promote the development of knowledge and learning to students?· What perceptions do teachers in grades 1-3 have regarding inductive and deductive concretization as a method of mathematics teaching? In order to answer the study's questions, qualitative methods have been used through interviews with teachers and observations in classrooms. The conclusions of the analysis of material shows that concretization through inductive and deductive methods helps students to participate in situations where different mathematical didactic consequences arise in the teaching based on the theories.

Testing is recognized as a key and challenging factor that can either boost or halt the game development in the mobile game industry. On one hand, manual testing is expensive and time-consuming, especially the wide spectrum of device hardware and software, so called fragmentation, significantly increases the cost to test applications on devices manually. On the other hand, automated testing is also very difficult due to more inherent technical issues to test games as compared to other mobile applications, such as non-native widgets, nondeterminism , complex game strategies and so on. Current testing frameworks (e.g., Android Monkey, Record and Replay) are limited because they adopt no domain knowledge to test games. Learning-based tools (e.g., Wuji) require tremendous resources and manual efforts to train a model before testing any game. The high cost of manual testing and lack of efficient testing tools for mobile games motivated the work presented in this thesis which aims to explore easy and efficient approaches to test mobile games efficiently and effectively. A new Android mobile game testing tool, called LIT, has been developed. LIT is a lightweight approach to generalize playtest tactics from manual testing, and to adopt the tactics for automatic game testing. LIT has two phases: tactic generalization and tactic concretization. In Phase I, when a human tester plays an Android game G for awhile (e.g., eight minutes), LIT records the tester's inputs and related scenes. Based on the collected data, LIT infers a set of context-aware, abstract playtest tactics that describe under what circumstances, what actions can be taken. In Phase II,LIT tests G based on the generalized tactics. Namely, given a randomly generated game scene, LIT tentatively matches that scene with the abstract context of any inferred tactic; if the match succeeds, LIT customizes the tactic to generate an action for playtest. Our evaluation with nine games shows LIT to outperform two state-of-the-art tools and are reinforcement learning (RL)-based tool, by covering more code and triggering more errors. This implies that LIT complements existing tools and helps developers better test certain games (e.g., match3). / Master of Science / Testing is recognized as a key and challenging factor that can either boost or halt the game development in mobile game industry. On the one hand, manual testing is expensive and time-consuming, especially the wide spectrum of device hardware and software significantly increase cost to test applications on devices manually. On the other hand, automated testing is also very difficult due to more inherent technical issues to test games as compared to other mobile applications. The two factors motivated the work presented in this thesis. A new Android mobile game testing tool, called LIT, has been developed. LIT is a light weight approach to generalize playtest tactics from manual testing, and to adopt the tactics for automatic game testing. A playtest is the process in which testers play video games for software quality assurance. When a human tester plays an Android game G for awhile (e.g., eight minutes),LIT records the tester's inputs and related scenes. Based on the collected data, LIT infers a set of context-aware, abstract playtest tactics that describe under what circumstances, what actions can be taken. In Phase II, LIT tests G based on the generalized tactics. Namely, given a randomly generated game scene, LIT tentatively matches that scene with the abstract context of any inferred tactic; if the match succeeds, LIT customizes the tactic to generate an action for playtest. Our evaluation with nine games shows LIT to outperform two state-of-the-art tools and a reinforcement learning (RL)-based tool, by covering more code and triggering more errors. This implies that LIT complements existing tools and helps developers better test certain games (e.g., match3)

The purpose of this study is to investigate how the teaching of mathematics is reflected in the students' understanding of the concept of the subtraction. The empirical data is based on observations in the classroom and student interviews. The understanding of the concept of the subtraction is shown through vocabulary and choice of examples and representations. The study used both qualitative methods and quantitative reports. The data is represented by one school and one classroom in grade three.  The theoretical framework is based on Liping Mas Subject Matter Knowledge and the variation theory of Marton and Booth and the relationship between these frameworks and concepts of variation, concretization, aids, subtraction and types of subtraction.  The results show that the impact of education is that subtraction is understood as the invers of addition. Complement and add to, is the type of strategy most frequently used, followed closely by the strategy remove and count down. The strategy compare is the least used. The observations in the classrooms shows several aspects and variations of the concept of the subtraction. Although the number line, and various forms of representation used in teaching has shown small effects of these aids in the students' own counting. The conclusions that can be drawn is that more and other metaphors and tools are needed in education to deepen students' understanding of the concept of the subtraction. They also need to be connected in the teaching. The language and the mathematical ideas discussed plays a critical role in the pupils’ acquisition of understanding.

Magister Artium - MA / This thesis will critically analyse two theatrical adaptations of J. M. Coetzee's Foe (1986). Primarily, this thesis will be seeking to understand the complex relationship of the primary text to its adaptations more closely, regarding them not only as second-order versions or interpretations of the novel, but also to consider the way they may retrospectively construct new readings and understandings of the source text. This thesis will not only consider the way in which Foe is used in the adaptations but also how Robinson Crusoe (1719) influenced the adaptors and adaptive process. Theories of adaptation will be discussed, drawing extensively on work by Linda Hutcheon (2006) and Robert Stam (2005). One of the key ideas in adaptation theory is that adaptive fidelity to the source text is neither possible nor desirable, but that adaptation is a more complex, multi-layered intertextual and intermedial interplay of fictional material. One of the aims of this thesis is to ask whether or not Foe can be successfully transposed to the stage. This thesis will serve as a close analysis of the two theatrical adaptations, focusing on the beginning and endings of the respective adaptations. This research will contribute a new approach to Coetzee studies and to Foe in particular by exploring how these texts can lead to a broader understanding of Coetzee's work and the way it crosses into different media.

Research indicates that a more hands-on education in mathematics could improve how students relate to mathematics. Laboratory mathematics is a way of making mathematics more concrete.  How is the purpose of laboratory mathematics perceived? This thesis has its focus on the pupils’ perceptions of the purpose of laboratory mathematics, but the intention of the teacher involved is also investigated. The main research questions asked were: What is the teacher's definition of laboratory mathematics? Which is the teacher's purpose in using laboratory education? How do the students perceive the purpose of the laboratory teaching of mathematics? To answer the questions, I conducted a series of qualitative interviews. Data has been collected in a 3rd grade in Stockholm.  I interviewed a teacher and 17 students.  Results show that the teacher uses laboratory materials to ease the learning of mathematics and to concretize the content of mathematics. By using the phenomenographic method, I got five different preconceptions that students have about the purpose of laboratory education: Laboratory mathematics is for students who have difficulty with mathematics, laboratory mathematics allows more concentration in the classroom, using laboratory materials makes it easier to calculate, laboratory mathematics will help me when I calculate mathematics in every day situations and, finally when I use laboratory mathematics, I work with my hands. The study reaches the conclusion that teachers need to a highlight better the pedagogic purpose for the pupils to use laboratory mathematics.  Laboratory mathematics is in need of a higher status so that more students want to work with laboratory materials.

This study focuses on the way in which Willem Boshoff aesthetically con-cretized the historical memories of Afrikaners and their influence on their notion of power and identity formation. For this purpose a selection was made of Boshoff’s language-based conceptual installations. During the colonial and apartheid eras South Africa had a long history, which was characterized by people in power who encountered other population groups from a vantage point of superiority implying subjection. This implied that the particular in-terests of the people in power were generalized across the whole of society and imposed on all population groups as generalized interests. Where the in-dividual interests did not correspond to the general interests of society in its totality, the interests of the individual were negated and ignored. It can there-fore be stated that the utopia of those in power became the proverbial hell of the other. The study emanates from Ricoeur’s plea for a critical and imaginative en-counter with history so that other perspectives on traumatic events can be developed. Such an approach creates the possibility of opening up the unreal-ized promises of the past for the present and leading to the future. It further proceeds from the assumption that if we are faithful to the past, we will also be faithful to “the more” of the past or that which transcends the past. My ap-proach is in line with that of Verbeeck, who – tying in with Ricoeur – ad-vocated an anachronistic encounter with and interpretation of history. What is meant by aesthetic concretization in this study is that Willem Boshoff conceptually expresses his artistic interpretation and visual manifestation of philosophical ideas on Afrikaners’ memories of power and identity. He makes real (real-ises) and gives shape to these philosophical ideas. For this purpose three dates in the historical narratives of Afrikaners were selected, which had an important impact on Afrikaners’ notions of power and identity formation: 31 May 1902 –The end of the Anglo-Boer War and the demise of the Boer Republics and the freedom of Afrikaners; 31 May 1961 – The formation of the Republic of South Africa under the leadership of the National Party, and 27 April 1994 – The first democratic elections in South Africa, and the Afrikaners’ total loss of power. The reading and interpretation of Boshoff’s installations were undertaken with-in the framework of Adorno’s dialectical distinction in his aesthetic theory be-tween the Inhalt and the Gehalt of works of art. Adorno regards everything that appears in the work of art, viz. everything that the artist gives form to, as Inhalt [content]. Gehalt, on the other hand, refers to the truth content of works of art, which according to him resides in the specific negation [German: bestimmte Negation] of the untruth of an inhuman society. For Adorno bestimmte Negation signifies a break both with that which exists [in other words a negation of the predominance of a false reality] and with the continuity between the present and the future [the salvation of the moment or element which holds promise of something, which goes beyond that which exists, and refers to something better]. In Adorno’s view works of art are tho-roughly historically determined. According to Adorno the history of society is sedimented in the material, the constellations and the form elements of works of art. What is meant by this is that the artistic material which an artist [in this study Boshoff] utilizes, is not only words, pigments, or rock, but is everything that is pre-formed by history that the artist uses. Because history sediments in the material and because the material of a work of art is taken from reality, but in a fragmented fashion, the work of art becomes a monad – that is auto-nomous and windowless, because the work of art, apparantly, has no links to or relationships with recognizable reality or with other works of art. I argue that the exposé of the memories of Afrikaners of cultural and political domination, with historical narratives as a source, and the influence of these on their visions of power and identity, offers a framework for the reading and interpretation of selected installations. In these selected installations, Boshoff offers immanent criticism of the above unequal power relations and con-comitant views of identity. Through striving for the harmonious and the good as ethical and aesthetic principles in his installations focused on social inter-action, he makes a contribution to the creation of a more humanitarian society. / Thesis (PhD (Art History))--North-West University, Potchefstroom Campus, 2012

This study focuses on the way in which Willem Boshoff aesthetically con-cretized the historical memories of Afrikaners and their influence on their notion of power and identity formation. For this purpose a selection was made of Boshoff’s language-based conceptual installations. During the colonial and apartheid eras South Africa had a long history, which was characterized by people in power who encountered other population groups from a vantage point of superiority implying subjection. This implied that the particular in-terests of the people in power were generalized across the whole of society and imposed on all population groups as generalized interests. Where the in-dividual interests did not correspond to the general interests of society in its totality, the interests of the individual were negated and ignored. It can there-fore be stated that the utopia of those in power became the proverbial hell of the other. The study emanates from Ricoeur’s plea for a critical and imaginative en-counter with history so that other perspectives on traumatic events can be developed. Such an approach creates the possibility of opening up the unreal-ized promises of the past for the present and leading to the future. It further proceeds from the assumption that if we are faithful to the past, we will also be faithful to “the more” of the past or that which transcends the past. My ap-proach is in line with that of Verbeeck, who – tying in with Ricoeur – ad-vocated an anachronistic encounter with and interpretation of history. What is meant by aesthetic concretization in this study is that Willem Boshoff conceptually expresses his artistic interpretation and visual manifestation of philosophical ideas on Afrikaners’ memories of power and identity. He makes real (real-ises) and gives shape to these philosophical ideas. For this purpose three dates in the historical narratives of Afrikaners were selected, which had an important impact on Afrikaners’ notions of power and identity formation: 31 May 1902 –The end of the Anglo-Boer War and the demise of the Boer Republics and the freedom of Afrikaners; 31 May 1961 – The formation of the Republic of South Africa under the leadership of the National Party, and 27 April 1994 – The first democratic elections in South Africa, and the Afrikaners’ total loss of power. The reading and interpretation of Boshoff’s installations were undertaken with-in the framework of Adorno’s dialectical distinction in his aesthetic theory be-tween the Inhalt and the Gehalt of works of art. Adorno regards everything that appears in the work of art, viz. everything that the artist gives form to, as Inhalt [content]. Gehalt, on the other hand, refers to the truth content of works of art, which according to him resides in the specific negation [German: bestimmte Negation] of the untruth of an inhuman society. For Adorno bestimmte Negation signifies a break both with that which exists [in other words a negation of the predominance of a false reality] and with the continuity between the present and the future [the salvation of the moment or element which holds promise of something, which goes beyond that which exists, and refers to something better]. In Adorno’s view works of art are tho-roughly historically determined. According to Adorno the history of society is sedimented in the material, the constellations and the form elements of works of art. What is meant by this is that the artistic material which an artist [in this study Boshoff] utilizes, is not only words, pigments, or rock, but is everything that is pre-formed by history that the artist uses. Because history sediments in the material and because the material of a work of art is taken from reality, but in a fragmented fashion, the work of art becomes a monad – that is auto-nomous and windowless, because the work of art, apparantly, has no links to or relationships with recognizable reality or with other works of art. I argue that the exposé of the memories of Afrikaners of cultural and political domination, with historical narratives as a source, and the influence of these on their visions of power and identity, offers a framework for the reading and interpretation of selected installations. In these selected installations, Boshoff offers immanent criticism of the above unequal power relations and con-comitant views of identity. Through striving for the harmonious and the good as ethical and aesthetic principles in his installations focused on social inter-action, he makes a contribution to the creation of a more humanitarian society. / Thesis (PhD (Art History))--North-West University, Potchefstroom Campus, 2012

In previous research it has been concluded that mathematical texts more often than not test a students reading comprehension rather than their mathematical knowledge. It has also been concluded that in order to promote language learning in the mathematics classroom the teacher has a great responsibility to not only make the oftentimes abstract mathematical key concepts clear and understandable but also the concepts, methods, calculations and operational rules. In order to do so teachers must be well equipped to teach and to keep the right focus when working with concretion such as supporting images or practical mathematics such as the use of manipulatives in the classroom. My study was aimed at further researching what learning activities are being used in the classroom to promote mathematical language development which is a fundamental part of the mathematics syllabus and how its being described in the view of teachers and of students alike. My study was also aimed at looking at the relation between the learning activities that are being used to promote language skills in the Swedish language classroom. I chose to do individual interviews of teachers, group interviews of students as well as a classroom observation. My theoretical foundation was a sociocultural perspective. The results of my study show that the verbal interaction between students and teachers or students and other students played an integral part in most learning activities. It was also in this interaction that most of the formative assessments were taking place. Furthermore the results showed that those students whose aim was to find mathematical connections and seeing how different mathematical concepts interact with each other had come farther in developing generalizable skills rather than the students whose focus was to understand key concepts.

Abstraction-guided simulation is a promising semi-formal framework for design validation in which an abstract model of the design is used to guide a logic simulator towards a target property. However, key issues still need to be addressed before this framework can truly deliver on it's promise. Concretizing, or finding a real trace from an abstract trace, remains a hard problem. Abstract traces are often spurious, for which no corresponding real trace exits. This is a direct consequence of the abstraction being an over-approximation of the real design. Further, the way in which the abstract model is constructed is an open-ended problem which has a great impact on the performance of the simulator. In this work, we propose a novel approaches to address these issues. First, we present a genetic algorithm to select sets of state variables directly from the gate-level net-list of the design, which are highly correlated to the target property. The sets of selected variables are used to build the Partition Navigation Tracks (PNTs). PNTs capture the behavior of expanded portions of the state space as they related to the target property. Moreover, the computation and storage costs of the PNTs is small, making them scale well to large designs. Our experiments show that we are able to reach many more hard-to-reach states using our proposed techniques, compared to state-of-the-art methods. Next, we propose a novel abstraction strengthening technique, where the abstract design is constrained to make it more closely resemble the concrete design. Abstraction strengthening greatly reduces the need to refine the abstract model for hard to reach properties. To achieve this, we efficiently identify sequentially unreachable partial sates in the concrete design via intelligent partitioning, resolution and cube enlargement. Then, these partial states are added as constraints in the abstract model. Our experiments show that the cost to compute these constraints is low and the abstract traces obtained from the strengthened abstract model are far easier to concretize. / Master of Science