Prof. Dr. Rainer Kaenders

E-mail: kaenders(at)
Phone: +49 228 73 62218
Room: 4.002
Location: Mathematics Center
Institute: Mathematical Institute
Date of birth: 15.May 1966

Academic Career

1992 - 1993

Research Assistant, University of Bonn

1993 - 1997

PhD, University of Nijmegen, Netherlands (advisor: Prof. Dr. J.H.M. Steenbrink)

1997 - 1998

Postdoc, University of Utrecht, NWO-Project, Netherlands

1998 - 1999

Postdoc, Heinrich-Heine-University Düsseldorf

1999 - 2000

Assistant Professor (C1), Heinrich-Heine-University Düsseldorf

2000 - 2001

Teacher Education, University of Nijmegen, Netherlands (after a first phase in 1996)

2000 - 2005

Mathematics Teacher, Canisius College Nijmegen, Netherlands

2001 - 2007

Assistant Professor, Graduate School of Teacher Education, University of Nijmegen, Netherlands

2005 - 2006

Assistant Professor, Technical University Delft, Netherlands

2006 - 2007

Head of Teacher Education, University of Nijmegen, Netherlands

2007 - 2013

Professor (W3) of Mathematics and its Education, University of Cologne

Since 2013

Professor (W3) of Mathematics and its Education, University of Bonn

Research Profile

In my current research, I am interested in subject-bound questions oriented towards mathematics teaching (so-called Stoffdidaktik). Recent works explored particular approaches to certain notions from analysis, algebra and projective geometry, all of them based on historical ideas. These works are conceptualized in contributions reflecting more general features of the role and the use of mathematics history in teaching. Moreover, I am interested in epistemological consequences and changes for the mathematical development in students, which are caused by the employment of digital tools. In mathematics education, elementary mathematics plays a crucial role and I am always concerned with questions of elementary mathematics. My research in the past was in intervention research in cooperation with mathematics teachers (see In the role of adviser, this work is pursued in projects of my PhD students Jennifer Klenzan (PhD 2014), Marc Sauerwein (Bigs-HCM, Bonn) and Chris Kooloos (Radboud University Nijmegen).

In the future, I will still be concerned with subject-bound questions in relation to history of mathematics that are relevant for mathematics teaching in school and in the early years of university. As far as epistemological questions in mathematics education are concerned, I further strive for a better understanding of mathematical awareness (in particular in relation to digital tools). In dealing with the above mentioned research activities, there will always be aspects of elementary mathematics that call my attention and invite to contribute to the mathematical culture in mathematics education. Given the presently predominant competence and output orientation supporting the No-Math movement characterized by anti-didactical omissions, the overall interest of mathematics education in the future must be to develop a modern practice of mathematics teaching that gives access to the rich mathematical culture and tradition. In this context, several colleagues and I will initiate an interdisciplinary project about the modern role of disciplines (and in particular of mathematics) at school in relation to science and society.

Research Projects and Activities

Exercise Committee for Mathematics B-day, Utrecht University (in Germany: macht mathe Wettbewerbe, NRW)
since 2004

Dutch Teaching Commission Mathematics, NOCW
Member, 2005 - 2008

cTWO, Committee for the Reform of Mathematics Teaching, Ministery for Teaching, Culture and Science,
Member, 2005 - 2008

The Education Committee of the European Mathematical Society
Member, 2005 - 2008

Programmacommissie Vakantiecursus Wiskunde, Zentrum für Mathematik und Informatik CWI, Amsterdam, Netherlands
Member, 2005 - 2008

GeoGebra-Institute Cologne-Bonn
Founding Member, since 2010

National Exercise Committee, Federal Mathematics Competition (Aufgabenkommission, Bundeswettbewerb Mathematik)
since 2011

Advisory Board, German Mathematical Olympiad (Beirat Mathematik-Olympiaden Deutschland)
since 2016

International Scientific Program Committee of the Eighth European Summer University on History and Epistemology in Mathematics Education (ESU-8), 20 to 24 July 2018 at Oslo & Akershus University College of Applied Sciences, Oslo, Norway

Selected Publications

[1] Christoph Kirfel, Rainer Kaenders
Integration aller Basisfunktionen der Schule mit Elementargeometrie - Ein Ansatz aus einem Guss
to appear in: Mathematische Semesterberichte
DOI: 10.1007/s00591-017-0191-6
[2] Christoph Kirfel, Rainer Kaenders
Integration by Symmetry
Mathematical Gazette
, 101.05:
[3] Rainer Kaenders, Y. Weiss-Pidstrygach
Skalen und Nomogramme
Perspektivwechsel bei der Begriffsentwicklung in der Analysis. Der Mathematikunterricht , 61: (4)
[4] Rainer Kaenders
Funktionen kann man nicht sehen. In: R. Kaenders & R. Schmidt (Hrsg) Mit GeoGebra mehr Mathematik verstehen
Vieweg-Teubner, Wiesbaden
[5] Rainer Kaenders, L. Kvasz
Mathematisches Bewusstsein. In: Helmerich, M., Lengnink, K., Nickel, G., Rathgeb, M., (Hrsg). Mathematik verstehen - philosophische und didaktische Perspektiven
[6] Rainer Kaenders
Von Wiskunde und Windmühlen - über den Mathematikunterricht in den Niederlanden, Beiträge zum Mathematikunterricht, Hauptvortrag GDM-Tagung in Oldenburg, GDM
WTM-Verlag Münster
[7] Rainer Kaenders
Zahlbegriff zwischen dem Teufel und der tiefen See
Der Mathematikunterricht
52: (5)
[8] Rainer H. Kaenders
The mixed Hodge structure on the fundamental group of a punctured Riemann surface
Proc. Amer. Math. Soc. , 129: (5): 1271--1281
[9] Ludwig Balke, Rainer Kaenders
On a certain type of Coxeter-Dynkin diagrams of plane curve singularities
Topology , 35: (1): 39--54
[10] Rainer Kaenders
The Seifert form of a plane curve singularity determines its intersection multiplicities
Indag. Math. (N.S.) , 7: (2): 185--197

Publication List

MathSciNet Publication List (external link)


• Nieuw Archief voor Wiskunde, Zeitschrift der „Königlichen Mathematikervereinigung“ KWG (3/2003 - 11/2007)
• Mit GeoGebra mehr Mathematik verstehen: Beispiele für die Förderung eines tieferen Mathematikverständnisses aus dem GeoGebra Institut Köln/Bonn (publ. with Reinhard Schmidt, 2011)
• Mit GeoGebra mehr Mathematik verstehen: Beispiele für die Förderung eines tieferen Mathematikverständnisses aus dem GeoGebra Institut Köln/Bonn (publ. with Reinhard Schmidt, 2014)
• Perspektivwechsel bei der Begriffsentwicklung in der Analysis. Der Mathematikunterricht, 61(4) (2015)
• Scientia in Educatione (Editorial Board, since 2016)
• Fachkulturen in der Lehrerbildung. Reihe Wissenschaft und Lehrerbildung (publ. with P. Geiss, R. Ißler, 2016)



Felix-Hausdorff-Gedächtnispreis, University of Bonn


Marie Curie Research Fellow, 5/93 - 4/95, University of Nijmegen, Netherlands


Maître des Conférences invité, University of Angers, France


NWO-Grant, 1/96 - 4/96, with Prof. Dr. R. Hain, Duke University, NC, USA

Selected Invited Lectures


“Von Wiskunde und Windmühlen: Über den Mathematikunterricht in den Niederlanden”, Keynote Lecture GDM-Tagung Oldenburg


“Parabool en kettinglijn, hyperbool en lemniscaat, Jakob en Johann”, Johann Bernoulli Lecture 23, University of Groningen, Netherlands

Selected PhD students

Stephan Berendonk (2014): “Erkundungen zum Eulerschen Polyedersatz – Genetisch, explorativ, anschaulich”,
now Postdoc, University of Bonn

Jennifer Klenzan (2014): “Selbstregulation im Mathematikunterricht gemeinsam entwickeln – Entwicklung, Durchführung und Evaluation einer Interventionsstudie zur Förderung von Selbstregulation im schulischen Kontext”

Mareike Mink (2016): “Geometrische Begriffsentwicklung anhand technischer Anwendungen der Kinematik”

Supervised Theses

  • PhD theses: 5, currently 2
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