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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.

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Dieses Open-Access-Buch beschreibt die theoriebasierte Entwicklung einer semesterbegleitenden Maßnahme zur Förderung der Problemlösekompetenz von Studienanfänger:innen der Fachmathematik und des gymnasialen Lehramts, sowie die zyklische Modifikation dieser Maßnahme im Sinne der Entwicklungsforschung. Begleitend dazu wurden, mit dem Ziel, grundlegende Erkenntnisse zum studentischen Problemlösen zu gewinnen, systematische Beobachtungen von Bearbeitungsprozessen zu typischen Übungsaufgaben durchgeführt. Hierbei hat sich insbesondere die Rolle des Vorwissens als entscheidender Faktor herausgestellt. Der Autor Thomas Stenzel arbeitet in der Mathematikdidaktik an der Universität Duisburg-Essen. Promoviert hat er 2021 bei Prof. Dr. Andreas Büchter. Sein Forschungsschwerpunkt liegt in der Hochschuldidaktik sowie im Bereich des Problemlösens.

Mathematics. --- General Mathematics and Education. --- Aufgabenbasierte Interviews --- Quantitative Forschung --- Problemlösekompetenz --- Studienanfänger --- Problemlösen --- Bearbeitungsprozesse --- Übungsaufgaben

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In diesem Open-Access-Buch wird gezeigt, dass ein Instrument zur sprachlichen adaptiven Anpassung benötigt wird, um auf die sprachlichen Lernvoraussetzungen bei Textaufgaben von Lernenden im Mathematikunterricht reagieren zu können. Auf Basis eines quantitativen Vorgehens werden die sprachlichen Variationen in mathematische Textaufgaben festgestellt und als Grundlage für sprachliche Veränderungspraktiken genutzt. Anhand der Ergebnisse dieser Arbeit werden fünf Faktoren herausgestellt, die für die Variation von Textaufgaben bedeutsam sind: der erklärende, komprimierende, beschreibende, informative und instruktive Faktor. Zur Konzeption des Instruments werden der Einfluss auf die Aufgabenschwierigkeit und die Verbindung zu fachlich-kontextuellen Merkmalen bestimmt.

Mathematics --- Mathematics, general --- General Mathematics and Education --- General Mathematics --- Sprachvariationen --- Mathematikdidaktik --- Textaufgaben --- Textverstehen --- Register --- Fachsprache --- Open Access

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This book is an autobiographical interview with Chinese Academician Yuan Wang on his experience in mathematical research. In the book Wang’s way of studying Goldbach conjecture is revealed in detail from motivation to method; Wang’s approach and viewpoint of doing applied mathematics are described by the research cases of his applying number theoretic method to numerical integration and mathematical statistics. Wang’s work on algebraic number theory is traced back in a separate chapter. The book ends with two chapters which introduce Wang’s interest in history of mathematics and his hobbies outside of mathematical research and show how a mathematician can in the same time be a historical and popular science writer and, in particular, a well-received calligrapher. The book is intended for undergraduate and graduate students studying number theory and its applications, researchers who are willing to learn from the experience of an established mathematician, as well as math amateurs and general audience who are interested in Wang's life story.

Mathematics. --- History. --- Number theory. --- Numerical analysis. --- Statistics. --- General Mathematics and Education. --- History of Mathematical Sciences. --- Number Theory. --- Numerical Analysis.

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With the help of tried and tested, carefully elaborated learning units, the authors convey fundamental mathematical techniques in this essential, which are important far beyond primary school. In the present volume I, path problems and word puzzles are modeled and solved using undirected and directed graphs. Simple math games are systematically analyzed and the optimal strategies are determined. Students learn to gradually reduce difficult problems to simpler ones and to provide evidence in different contexts. The tasks encourage mathematical thinking, imagination and creativity. The detailed sample solutions are designed for non-mathematicians. This book is a translation of the original German 1st edition Mathematische Geschichten I – Graphen, Spiele und Beweise by Susanne Schindler-Tschirner and Werner Schindler, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. The content Mathematical techniques and tasks Detailed sample solutions The target groups Leaders of study groups as well as support courses for mathematically gifted students in grades 3 and 4, teachers who practice differentiated mathematics lessons Committed parents for extracurricular support The authors Susanne Schindler-Tschirner is a philologist and after studying to become a teacher, she was a project manager at a science publisher. She works in the field of student development and is the author of didactic-oriented publications. Werner Schindler has a PhD in mathematics. He is head of section at the Federal Office for Information Security (BSI) and an adjunct professor in the mathematics department at TU Darmstadt.

Mathematics. --- Mathematics—Study and teaching . --- Mathematics, general. --- Mathematics Education. --- Math --- Science --- Mathematics --- Study and teaching. --- Ensenyament de la matemàtica --- Aprenentatge de la matemàtica --- Ensenyament de les matemàtiques --- Ensenyament --- Didàctica de la matemàtica --- Matemàtica --- General Mathematics and Education. --- Study and teaching .