Table Of ContentMINTUS – 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,
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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”.
