This survey confirms that one of the research trends in early geometrical reasoning has been a focus on creating a theoretical basis for research in this area. The main reason for the work on the theoretical foundations has been the fact that building geometrical concepts proceeds according to other regularities more than it takes place while building arithmetic knowledge. In this way, a broad …
This book presents a synopsis of six emerging themes in adult mathematics/numeracy and a critical discussion of recent developments in terms of policies, provisions, and the emerging challenges, paradoxes and tensions. It also offers an extensive review of the literature adult mathematics education. Why do adults want to learn mathematics? Did they enjoy mathematics at school so much that they …
This open access book contains a structured collection of complete solutions of all significant axially symmetric contact problems. It provides solutions for classical profiles such as the sphere, cone or flat cylindrical punch as well as a multitude of other technically relevant shapes, e.g. the truncated cone, the worn sphere, rough profiles, hollow cylinders, etc. Normal, tangential and tors…
This open access book is intended to assist teachers, teacher trainers, curriculum designers, editors and authors of textbooks in developing strategies to teach the multiplication of natural numbers based on the experience of the Lesson Study in Japan. This approach to mathematics education dates back to the 1870s and reconciles the emphasis on problem solving with the treatment of the curricul…
This open access book offers an initial introduction to programming for scientific and computational applications using the Python programming language. The presentation style is compact and example-based, making it suitable for students and researchers with little or no prior experience in programming. The book uses relevant examples from mathematics and the natural sciences to present prog…
This Open Access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher …
This open access book chronicles the rise of a new scientific paradigm offering novel insights into the age-old enigmas of existence. Over 300 years ago, the human mind discovered the machine code of reality: mathematics. By utilizing abstract thought systems, humans began to decode the workings of the cosmos. From this understanding, the current scientific paradigm emerged, ultimately discover…
This open access book discusses firm valuation, which is of interest to economists, particularly those working in finance. Firm valuation comes down to the calculation of the discounted cash flow, often only referred to by its abbreviation, DCF. There are, however, different coexistent versions, which seem to compete against each other, such as entity approaches and equity approaches. Acronyms …
This ICME-13 Topical Survey reviews the state-of-the-art by first exploring the roots and scope of design science. Second, it presents two examples of current design science projects that focus on substantial learning environments including a student and a teacher perspective. Subsequently, the book elaborates on how empirical research can be conceptualised within design science. Lastly, it exp…
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting…