Connecting Mathematics and Mathematics Education

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 education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account

Connecting Mathematics and Mathematics Education

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 education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account

Applying science of learning in education: Infusing psychological science into the curriculum

The field of specialization known as the science of learning is not, in fact, one field. Science of learning is a term that serves as an umbrella for many lines of research, theory, and application. A term with an even wider reach is Learning Sciences (Sawyer, 2006). The present book represents a sliver, albeit a substantial one, of the scholarship on the science of learning and its application in educational settings (Science of Instruction, Mayer 2011). Although much, but not all, of what is presented in this book is focused on learning in college and university settings, teachers of all academic levels may find the recommendations made by chapter authors of service. The overarching theme of this book is on the interplay between the science of learning, the science of instruction, and the science of assessment (Mayer, 2011). The science of learning is a systematic and empirical approach to understanding how people learn. More formally, Mayer (2011) defined the science of learning as the “scientific study of how people learn” (p. 3). The science of instruction (Mayer 2011), informed in part by the science of learning, is also on display throughout the book. Mayer defined the science of instruction as the “scientific study of how to help people learn” (p. 3). Finally, the assessment of student learning (e.g., learning, remembering, transferring knowledge) during and after instruction helps us determine the effectiveness of our instructional methods. Mayer defined the science of assessment as the “scientific study of how to determine what people know” (p.3). Most of the research and applications presented in this book are completed within a science of learning framework. Researchers first conducted research to understand how people learn in certain controlled contexts (i.e., in the laboratory) and then they, or others, began to consider how these understandings could be applied in educational settings. Work on the cognitive load theory of learning, which is discussed in depth in several chapters of this book (e.g., Chew; Lee and Kalyuga; Mayer; Renkl), provides an excellent example that documents how science of learning has led to valuable work on the science of instruction. Most of the work described in this book is based on theory and research in cognitive psychology. We might have selected other topics (and, thus, other authors) that have their research base in behavior analysis, computational modeling and computer science, neuroscience, etc. We made the selections we did because the work of our authors ties together nicely and seemed to us to have direct applicability in academic settings

Instructional strategies in explicating the discovery function of proof for lower secondary school students

In this paper, we report on the analysis of teaching episodes selected from our pedagogical and cognitive research on geometry teaching that illustrate how carefully-chosen instructional strategies can guide Grade 8 students to see and appreciate the discovery function of proof in geometr

What's a face worth: Noneconomic factors in game playing

Where behavior defies economic analysis, one explanation is that individuals consider more than the immediate payoff. We present evidence that noneconomic factors influence behavior. Attractiveness influences offers in the Ultimatum and Dictator Games. Facial resemblance, a cue of relatedness, increases trusting in a two-node trust game. Only by considering the range of possible influences will game-playing behavior be explained

Selected Computing Research Papers Volume 1 June 2012

An Evaluation of Anti-phishing Solutions (Arinze Bona Umeaku) ..................................... 1 A Detailed Analysis of Current Biometric Research Aimed at Improving Online Authentication Systems (Daniel Brown) .............................................................................. 7 An Evaluation of Current Intrusion Detection Systems Research (Gavin Alexander Burns) .................................................................................................... 13 An Analysis of Current Research on Quantum Key Distribution (Mark Lorraine) ............ 19 A Critical Review of Current Distributed Denial of Service Prevention Methodologies (Paul Mains) ............................................................................................... 29 An Evaluation of Current Computing Methodologies Aimed at Improving the Prevention of SQL Injection Attacks in Web Based Applications (Niall Marsh) .............. 39 An Evaluation of Proposals to Detect Cheating in Multiplayer Online Games (Bradley Peacock) ............................................................................................................... 45 An Empirical Study of Security Techniques Used In Online Banking (Rajinder D G Singh) .......................................................................................................... 51 A Critical Study on Proposed Firewall Implementation Methods in Modern Networks (Loghin Tivig) .................................................................................................... 5