There is a wide consensus that including mathematical modeling into the curricula is an important aim. A lot of attention has been spent on the realistic problems whereas their embedding in a classroom situation is less investigated so far, although the methodical arrangements are of major importance for initiating students’ activities. In this paper, the implementation of the modeling task “swimming pool” in mathematics education in two lessons is compared concerning learning arrangement and teaching methods in depth with respect to the students’ activities. Two videos about this implementation will be shown and discussed in this workshop. They are supposed to demonstrate in which different ways teachers engage in modeling. The aim is to show teachers, especially those without experience in teaching modeling, how modeling tasks can be implemented.

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Due to its economic importance engineering design as a creative design problem solving has been the research subject of psychologists and design engineers for several years. Observations of designer's thinking and action processes show that especially in the early stages of the design process, in which requirements are clarified and ideas are developed, generating solutions is largely associated with the use of simple external representations such as sketches and material (physical) models. In the represented thesis the use and functions of such external aids were investigated at first with a questionnaire study consulting designers (N = 106) of different industries. The results demonstrate the dominance of sketches as well as the increasing use of CAD already in the early stages of product development. In contrast models are applied to a lesser extent. Thereby simple external aids are not only used as memory-relieving external information storages, but do also support solution development and testing, serve as an analysis aid and contribute helpfully to documentation and communication. Further in an experimental study the use and functions of sketching and manual modelling applied by engineering students and designers (N = 61) while working on two design problems of different complexity with free choice of the support form were analysed. The results verify the essential importance of sketching for the design process, since almost all subjects used sketches to deal with the two design problems, while material models were hardly applied. Again the sketches fulfil different functions, so besides documentation they mainly support solution development. These statement based findings that sketches in addition to their function as external storages for memory relief serve also as thinking aids, thus support the generating and further developing of solution concepts, could be confirmed by observation data based on the analysis of the individual design processes. Finally recommendations for the design of new and advanced computer-assisted design aids could be given. / Das Konstruieren als schöpferisch-entwerfendes Problemlösen (design problem solving) ist aufgrund seiner wirtschaftlichen Bedeutung seit längerem Gegenstand der Forschung von Psychologen und Konstruktionswissenschaftlern. Beobachtungen des Vorgehens des Konstrukteurs zeigen, daß insbesondere in den frühen Phasen des konstruktiven Entwurfsprozesses, in denen Anforderungen geklärt und Ideen generiert werden, die Lösungsentwicklung in hohem Maße durch einfache externe Hilfsmittel, wie Skizzen und gegenständliche Modelle, unterstützt wird. In der dargestellten Dissertation wurde Einsatz und Nutzen dieser Hilfsmittel zunächst anhand einer Befragung von Konstrukteuren (N = 106) verschiedener Branchen untersucht. Die Ergebnisse belegen die Dominanz von Skizzen sowie die Zunahme der Nutzung von CAD bereits in den frühen Phasen der Produktentwicklung. Modelle finden dagegen weniger häufig Verwendung. Einfache externe Hilfsmittel werden dabei nicht nur als gedächtnisentlastende externe Speicher eingesetzt, sondern unterstützen ebenso die Lösungsentwicklung und -überprüfung, dienen als Analysehilfe und tragen hilfreich zur Dokumentation und Kommunikation bei. Weiterhin wurde in einer experimentellen Studie der Einsatz und die Funktionen des Skizzierens und manuellen Modellierens bei der Bearbeitung zweier Konstruktionsprobleme unterschiedlicher Komplexität durch Maschinenbaustudenten und Konstrukteure (N = 61) bei freier Wahl der Unterstützungsform näher untersucht. Die Ergebnisse verifizieren die essentielle Bedeutung des Skizzierens für den konstruktiven Entwurfsprozeß, da nahezu alle Probanden die beiden Konstruktionsprobleme von Anfang an skizzierend bearbeiteten, während einfache Modelle so gut wie gar nicht eingesetzt wurden. Die Skizzen erfüllten wiederum verschiedene Funktionen, neben der Dokumentation wurden sie v.a. zur Lösungsentwicklung verwendet. Dabei konnten diese auf Aussagen beruhenden Erkenntnisse, daß Skizzen neben der Gedächtnisentlastung auch eine Denkhilfe bieten, durch aus der Analyse der Entwurfsprozesse gewonnene Beobachtungsdaten bestätigt werden. Abschließend wurden Gestaltungsempfehlungen für die Neu- und Weiterentwicklung computergestützter Hilfsmittel des konstruktiven Entwurfsprozesses formuliert.

Nowadays, one of the urgent issues in the management of river basin resources as land degradation, especially soil erosion risk occurs due to complex factors of climate, cultivation practices of human and impacting of the operation of socio-economic development taking place in the basin. Soil erosion has been considered as the primary cause of soil degradation since soil erosion leads to the loss of topsoil and soil organic matters, which are essential for the growing of plants. Ta Trach river watershed, is a mountainous basin lying to the West - South of Thua Thien Hue province, having complex terrain. The result of this study showed that the amount of sediment yield accounts for high percentage. The average annual sedimentation is 41.60 tones per hectometer in the period of 2005 to 2010, soil erosion were classified by 5 levels. In which, the less deleterious erosion level still occupies high percentage with more than 55 % of watershed area. The main area of less deleterious soil erosion was located at high topography and high slope. The area of deleterious soil erosion occupies percentage lower than 22.63% of the entire basin, but it is also a warning sign to the extent of land degradation taking place in the basin if the erosion rate increases in the future. / Ngày nay, một trong những vấn đề cấp bách trong quản lý tài nguyên lưu vực sông là sự thoái hóa đất và đặc biệt là nguy cơ xói mòn đất xảy ra do yếu tố khí hậu phức tạp, phương thức canh tác của con người và tác động của những hoạt động phát triển kinh tế - xã hội đang diễn ra ở lưu vực. Lưu vực sông Tả Trạch là một lưu vực miền núi nằm về phía Tây - Nam của tỉnh Thừa Thiên Huế, có địa hình khá phức tạp. Mục tiêu của nghiên cứu này là ứng dụng công cụ SWAT để mô phỏng xói mòn đất ở lưu vực sông Tả Trạch thuộc tỉnh Thừa Thiên Huế từ năm 2005 đến năm 2010. Kết quả của nghiên cứu cho thấy lượng đất bồi lắng ở lưu vực chiếm tỷ lệ cao, trung bình mỗi năm bồi lắng 41.60 tấn/ha trong giai đoạn 2005 đến 2010, mức độ xói mòn được phân cấp thành 5 cấp xói mòn. Trong đó, mức độ xói mòn ít nguy hại chiếm ở tỷ lệ cao hơn 55 % diện tích lưu vực, chủ yếu phân bố ở những khu vực có địa hình cao, độ dốc lớn. Diện tích xói mòn nguy hại chiếm tỷ lệ thấp hơn 22,63% diện tích toàn lưu vực nhưng đây cũng là một dấu hiệu báo động cho mức độ thoái hóa đất diễn ra ở lưu vực trong tương lai nếu mức xói mòn này tăng lên.

The Comenius Network Project “Developing Quality in Mathematics Education II” funded by the European Commission consists of partners from schools, universities and teacher training centres from eleven European countries. One advantage of the project is the mutual exchange between teachers, teacher trainers and researchers in developing learning material. To support the teachers most effectively the researchers asked the teachers what they wanted the researchers to do. The answer was also a question: How can we identify (good) modelling tasks? A discussion ensued in the research group of this project which resulted in a list of descriptors characterising modelling tasks. This paper focuses on the theoretical background of mathematical modelling and will thereby substantiate the list of descriptors for modelling tasks.

Visual modeling concept of integrated constructs (essence) of mathematical objects in teacher training of humanistic area is presented as technology of education in problem solving. The main goal of innovative approach is student’s activity in mathematics on generating of concrete essence manifestations on concepts, methods, theorems, algorithms, procedures and so on. Such student’s activity should be: · Success in an area of actual interests and person’s experience and reached by perception; · Have high level of variability in visual modeling; · Success in domain of reflection process stimulation. Similar creative behavior of persons is typical for actors, dancing, and figure skating and so on. Now we show that such technology will be fruitful for teacher training in mathematics for humanistic specialties.

Keine andere Wissenschaft ist in einem so hohen Maße mathematisiert wie die Physik. Aufgrund dieser engen Verbindung beider Wissenschaften muss geklärt werden, welche Rolle die Mathematik im Physikunterricht spielen soll. Um einen theoretischen Rahmen bereitzustellen, wird ein didaktisches Modell erarbeitet, das mathematik- und physikdidaktische Erkenntnisse mit wissenschaftstheoretischen Argumenten zur Rolle der Mathematik in der Physik verbindet. Unter der daraus resultierenden Perspektive der konzeptuell-mathematischen Physik wird die Aufgabenkultur im Physikunterricht beleuchtet und neue Aufgaben zum Themengebiet der Mechanik konstruiert, die die Übersetzung zwischen physikalischer Bedeutung und mathematischen Strukturen thematisieren. Auf diesen Aufgaben basiert die qualitative empirische Studie, die die Verständnisprobleme von Schülerinnen und Schülern neunter und zehnter Klassen verschiedener Gymnasien beim Verbinden von Physik und Mathematik untersucht. Die Analyse ergibt verschiedene Problembereiche, wobei sich insbesondere beim Übersetzen zwischen physikalischer Bedeutung und mathematischen Strukturen problematische Vorstellungen zeigen. So werden teilweise funktionale Abhängigkeiten zwischen den Faktoren eines Produktes gesehen. Andererseits zeigt sich aber auch, dass der Abgleich zwischen der mathematischen Herleitung und der physikalischen Interpretation der entscheidende Faktor für das erfolgreiche Lösen einer Aufgabe sein kann.

Modeling is an essential discipline that is especially important in the field of software engineering. Students and developers alike employ models to describe systems on an abstract level, capture requirements, and communicate with other teams. For that purpose, UML diagrams are usually the instrument of choice. Over the course of the last decade, mobile devices increased in prevalence and popularity and flexible work arrangements were introduced in a larger number of workplaces. Effective collaboration is more important than ever. However, the tools have not kept up with these developments. There exists no semantics-aware mobile modeling application that supports collaboration in real time, a gap in the market. This thesis investigates existing applications in the mobile modeling space and their shortcomings, technologies for developing cross-platform apps, and methodologies for facilitating conflict-free collaboration. Based on the findings, it conceptualizes and implements CoMod, a proof of concept allowing users to collaboratively edit UML class diagrams in real time. The system consists of a Flutter-based client application for Android and iOS and a Node.js-based server executable. These components utilize conflict-free replicated data types (CRDTs) to merge participants' changes and communicate via WebSocket connections. Moreover, CoMod's feasibility is evaluated by means of a case study investigating the system's scalability and performance characteristics. It has been shown that CoMod is able to handle common use cases arising in software engineering teams or group projects at university. It is further kept sufficiently general to allow other types of models to be supported without having to alter the entire system.:1 Introduction 1.1 Requirements 1.2 Problem Description 1.3 Objectives 1.4 Structure 2 Background 2.1 Software Modeling 2.1.1 Unified Modeling Language 2.2 Cross-Platform Application Development 2.2.1 Web Apps 2.2.2 Hybrid Apps 2.2.3 Native cross-platform apps 2.2.4 Summary 2.3 Real-Time Collaboration 2.3.1 Conflict-Free Replicated Data Types (CRDTs) 2.3.2 Operational Transformation 3 Related Work 3.1 Astah UML 3.2 Lucidchart 3.3 System Designer 3.4 Summary 4 Concept 4.1 Objectives 4.2 User Interface 4.3 Data Model 4.4 Collaboration 4.4.1 Conflict handling 4.4.2 System architecture 4.4.3 Client-server communication 4.5 Summary 5 Solution 5.1 Client 5.1.1 Walkthrough 5.1.2 Data model 5.1.3 JavaScript subsystem 5.1.4 Dependencies 5.2 Server 5.2.1 Dependencies 5.3 Collaboration 5.3.1 Client-server communication 5.3.2 Client data flow 5.4 Testing 5.4.1 Unit tests 5.4.2 Integration tests 5.4.3 End-to-end tests 5.5 Extensibility 6 Evaluation 6.1 Case Study 6.2 Technical Analysis 6.2.1 Test data generator 6.2.2 Client analysis 6.2.3 Server analysis 6.3 Threats to Validity 7 Conclusion 7.1 Fulfillment of Objectives 7.2 Future Work Acronyms Bibliography

Role-based modeling has been investigated for over 35 years as a promising paradigm to model complex, dynamic systems. Although current software systems are characterized by increasing complexity and context-dependence, all this research had almost no influence on current software development practice, still being discussed in recent literature. One reason for this is the lack of a coherent, comprehensive, readily applicable notion of roles. Researchers focused either on relational roles or context-dependent roles rather then combining both natures. Currently, there is no role-based modeling language sufficiently incorporating both the relational and context-dependent nature of roles together with the various proposed constraints. Hence, this paper formalizes a full-fledged role-based modeling language supporting both natures. To show its sufficiency and adequacy, a real world example is employed.

The Comenius Network Project “Developing Quality in Mathematics Education II” funded by the European Commission consists of partners from schools, universities and teacher training centres from eleven European countries. One advantage of the project is the mutual exchange between teachers, teacher trainers and researchers in developing learning material. To support the teachers most effectively the researchers asked the teachers what they wanted the researchers to do. The answer was also a question: How can we identify (good) modelling tasks? A discussion ensued in the research group of this project which resulted in a list of descriptors characterising modelling tasks. This paper focuses on the theoretical background of mathematical modelling and will thereby substantiate the list of descriptors for modelling tasks.