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Augmented and virtual reality (AR/VR) are technologies of increasing importance in our society. In the field of mathematics education, these innovative technologies may offer a wide range of opportunities to support immersive, individual, and active learning processes. At the same time, many new challenges arise that need to be mastered by teachers and students in the classroom. With this book we want to contribute to the discourse by presenting innovative insights by bringing parties from research and practice together. The papers cover a wide range of relevant topics including cooperation and communication, STEM and modelling, development and application of design criteria, spatial geometry and imagination or teacher-trainings. The contributions include in-depth theoretical considerations, concrete developed applications and learning environments, and findings from empirical studies. The Editors Dr. Frederik Dilling is a research associate in mathematics education at the University of Siegen. His research focuses on digitization and interdisciplinarity in mathematics education. Prof. Dr. Ingo Witzke is professor for mathematics education at the University of Siegen. His research group investigates the development of mathematical knowledge in empirical contexts.

Mathematics. --- General Mathematics and Education.

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This colorful and concise little book is uniquely tailored for those who write mathematical texts at any level and are eager to improve their English writing skills. The easy-to-read guide focuses on helping the writer avoid common English mistakes in mathematical writing. With just a few minutes of engaging, light reading each day, the reader will learn to create clearer, more readable math texts. The book covers 23 crucial topics, ranging from correct article and preposition usage to proper usage of dashes, conjunctions, and prepositions. It also addresses the construction of direct sentences, effective introductory phrases for formulas, and more. As a bonus to the reader, ‘Practice makes perfect’ exercises relating to each topic are freely accessible on this book’s Springer website. Appendix A gives a quick tutorial on grammatical terms and constructs. Appendix B looks at ChatGPT and the positive aspects of its powerful capabilities. Additionally, Paul Halmos’s article on ‘How to write mathematics’ is included in Appendix C. It deals with the mathematical aspects of writing.

Mathematics. --- Penmanship. --- General Mathematics. --- Writing Skills.

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This book answers, in the form of short and entertaining vignettes, the question: "What do mathematicians really do?" Readers will learn that mathematicians use numbers in the same way that novelists use letters. The individual letters are typed while the author thinks on a much grander scale, invisible to the observer. Requiring only familiarity with the multiplication table (and that for only one vignette), the book makes accessible a variety of mathematical concepts, such as game theory, chaos, and, as the author puts it, the c******* of variations. The author accomplishes this with a light, engaging style, and a range of real-world examples that includes everything from barbershops to President James Garfield. Mathematicians Don't Work With Numbers will be of interest to the large audience of people who have always assumed that mathematicians do, in fact, work with numbers.

Mathematics --- wiskunde --- Mathematics. --- General Mathematics. --- Mathematics in Popular Science. --- General Mathematics and Education.

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This book introduces readers to key concepts in group theory through engaging puzzles. The early sections of the book show how the rules of group theory emerge naturally from solving puzzles. Different classes of groups, such as cyclic, dihedral and permutation groups are introduced, accompanied by numerous puzzles to facilitate the understanding of the underlying group structures. Later chapters explain how further group theory principles can be applied to puzzle-solving. This book is intended as a highly motivating supplementary text for an undergraduate abstract algebra course. It is also ideal for anyone seeking a fun, hands-on approach to learning group theory. Additionally, the book's many puzzles will be enjoyable for readers already familiar with group theory.

Group theory. --- Mathematics. --- Group Theory and Generalizations. --- General Mathematics.

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Mathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights. The Editors Deniz Sarikaya is a guest researcher at the University of Copenhagen and the Technical University of Denmark (funded by the DAAD) and postdoctoral researcher at the Vrije Universiteit Brussel (within an FWO-project). Lukas Baumanns did his doctorate on problem posing at the University of Cologne. Currently he works at the Chair of Special Education in Mathematics and focuses on early mathematics learning and mathematical difficulties. Karl Heuer is an assistant professor in Discrete Mathematics at the Technical University of Denmark. He mainly works in Graph Theory, but is also active in enrichment programmes. He obtained his PhD in mathematics at the University of Hamburg. Benjamin Rott is a professor of Mathematics Education at the University of Cologne. He obtained a PhD at the University of Hannover, worked at the University of Education Freiburg and the University of Duisburg-Essen. His research interests include problem posing/solving, giftedness, and beliefs. .

Mathematics. --- General Mathematics and Education. --- General Mathematics. --- Mathematics --- Study and teaching. --- Matemàtica --- Ensenyament de la matemàtica --- Problemes i exercicis