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Serious games are digital games that have an additional goal beyond entertainment. Recently, many studies have explored different quality criteria for serious games, including effectiveness and attractiveness. Unfortunately, the double mission of serious games, that is, simultaneous achievement of intended effects (serious part) and entertainment (game part), is not adequately considered in these studies. This paper aims to identify essential quality criteria for serious games. The fundamental goal of our research is to identify important factors of serious games and to adapt the existing principles and requirements from game-related literature to effective and attractive serious games. In addition to the review of the relevant literature, we also include workshop results. Furthermore, we analyzed and summarized 22 state-of-the-art serious games for education and health. The selected best-practice serious games either prove their effectiveness through scientific studies or by winning game awards. For the analysis of these games, we refer to “DIN SPEC 91380 Serious Games Metadata Format.” A summarized text states quality criteria for both the serious and the game part, and especially the balance between them. We provide guidelines for high-quality serious games drawn from literature analysis and in close cooperation with domain experts.

In Germany, the Abitur is the highest qualification granted at the end of secondary education after 12 or 13 years of schooling; it provides a general university entrance qualification. Traditionally, written and oral examinations are required to obtain the Abitur. Until 1990, there were mainly decentralized examinations in mathematics in West Germany (Federal Republic of Germany [FRG]), which were taken after 13 school years, and a centralized examination that students took after 12 years of school in East Germany (German Democratic Republic [GDR]). In the unified Germany, examinations are now increasingly set by the 16 individual federal states. This paper has a special focus on changes and permanent features in the written Abitur examination in mathematics in Germany in the context of the social changes caused by the German reunification in 1990. These changes since 1990 are described with regard to the initial situation and framing conditions for the written Abitur examination. Two time periods are considered: (1) the examination situation in the FRG and GDR before 1990 and (2) the changes in the five eastern German federal states (former GDR) under the system change and accession to the FRG after 1990 but before the PISA shock.

This paper presents the outcomes of the work of the ICME 13 Survey Team on "Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research". It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as mathematical competence and competencies, mathematical proficiency, and mathematical practices, amongst others. The paper provides theoretical analyses of these notions--under the generic heading of mathematical competencies--and gives an overview of selected research on and by means of them. Furthermore, an account of the introduction and implementation of competency notions in the curricula in various countries and regions is given, and pertinent issues are reviewed. The paper is concluded with a set of reflections on current trends and challenges concerning mathematical competencies.

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence structure model comprising five competence dimensions was developed. These are based on four types of representation (graph, numerical table, algebraic equation and situational description) and correspond to the skill to translate from one type of representation to another. The following study was aimed to examine the facets of the model. The 5-dimensional model was empirically tested with a sample of N = 645 students of grades 9 and 10. This was accomplished by comparing competing item response models with regard to model fit using information criteria measures. In comparison with other possible model structures, our postulated 5-dimensional model showed the best model fit, suggesting that all translations are relevant for competence assessment and development. Furthermore, in order to allow for the identification of structural components of cognitive actions, the employed tasks used in the empirical testing were divided into categories with regard to the different demands of cognitive action. Our results suggest that cognitive actions may have a specific dimensional structure. These findings can contribute to a better diagnostic approach concerning specific strengths and weaknesses and can therefore foster students' competencies.

The basis for individual students' instructional support by teachers is an individual diagnosis of one's learning advances and difficulties. Even though sophisticated diagnostic tools exist, it remains an open question how diagnosis and learning can be merged into a consistent pedagogical method to support both teachers and students with feedback about the learning process. Aspects like the usage of open format questions, social interdependencies and heterogeneity, group-forming processes and the teachers supervision issue are taken into account. We propose a model for integration of peer assessment functionality for learning into a computer-based Adaptive Diagnostic Learning Environment to solve central problems of classroom diagnostic assessment, adaptive learning and knowledge transfer between peers in a classroom environment. The research approach focused on math learning scenarios for evaluation, but is expected to be applicable for other educational content as well. In the following paragraphs we identify several problems in classroom scenarios to be addressed, describe the model of the underlying approach, show the implementation details and explain the evaluation setup. (Contains 5 figures.)