This essay is about how thinking skills are requested in examinations in the course religion 1 in Swedish upper secondary schools. To investigate this an analysis template has been created which is constructed from Göran Svanelids theory the big five, who explains which abilities the Swedish curriculum demands. The main question for this study is How clear and to what extent are the abilities who Göran Svanelids theory the big five points out in exams within the course religion 1? To answer this, three support questions has been made. The First is about how these abilities change between the program they are used. The second one is how the form of examination affects the possibilities to show the abilities and lastly how the kind of question affects the possibility to show the abilities. The analysis template and theory derive from the Swedish curriculum and the lecturer Göran Svaneldis analysis of the curriculum. He found five thinking skills or abilities which all subjects value and who the pupils are supposed to learn. These are; concept skills, the skill to analyse, communicative skills, the ability to perform a procedure and metacognition. These abilities have been operationalized to become a theory to inspect how well and to what extent they are asked for in an examination. Therefore, this study is based on text interpretation of the examinations, with an aim of being both qualitative and quantitative. Out of the total amount of 106 emails sent to principals, teachers and administrative personnel at upper secondary school’s total of 38 examinations were collected1. 14 out of these were written tests, 16 were written essays and eight were oral examinations. The result displays that all examinations ask for the abilities but not all types of questions in the examinations ask for all abilities. The closed type of question only gives the opportunity to show concept skills. The concept skill is the most visible ability in all exams, the secondly most visible skill is the communicative skill, thirdly the analysis skill, fourthly is the skill of procedure and fifth and lastly, the metacognitive skill. The conclusion is that programs who aim to ensue further studies ask for all abilities to a larger extent and with a higher level of clarity. While the vocational program who aim to ensure a working career after upper secondary school ask for the abilities with a lesser clarity. Written essays are the best form of examination to ask for the abilities to a larger extent and with a higher clarity than oral examinations or written tests.

Esta tesis muestra una radiografía de las evaluaciones de Historia de España en COU y Bachillerato (a través de los recuerdos de 1523 alumnos entre 1993-2003), y de los protocolos de los exámenes (410 realizados por el profesorado entre 2002-2004), en la CC.AA. de la Región de Murcia. Entre los resultados más relevantes, destacar: la influencia que los aspectos formales de las evaluaciones y los exámenes tienen tanto en los contenidos por los que se les pregunta a los alumnos como en el tipo de aprendizaje que éstos adquieren; la presencia predominante de preguntas que requieren principalmente la memorización de los conocimientos; las relaciones existentes entre los tipos de preguntas y las capacidades cognitivas solicitadas en las pruebas; la evaluación de unos temas de la Historia de España en detrimento de otros; y la influencia que dos referentes como son selectividad y decreto de currículum, tienen en las pruebas estudiadas. / This thesis shows a radiograph of the assessments of History of Spain in COU and Bachillerato (through the memories of 1523 students between 1993-2003), and the protocols of the examinations (410 made by teachers between 2002-2004) in the Autonomous Community of the Region of Murcia. Among the most relevant results, include: the influence of the formal aspects of assessments and examinations have so much in the content for which one asks the students as the type of learning that they acquire, the predominance of questions mainly require the memorization of knowledge, relations between the types of questions and cognitive abilities tests requested and the evaluation of the subjects of the History of Spain at the expense of others, and the influence of two references such as selectivity and Decree of the curriculum, the tests are studied.

In this thesis I study metric aspects of finite nearly simple groups. Its four distinct chapters deal with four different questions. In the first chapter, I give a full description of the normal subgroup lattice of any algebraic ultraproduct of universal finite quasisimple groups. In the second, I investigate approximation questions for arbitrary abstract and topological groups by families of finite groups with conjugacy-invariant norms. In the third chapter, I prove that the map induced by any non-trivial word on the metric ultraproduct of classical groups of Lie type of unbounded rank is always surjective using cohomological and algebraic methods. In the last chapter, it is proved that (simple) metric ultraproducts of finite classical groups of Lie type of unbounded rank with different field sizes are always non-isomorphic. Also, if the field sizes are equal, two such ultraproducts can only be isomorphic if the Lie types are equal or one Lie type is orthogonal and the other symplectic.:Introduction 0 Notation, basic definitions, and facts 0.1 Group theory 0.2 Some ring and field theory 0.3 Ultraproducts and norms 1 The normal subgroup lattice of an algebraic ultraproduct 1.1 Introduction 1.2 Auxiliary geometric results 1.3 Relative bounded normal generation in universal finite quasisimple groups 1.4 The lattice of normal subgroups 2 Metric approximation of groups by finite groups 2.1 Introduction 2.2 Preliminaries 2.2.1 On C-approximable abstract groups 2.2.2 On C-approximable topological groups 2.3 On Sol-approximable groups 2.4 On Fin-approximable groups 2.5 On the approximability of Lie groups 3 Word maps are surjective on metric ultraproducts 3.1 Introduction 3.2 Symmetric groups 3.2.1 Power words 3.2.2 The cycle structure of elements from PSL_2(q) 3.2.3 Effective surjectivity of word maps over finite fields 3.2.4 Proof of Theorem 3.1 3.3 Unitary groups 3.3.1 Proof of Theorem 3.3 3.3.2 Further implications 3.3.3 Concluding remarks 3.4 Finite groups of Lie type 3.4.1 The linear case 3.4.2 The case of quasisimple groups of Lie type stabilizing a form 3.4.3 An alternative way of proving Theorem 3.1 using wreath products 4 Isomorphism questions for metric ultraproducts 4.1 Introduction 4.2 Description of conjugacy classes in S_U, GL_U(q), and PGL_U(q) 4.3 Characterization of torsion elements in S_U , GL_U(q), and PGL_U(q) 4.4 Faithful action of S_U and PGL_U(q) 4.5 Centralizers in S_U , GL_U(q), Sp_U(q), GO_U(q), and GU_U(q) 4.6 Centralizers in PGL_U(q), PSp_U(q), PGO_U(q), and PGU_U(q) 4.7 Double centralizers of torsion elements 4.7.1 The case S_U 4.7.2 The case PGL_U(q), PSp_U(q), PGO_U(q), and PGU_U(q) 4.8 Distinction of metric ultraproducts 4.8.1 Computation of e_G(o) when gcd{o,p}=gcd{o,|Z|}=1 4.8.2 Proof of Theorem 4.1 Index of Symbols Index Bibliography / In dieser Doktorarbeit studiere ich metrische Aspekte von endlichen fast-einfachen Gruppen. Ihre vier Kapitel beschäftigen sich mit vier unterschiedlichen Themenfeldern. Im ersten Kapitel gebe ich eine vollständige Beschreibung des Normalteilerverbandes eines algebraischen Ultraproduktes von universellen endlichen quasieinfachen Gruppen. Im zweiten beschäftige ich mich mit Approximationsfragen für beliebige abstrakte und topologische Gruppen durch Familien von endlichen Gruppen, auf denen eine konjugationsinvariante Norm erklärt ist. Im dritten Kapitel beweise ich, dass die Abbildung auf einem metrischen Ultraprodukt von klassischen Gruppen vom Lie-Typ von unbeschränktem Rang, die von einem beliebigen nicht-trivialen Wort induziert wird, immer surjektiv ist. Dabei verwende ich sowohl kohomologische als auch algebraische Methoden. Im letzten Kapitel beweise ich, dass (einfache) metrische Ultraprodukte von klassischen endlichen Gruppen vom Lie-Typ von unbeschränktem Rang mit unterschiedlicher Körpergröße immer nicht-isomorph sind. Ist die Körpergröße gleich, so können zwei solche Gruppen nur dann isomorph sein, falls sie auch denselben Lie-Typ haben, oder eine vom orthogonalen Typ und die andere vom symplektischen ist.:Introduction 0 Notation, basic definitions, and facts 0.1 Group theory 0.2 Some ring and field theory 0.3 Ultraproducts and norms 1 The normal subgroup lattice of an algebraic ultraproduct 1.1 Introduction 1.2 Auxiliary geometric results 1.3 Relative bounded normal generation in universal finite quasisimple groups 1.4 The lattice of normal subgroups 2 Metric approximation of groups by finite groups 2.1 Introduction 2.2 Preliminaries 2.2.1 On C-approximable abstract groups 2.2.2 On C-approximable topological groups 2.3 On Sol-approximable groups 2.4 On Fin-approximable groups 2.5 On the approximability of Lie groups 3 Word maps are surjective on metric ultraproducts 3.1 Introduction 3.2 Symmetric groups 3.2.1 Power words 3.2.2 The cycle structure of elements from PSL_2(q) 3.2.3 Effective surjectivity of word maps over finite fields 3.2.4 Proof of Theorem 3.1 3.3 Unitary groups 3.3.1 Proof of Theorem 3.3 3.3.2 Further implications 3.3.3 Concluding remarks 3.4 Finite groups of Lie type 3.4.1 The linear case 3.4.2 The case of quasisimple groups of Lie type stabilizing a form 3.4.3 An alternative way of proving Theorem 3.1 using wreath products 4 Isomorphism questions for metric ultraproducts 4.1 Introduction 4.2 Description of conjugacy classes in S_U, GL_U(q), and PGL_U(q) 4.3 Characterization of torsion elements in S_U , GL_U(q), and PGL_U(q) 4.4 Faithful action of S_U and PGL_U(q) 4.5 Centralizers in S_U , GL_U(q), Sp_U(q), GO_U(q), and GU_U(q) 4.6 Centralizers in PGL_U(q), PSp_U(q), PGO_U(q), and PGU_U(q) 4.7 Double centralizers of torsion elements 4.7.1 The case S_U 4.7.2 The case PGL_U(q), PSp_U(q), PGO_U(q), and PGU_U(q) 4.8 Distinction of metric ultraproducts 4.8.1 Computation of e_G(o) when gcd{o,p}=gcd{o,|Z|}=1 4.8.2 Proof of Theorem 4.1 Index of Symbols Index Bibliography