Models and Modeling Perspectives


Book Description

This special issue of Mathematical Thinking and Learning describes models and modeling perspectives toward mathematics problem solving, learning, and teaching. The concern is not only the mature forms of models and modeling in communities of scientists and mathematicians, but also the need to initiate students in these forms of thought. The contributions of this issue suggest a variety of ways that students (children through adults) can be introduced to highly productive forms of modeling practices. Collectively, they illustrate how modeling activities often lead to remarkable mathematical achievements by students formerly judged to be too young or too lacking in ability for such sophisticated and powerful forms of mathematical thinking. The papers also illustrate how modeling activities often create productive interdisciplinary niches for mathematical thinking, learning, and problem solving that involve simulations of similar situations that occur when mathematics is useful beyond school.




Beyond Constructivism


Book Description

This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.




Beyond Constructivism


Book Description

This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.




Beyond Constructivism


Book Description




Conceptual Modeling Perspectives


Book Description

Conceptual modeling has always been one of the main issues in information systems engineering as it aims to describe the general knowledge of the system at an abstract level that facilitates user understanding and software development. This collection of selected papers provides a comprehensive and extremely readable overview of what conceptual modeling is and perspectives on making it more and more relevant in our society. It covers topics like modeling the human genome, blockchain technology, model-driven software development, data integration, and wiki-like repositories and demonstrates the general applicability of conceptual modeling to various problems in diverse domains. Overall, this book is a source of inspiration for everybody in academia working on the vision of creating a strong, fruitful and creative community of conceptual modelers. With this book the editors and authors want to honor Prof. Antoni Olivé for his enormous and ongoing contributions to the conceptual modeling discipline. It was presented to him on the occasion of his keynote at ER 2017 in Valencia, a conference that he has contributed to and supported for over 20 years. Thank you very much to Antoni for so many years of cooperation and friendship.




Multiscale Modeling


Book Description

This highly useful book contains methodology for the analysis of data that arise from multiscale processes. It brings together a number of recent developments and makes them accessible to a wider audience. Taking a Bayesian approach allows for full accounting of uncertainty, and also addresses the delicate issue of uncertainty at multiple scales. These methods can handle different amounts of prior knowledge at different scales, as often occurs in practice.




X-Machines for Agent-Based Modeling


Book Description

From the Foreword: "This book exemplifies one of the most successful approaches to modeling and simulating [the] new generation of complex systems. FLAME was designed to make the building of large scale complex systems models straightforward and the simulation code that it generates is highly efficient and can be run on any modern technology. FLAME was the first such platform that ran efficiently on high performance parallel computers and a version for GPU technology is also available. At its heart, and the reason why it is so efficient and robust, is the use of a powerful computational model ‘Communicating X-machines’ which is general enough to cope with most types of modelling problems. As well as being increasingly important in academic research, FLAME is now being applied in industry in many different application areas. This book describes the basics of FLAME and is illustrated with numerous examples." —Professor Mike Holcombe, University of Sheffield, UK Agent-based models have shown applications in various fields such as biology, economics, and social science. Over the years, multiple agent-based modeling frameworks have been produced, allowing experts with non-computing background to easily write and simulate their models. However, most of these models are limited by the capability of the framework, the time it takes for a simulation to finish, or how to handle the massive amounts of data produced. FLAME (Flexible Large-scale Agent-based Modeling Environment) was produced and developed through the years to address these issues. This book contains a comprehensive summary of the field, covers the basics of FLAME, and shows how concepts of X-machines, can be stretched across multiple fields to produce agent models. It has been written with several audiences in mind. First, it is organized as a collection of models, with detailed descriptions of how models can be designed, especially for beginners. A number of theoretical aspects of software engineering and how they relate to agent-based models are discussed for students interested in software engineering and parallel computing. Finally, it is intended as a guide to developers from biology, economics, and social science, who want to explore how to write agent-based models for their research area. By working through the model examples provided, anyone should be able to design and build agent-based models and deploy them. With FLAME, they can easily increase the agent number and run models on parallel computers, in order to save on simulation complexity and waiting time for results. Because the field is so large and active, the book does not aim to cover all aspects of agent-based modeling and its research challenges. The models are presented to show researchers how they can build complex agent functions for their models. The book demonstrates the advantage of using agent-based models in simulation experiments, providing a case to move away from differential equations and build more reliable, close to real, models. The Open Access version of this book, available at https://doi.org/10.1201/9781315370729, has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.




Modeling Students' Mathematical Modeling Competencies


Book Description

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.




Modelling-based Teaching in Science Education


Book Description

This book argues that modelling should be a component of all school curricula that aspire to provide ‘authentic science education for all’. The literature on modelling is reviewed and a ‘model of modelling’ is proposed. The conditions for the successful implementation of the ‘model of modelling’ in classrooms are explored and illustrated from practical experience. The roles of argumentation, visualisation, and analogical reasoning, in successful modelling-based teaching are reviewed. The contribution of such teaching to both the learning of key scientific concepts and an understanding of the nature of science are established. Approaches to the design of curricula that facilitate the progressive grasp of the knowledge and skills entailed in modelling are outlined. Recognising that the approach will both represent a substantial change from the ‘content-transmission’ approach to science teaching and be in accordance with current best-practice in science education, the design of suitable approaches to teacher education are discussed. Finally, the challenges that modelling-based education pose to science education researchers, advanced students of science education and curriculum design, teacher educators, public examiners, and textbook designers, are all outlined.




Teaching Mathematical Modelling: Connecting to Research and Practice


Book Description

This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.​