Comparison of Mathematics and Physics Education II: Examples of Interdisciplinary Teaching at School PDF
Preview Comparison of Mathematics and Physics Education II: Examples of Interdisciplinary Teaching at School
MINTUS – Beiträge zur mathematisch- naturwissenschaftlichen Bildung Series Editors Ingo Witzke, Mathematikdidaktik, Universität Siegen, Siegen, Germany Oliver Schwarz, Didaktik der Physik, Universität Siegen, Siegen, Nordrhein-Westfalen, Germany MINTUS ist ein Forschungsverbund der MINT-Didaktiken an der Universität Siegen. Ein besonderes Merkmal für diesen Verbund ist, dass die Zusammenar- beit der beteiligten Fachdidaktiken gefördert werden soll. Vorrangiges Ziel ist es, gemeinsame Projekte und Perspektiven zum Forschen und auf das Lehren und Lernen im MINT-Bereich zu entwickeln. Ein Ausdruck dieser Zusammenarbeit ist die gemeinsam herausgegebene Schriftenreihe MINTUS – Beiträge zur mathematisch-naturwissenschaftlichen Bildung. Diese ermöglicht Nachwuchswissenschaftlerinnen und Nachwuchswis- senschaftlern, genauso wie etablierten Forscherinnen und Forschern, ihre wissen- schaftlichen Ergebnisse der Fachcommunity vorzustellen und zur Diskussion zu stellen. Sie profitiert dabei von dem weiten methodischen und inhaltlichen Spek- trum, das MINTUS zugrunde liegt, sowie den vielfältigen fachspezifischen wie fächerverbindenden Perspektiven der beteiligten Fachdidaktiken auf den gemein- samen Forschungsgegenstand: die mathematisch-naturwissenschaftliche Bildung. More information about this series at https://link.springer.com/bookseries/16267 Frederik Dilling · Simon F. Kraus Editors Comparison of Mathematics and Physics Education II Examples of Interdisciplinary Teaching at School Editors Frederik Dilling Simon F. Kraus Mathematics Education Physics Education University of Siegen University of Siegen Siegen, Germany Siegen, Germany ISSN 2661-8060 ISSN 2661-8079 (electronic) MINTUS – Beiträge zur mathematisch-naturwissenschaftlichen Bildung ISBN 978-3-658-36414-4 ISBN 978-3-658-36415-1 (eBook) https://doi.org/10.1007/978-3-658-36415-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachme- dien Wiesbaden GmbH, part of Springer Nature 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Responsible Editor: Marija Kojic This Springer Spektrum imprint is published by the registered company Springer Fachmedien Wiesbaden GmbH part of Springer Nature. The registered company address is: Abraham-Lincoln-Str. 46, 65189 Wiesbaden, Germany Contents 1 Introductory Remarks and Concept of the Book . . . . . . . . . . . . . . . 1 Frederik Dilling and Simon F. Kraus 2 Historical Relations of Mathematics and Physics—an Overview and Implications for Teaching . . . . . . . . . . . . . . . . . . . . . . 7 Frederik Dilling and Simon F. Kraus 3 Educational Use of Ludwig’s Methodology Using the Example of the Lens Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Jochen Geppert 4 Equations as a Tool for Hypothesis Formulation in Physics . . . . . . . 57 Jochen Geppert 5 Comparison: Numbers, Quantities and Units . . . . . . . . . . . . . . . . . . 79 Daniela Götze and Philipp Raack 6 Lesson Plan: Measuring Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Nguyen Phuong Chi 7 Comparison: Equations in Mathematics and Physics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Sascha Hohmann and Felicitas Pielsticker 8 Lesson Plan: Trigonometric Equations . . . . . . . . . . . . . . . . . . . . . . . . 117 Vu Dinh Phuong 9 Comparison: Functions in Mathematics and Physics Education . . . 129 Frederik Dilling and Simon F. Kraus v vi Contents 10 Lesson Plan: Quadratic Functions—Graphs and Applications . . . . 151 Chu Cam Tho 11 Lesson Plan: Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Tuong Duy Hai 12 Lesson Plan: The Dependence of Resistance on Temperature . . . . . 173 Tran Ngoc Chat 13 Lesson Plan: Simple Harmonic Oscillation . . . . . . . . . . . . . . . . . . . . 183 Nguyen Van Bien 14 Comparison: Vectors in Mathematics and Physics Education . . . . . 193 Frederik Dilling 15 Lesson Plan: Combining Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Nguyen Van Bien 16 Lesson Plan: Basic Concepts Related to Vectors . . . . . . . . . . . . . . . . 217 Le Tuan Anh 17 Comparison: Differential Calculus Through Applications . . . . . . . . 227 Gero Stoffels, Ingo Witzke and Kathrin Holten 18 Lesson Plan: Differential Calculus Through Applications . . . . . . . . 243 Chu Cam Tho 19 Lesson Plan: Capacitor Charge and Discharge Process. Capacitor Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Tran Ngoc Chat 20 Comparison: Stochastics with a Focus on Probability Theory . . . . . 277 Gero Stoffels and Sascha Hohmann 21 Lesson Plan: Probabilities and Statistics . . . . . . . . . . . . . . . . . . . . . . 299 Nguyen Phuong Chi 22 Comparison: Light Rays and the Intercept Theorem in Mathematics and Physics Education . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Frederik Dilling and Ina Stricker 23 Lesson Plan: Straight Lines and Conic Sections . . . . . . . . . . . . . . . . 331 Le Tuan Anh List of Contributors Le Tuan Anh Faculty of Mathematics and Informatics, Hanoi National Univer- sity of Education, Hanoi, Vietnam Nguyen Van Bien Faculty of Physics, Hanoi National University of Education, Hanoi, Vietnam Tran Ngoc Chat Faculty of Physics, Hanoi National University of Education, Hanoi, Vietnam Nguyen Phuong Chi Faculty of Mathematics and Informatics, Hanoi National University of Education, Hanoi, Vietnam Frederik Dilling Mathematics Education, University of Siegen, Siegen, Germany Jochen Geppert Mathematics Education, University of Siegen, Siegen, Germany Daniela Götze Mathematics Education, University of Siegen, Siegen, Germany Tuong Duy Hai Faculty of Physics, Hanoi National University of Education, Hanoi, Vietnam Sascha Hohmann Physics Education, IPN—Leibniz Institute for Science and Mathematics Education, Kiel, Germany Kathrin Holten Mathematics Education, University of Siegen, Siegen, Germany Simon F. Kraus Physics Education, University of Siegen, Siegen, Germany Vu Dinh Phuong Faculty of Mathematics and Informatics, Hanoi National Uni- versity of Education, Hanoi, Vietnam vii viii List of Contributors Felicitas Pielsticker Mathematics Education, University of Siegen, Siegen, Germany Philipp Raack Physics Education, University of Siegen, Siegen, Germany Gero Stoffels Mathematics Education, University of Siegen, Siegen, Germany Ina Stricker Physics Education, University of Siegen, Siegen, Germany Chu Cam Tho Research Division On Educational Assessment (RDEA), The Viet Nam Institute of Educational Sciences (VNIES), Hanoi, Vietnam Ingo Witzke Mathematics Education, University of Siegen, Siegen, Germany 1 Introductory Remarks and Concept of the Book Frederik Dilling and Simon F. Kraus The presented volume is the outcome of our efforts to enhance and further develop cooperation and cross-linking between mathematics and physics education. Like the first volume (Kraus & Krause, 2020), this book is based on a collaborative project between the Hanoi National University of Education in Vietnam and the University of Siegen in Germany. The Inter TeTra (Interdisciplinary Teacher Training) project aims to contribute to the development of teacher training in Vietnam by promoting the integration and interweaving of content from math- ematics and physics at theoretical and practical levels. In each case, educational approaches and concepts should be given greater consideration in order to foster optimal learning outcomes and advance the development of competencies. The main outcome of the Inter TeTra project is the conception of a university module, consisting of a lecture, a seminar, and in-service teacher training. The project is supported by the German Academic Exchange Service (DAAD) with funds from the Ministry for Economic Cooperation and Development (see Fig. 1.1). While the first volume was dedicated to a comparison of the theoretical founda- tions of the aforementioned subjects, this volume will focus on practical implemen- tation in the classroom. With this division into theoretical and practical volumes, the books reflect the conception of the Inter TeTra project (Kraus et al., 2018; Krause F. Dilling Mathematics Education, University of Siegen, Siegen, Germany e-mail: [email protected] S. F. Kraus (*) Physics Education, University of Siegen, Siegen, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden 1 GmbH, part of Springer Nature 2022 F. Dilling and S. F. Kraus (eds.), Comparison of Mathematics and Physics Education II, MINTUS – Beiträge zur mathematisch-naturwissenschaftlichen Bildung, https://doi.org/10.1007/978-3-658-36415-1_1 2 F. Dilling and S. F. Kraus Fig. 1.1 This book was written as part of the Inter TeTra project, which is funded by the German Academic Exchange Service with funds from the Ministry for Economic Cooperation and Development Fig. 1.2 The structure of the underlying courses relies on the interconnection of theoreti- cal considerations and practical applications et al., 2019). The courses also start with a theoretical comparison, based on which concrete teaching proposals are developed (Fig. 1.2). The theory-based development as well as the final evaluation and reflection on the results of the implementation represent an essential design element of the courses of the Inter TeTra project. As a transition between the theory-oriented first volume and the practice-ori- ented volume realized here, the connection is exemplified in two chapters. The first chapter1 shows how a teaching sequence on the lens equation in geometrical 1 See Chapter “Educational use of Ludwig’s methodology using the example of the lens equation”.
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