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This doctoral thesis concerns the theoretical basis, development and validation of a multipart instrument to provide students of educational sciences with some feedback about their competence-development (instrument KIPBI) and report to their experiences in practical training (instrument EIPRA). It thus supports the reflection capability of the student teachers. Both instruments are part of an online self-assessment (Tour 3-RLP), which is similar to the Career-Counselling for Teachers (CCT, see cct-germany.de) but unlike this, does not focus on ability but on competence-development. The instruments serve to promote the professional development of student teachers. This is a goal of the reformed concept of teacher training in Rhineland-Palatinate, the so-called KMK-standards for teacher training and education, the Rhineland-Palatinate "Framework School Quality" as well as of handouts and manuals for the implementation of in-depth practical training in teacher education. The first part of this dissertation describes the theoretical framework for the development of instruments for the "CCT-Tour 3-RLP" starting with the issue of professionalization in teacher profession. Historical dimensions and their associated approaches to teacher education research are manifold. They range from the aspect of "teacher personality" to the implementation of teaching-standards and standards for teacher education and output orientation. While within the 60s and 70s the personality approach was pivotal in teacher education research, nowadays expertise-development and models of skills-development are discussed as central issues. Therefore, the theory section describes the influence of previous research-paradigms and their semantic content upon the current trend. As one part of the analysis the construct of "teacher self-efficacy" will be explained, along topological and typological models of competence-development.
Furthermore the practical elements of teacher education and their contribution to the professionalization of future teachers are presented. Professional reflection is assumed to be a basis for developing expertise. Therefore it is necessary to investigate how theoretical knowledge can be "transferred" to practical performance. A unifying theory connecting the integration hypothesis (assuming that knowledge is directly transferable into practice) with the differentiation hypothesis (teacher skills form their own knowledgebase independent from both theoretical and practical knowledge) is provided by cognitive psychology (particularly by research on expertise). Endpoint of the theoretical discourse is the evaluation of the referred theoretical positions and their meaning for the Rhineland-Palatinate reform of teacher education and teacher training and the role that the "Tour 3-RLP" is going to play in this context.In the empirical part the methodical and methodological steps for validation of the instruments are discussed. At first the Swiss standards for teacher profession (developed by the Pädagogische Hochschule Schwyz, Central Switzerland) are presented. They can serve as a model building a competency-oriented tool that refers to competency stages.
An analysis of various methods for the setting of cut-scores aiming to develop appropriate competency levels is also a fundament for the procedures developed in the context of the empirical investigations. The results of the pilot-study and a follow-up study conducted with both described instruments (KIPBI and EIPRA) show that the instruments for competence-measurement fulfil the requirements of psychometric criteria (like a scale-structure) and tend to support student teachersÂ´ self-reflection. Core concern of both instruments is the promotion of students, realized by the online-self-assessment by the use of appropriate feedback structures and related recommendations for action.The final chapter of this thesis includes the discussion of the results of the validation and implementation study. This final view is devoted to the question whether or not competency-modeling or standard-based approaches to professionalization are the only possible accesses to map and explain skills development. The role of reflection seems to be important for both the integral and the differential approach and interconnects them.

Mathematical modeling describes the processes being performed by people who try to solve real world problems mathematically or who try to solve mathematical word problems. The literature on mathematical modeling is based on the so-called modeling cycle (Blum, 2003), which consists of five substages, that describe the course of the problem-solving process. As a first step (Structuring), the problem situation is being understood by the modeler and the most crucial elements of the problem are identified. The modeler then translates those elements to a mathematical language (Mathematising), where they are now presented in the form of equations, numbers, operators and symbols, i.e. in the form of a mathematical model. In the third step (Solving), the model is used to come to a mathematical solution to the problem, which in the next step (Interpretation) is then re-translated into real-world information and gives an answer to the question that has been raised in the problem. The last step describes the Validation of the whole problem-solving process. If the modeler comes to the conclusion that his solution is wrong or not optimal, the modeling cycle starts from the beginning. The modeling cycle functions as a descriptive model of modeling processes, because it describes how modeling is carried out by students. On the other hand, it also functions as a normative model, because it makes prescriptions on how one should behave, when solving problems mathematically. However, there do not exist any empirical studies to prove neither the descriptive nor the normative character of the modeling cycle. This thesis shows, that the suitability as a descriptive model can only be affirmed with restrictions. Validation could not be observed in any of the subjects taking part in the first study and the sequence of the remaining four processes also diverged from the theoretically postulated order. A revised version of the modeling cycle as a recursive model is therefore proposed. In the second study, the suitability as a normative model was explored, by separately assessing the four processes Structuring, Mathematising, Solving and Interpretation with newly designed items. The four scales were validated with several criteria, one of them the ability to solve modeling tasks, which confirms the normative function of the modeling cycle. In order to help promote modeling competency in young learners, it is necessary to find ways for diagnosing modeling competency as early as at the end of primary school. By generating items for the four sub-competencies Structuring, Mathematising, Solving and Interpretation a basis has been founded to do this in an objective, reliabel and valid way.