@inbook {414, title = {Touch2Learn: Multi-Touch Lernumgebungen explorativ erforschen}, booktitle = {Mediales Lernen {\textendash} Beispiele f{\"u}r eine inklusive Mediendidaktik}, year = {2016}, pages = {95-104}, publisher = {Markus Peschel}, organization = {Markus Peschel}, keywords = {multi-touch}, issn = {978-3-8340-1549-5}, url = {http://paedagogik.de/index.php?m=wd\&wid=2798}, author = {Dohrmann, Christian} } @inbook {454, title = {Winkel in der Sekundarstufe I {\textendash} Sch{\"u}lervorstellungen erforschen}, booktitle = {Geometrie zwischen Grundbegriffen und Grundvorstellungen}, year = {2015}, pages = {29-42}, publisher = {Springer Verlag}, organization = {Springer Verlag}, address = {Berlin}, url = {http://link.springer.com/book/10.1007/978-3-658-06835-6}, author = {Christian Dohrmann and Ana Kuzle}, editor = {Andreas Filler and Anselm Lambert} } @proceedings {457, title = {Begriffsbildung zum Winkel in der Sek I: Auf der Suche nach Grundvorstellungen}, journal = {48. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik}, year = {2014}, pages = {301-304}, publisher = {WTM-Verlag.}, address = {Koblenz}, author = {Dohrmann, Christian and Ana Kuzle and J{\"u}rgen Roth and J. Ames} } @proceedings {456, title = {GeKoDyn: Eine Fortbildungsreihe zur dynamischen und kompetenzorientierten Sicht auf die euklidische Geometrie}, journal = {48. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik}, year = {2014}, pages = {181{\textendash}184}, publisher = {WTM-Verlag.}, address = {Koblenz}, author = {Rolf Biehler and Ana Kuzle and Wilfried Dutkowski and Elschenbroich, Hans-J{\"u}rgen and Gaby Heintz}, editor = {J{\"u}rgen Roth and J. Ames} } @article {455, title = {Geometrie lehren und lernen {\textendash} kompetenzorientiert und dynamisc}, journal = {Meidenbrief Mathematik}, year = {2014}, pages = {29{\textendash}30}, author = {Rolf Biehler and Wilfried Dutkowski and Elschenbroich, Hans-J{\"u}rgen and Gaby Heintz and Katrin Hollendung and Ana Kuzle} } @conference {449, title = {Unpacking Children{\textquoteright}s Angle "Grundvorstellungen{\textquotedblright}: The Case of Distance {\textquotedblleft}Grundvorstellung{\textquotedblright} of 1{\textdegree} Angle}, booktitle = {PME 38}, year = {2014}, month = {2014}, address = {Vancouver, Canada}, author = {Ana Kuzle and Christian Dohrmann}, editor = {Peter Liljedahl and Natalie Sinclare} } @proceedings {412, title = {Begriffsbildung im Mathematikunterricht der Sek I zum Thema Winkel}, journal = {Tagung des GDM-Arbeitskreises Geometrie 2012}, year = {2013}, address = {Saabr{\"u}cken}, abstract = {

Der Winkelbegriff als elementarer Begriff der ebenen Geometrie und Raumgeometrie ist aufgrund vielf{\"a}ltiger Aspekte und Definitionen ein komplexer Lehr- \& Lerngegenstand des Geometrieunterrichts. S{\"a}tze {\"u}ber Gleichheit, Summen und Differenzen von Winkeln, sowie der Winkel als Objekt-, Relations- und Ma{\ss}begriff sind f{\"u}r die gesamte (Schul-)Geometrie relevant. Der Winkelbegriff muss folglich im Mathematikunterricht systematische und ganzheitliche ausgebildet werden (KRAINER, 1989). Ergebnisse fachdidaktischer Forschung zum Thema innerhalb der letzten 30 Jahre stellen aufgrund nachweisbarer Fehlkonzepte und Fehlermuster die Bedeutung einer operativen Begriffsentwicklung heraus, bei der sowohl geeignete (digitale) Werkzeuge, als auch anschauliche Materialen und Darstellungsformen zum Einsatz kommen (u.a. KRAINER, 1989; MITCHELMORE \& WHITE, 2000; BERRY III \& WIGGINS, 2001). Weiterhin wird festgesellt, dass bestimmte Fehlkonzepte mit der systematischen Begriffseinf{\"u}hrung nach dem Grundschul{\"u}bergang dauerhaft und resistent {\"u}ber die Schullaufbahn {\quotedblbase}erworben{\textquotedblleft} werden. Als Einflussfaktoren gelten hierbei mentale Operationen und Vorstellungen zu Winkelaspekten, die eng mit den vorhandenen Fehlkonzepten verkn{\"u}pft sind. Konrad KRAINER (1989) stellt bereits den relevanten Bezug von Vorstellungen zu Begriffsaspekten bei Winkeln heraus: Winkel als {\quotedblbase}abgeknickte{\textquotedblleft} Gerade; Winkel als Ebenenteil; Winkel als Umlaufwinkel.

Der Artikel thematisiert die Analyse von Schulb{\"u}chern hinsichtlich verwendeter Repr{\"a}sentationen und Darstellungsformen zum Winkel in der Sek I. Bez{\"u}ge zur didaktischen Genese zum Winkelbegriff werden eingangs basierend auf der Arbeit von KRAINER (1989) hergestellt. Dar{\"u}ber hinaus werden erste Ergebnisse einer Untersuchung zu Winkelvorstellungen von F{\"u}nft- und Zehntkl{\"a}sslern vorgestellt und mit ausgew{\"a}hlten Forschungsbefunden kontrastiert. Die vorliegende Arbeit versteht sich als Ann{\"a}herung an die didaktische Auseinandersetzung zur Begriffsausbildung zum Winkel.

}, keywords = {angle}, author = {Dohrmann, Christian and Kuzle, Ana} } @proceedings {411, title = {Past-Present-Future: Winkel anschaulich unterrichten!}, journal = {47. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik}, year = {2013}, address = {M{\"u}nster}, abstract = {

Der Winkelbegriff und das Messen von Winkeln sind von zentraler Bedeu- tung f{\"u}r die ebene Geometrie und Raumgeometrie. Im Alltag begegnet man vielf{\"a}ltigen Winkelsituationen, wie z.B. beim Autofahren oder in Orientie- rungssituationen. Dar{\"u}ber hinaus ist die Winkelmessung in vielen Berufs- zweigen von gr{\"o}{\ss}ter Bedeutung, wie z.B. bei Architekten, (Bau-) Ingenieu- ren, Schreinern oder Piloten (Berry III \& Wiggins, 2001). Der Winkelbe- griff ist aufgrund vielf{\"a}ltiger Aspekte und Definitionen ein komplexer Ge- genstand des Geometrieunterrichts.

Im Mathematikunterricht sind S{\"a}tze {\"u}ber Gleichheit, Summen und Diffe- renzen von Winkeln in der gesamten Geometrie relevant. Sch{\"u}lerInnen zeigen Schwierigkeiten bei der operativen und konzeptuellen Winkelbe- griffsentwicklung (z.B. Krainer, 1989; Mitchelmore \& White, 2000). Im Beitrag werden Schulbuchanalysen mit typischen Fehlermustern und Fehl- konzepten kontrastiert und Schlussfolgerungen f{\"u}r eine anschauliche Be- griffsbildung diskutiert.

}, keywords = {angle}, author = {Dohrmann, Christian and Kuzle, Ana} } @article {KorDoh-duo-2011, title = {多触摸{\textquoteright}{\textquoteright}使用者界面的几何教育意义分析}, journal = {数学教学}, number = {4}, year = {2011}, keywords = {lehrer}, author = {Kortenkamp, Ulrich and Dohrmann, Christian} } @article {KorDoh-UIDDGS-2010, title = {User Interface Design for {D}ynamic {G}eometry Software}, journal = {Proceedings of CADGME 2009}, volume = {3}, number = {2}, year = {2010}, pages = {59-66}, abstract = {

In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch- capable DGS. We also give some hints on the educational benefits of proper user interface design.

}, keywords = {refereed}, url = {http://dppd.ubbcluj.ro/adn/article_3_2_6.pdf}, author = {Kortenkamp, Ulrich and Dohrmann, Christian} } @conference {KorBleDohKreLibMer-IIGEFTERFCIP-2009, title = {Interoperable Interactive Geometry For Europe {\textendash} First Technological and Educational Results and Future Challenges of the Intergeo Project}, booktitle = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France)}, year = {2009}, month = {January}, publisher = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education}, organization = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education}, address = {Lyon (France)}, abstract = {In this overview article we describe the manifold achievements and challenges of Intergeo, a project co-funded within the eContentplus programme2 of the European Union.}, keywords = {Intergeo, refereed}, url = {http://www.inrp.fr/publications/edition-electronique/cerme6/wg7-11-kortenkamp.pdf}, author = {Kortenkamp, Ulrich and Blessing, Axel M. and Dohrmann, Christian and Kreis, Yves and Libbrecht, Paul and Mercat, Christian} } @conference {KorBleDohKreLibMer-IIGEFTERFCIP-2009, title = {Interoperable Interactive Geometry For Europe {\textendash} First Technological and Educational Results and Future Challenges of the Intergeo Project}, booktitle = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France)}, year = {2009}, month = {January}, publisher = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education}, organization = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education}, address = {Lyon (France)}, abstract = {

In this overview article we describe the manifold achievements and challenges of Intergeo, a project co-funded within the eContentplus programme2 of the European Union.

}, keywords = {refereed}, url = {http://www.inrp.fr/publications/edition-electronique/cerme6/wg7-11-kortenkamp.pdf}, author = {Kortenkamp, Ulrich and Blessing, Axel M. and Dohrmann, Christian and Kreis, Yves and Libbrecht, Paul and Mercat, Christian} } @conference {LadKor-RMMERMMELREMS-2009, title = {Realisations of {MERS} (Multiple Extern Representations) and {MELRS} (Multiple Equivalent Linked Representations) in Elementary Mathematics Software}, booktitle = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France)}, year = {2009}, abstract = {

Assumptions of multiple mental representations lead to the presumption of an enhanced mathematical learning, especially of the process of internalization, due to MERs (Ainsworth 1999) and MELRs (Harrop 2003). So far, most educational software for mathematics at the primary level aims to help children to automatize mathematical operations, whereby symbolical representations are dominating. However, what is missing is software and principles for its design that support the process of internalization and the learning of external representations and their meaning themselves {\textendash} in primary school these are in particular symbols. This paper summarizes the current state of research and presents a prototype that aims to the above-mentioned purpose.

}, keywords = {refereed}, url = {http://www.inrp.fr/publications/edition-electronique/cerme6/wg7-01-ladel.pdf}, author = {Ladel, Silke and Kortenkamp, Ulrich}, editor = {Durand-Guerrier, Viviane and Soury-Lavergne, Sophie and Arzarello, Ferdinando} } @conference {KorRol-UTTLP-2009, title = {Using Technology in the Teaching and Learning of Box Plots}, booktitle = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France)}, year = {2009}, abstract = {

Box plots (or box-and-whisker-plots) can be used as a powerful tool for visualising sets of data values. Nevertheless, the information conveyed in the representation of a box plot is restricted to certain aspects. In this paper, we discuss both the potential and limitations of box plots. We also present a design for an empirical study in which the use of a variety of tasks explicitly addresses this duality. The activities used in the study are based on an interactive box plot applet that surpasses the currently available tools and offers new ways of experiencing box plots.

}, keywords = {refereed}, url = {http://www.inrp.fr/publications/edition-electronique/cerme6/wg7-03-kortenkamp-rolka.pdf}, author = {Kortenkamp, Ulrich and Rolka, Katrin}, editor = {Durand-Guerrier, Viviane and Soury-Lavergne, Sophie and Arzarello, Ferdinando} } @conference {KorDohKreDor-UIPTR-2009, title = {Using the {I}ntergeo Platform for Teaching and Research}, booktitle = {Proceedings of the 9th International Conference on Technology in Mathematics Teaching}, year = {2009}, publisher = {ICTMT-9}, organization = {ICTMT-9}, address = {Metz}, abstract = {We describe the key achievements of Intergeo, a project co-funded within the eContentplus programme of the European Union, and their impact on teacher education, based on the technical and educational concepts of the Intergeo Platform.}, keywords = {Intergeo, refereed}, author = {Kortenkamp, Ulrich and Dohrmann, Christian and Kreis, Yves and Dording, Carole}, editor = {Bardini, C. and Fortin, C. and Oldknow, Adrian and Vagost, D.} } @conference {KorDohKreDor-UIPTR-2009, title = {Using the {I}ntergeo Platform for Teaching and Research}, booktitle = {Proceedings of the 9th International Conference on Technology in Mathematics Teaching}, year = {2009}, publisher = {ICTMT-9}, organization = {ICTMT-9}, address = {Metz}, abstract = {

We describe the key achievements of Intergeo, a project co-funded within the eContentplus programme of the European Union, and their impact on teacher education, based on the technical and educational concepts of the Intergeo Platform.

}, keywords = {refereed}, author = {Kortenkamp, Ulrich and Dohrmann, Christian and Kreis, Yves and Dording, Carole}, editor = {Bardini, C. and Fortin, C. and Oldknow, Adrian and Vagost, D.} } @conference {Kor-PAEWQT-2006, title = {Paving the {A}lexanderplatz Efficiently with a quasi-periodic tiling}, booktitle = {Nexus VI: Architecture and Mathematics}, year = {2006}, pages = {57-62}, publisher = {Kim Williams Books}, organization = {Kim Williams Books}, address = {Turin}, abstract = {In this paper we describe a mathematical approach to create an organic, yet efficient to create tiling for a large non-rectangular space, the Alexanderplatz in Berlin. We show how to use the refinement algorithm for Penrose tilings in order to create a polygonal tiling that consist of four different tiles and is quasi-periodic. We also derive, based on the refinement algorithm, bounds for the percentage of tiles of each type needed. Another question that is addressed is whether it is possible to describe the calculated tiling in a linear form. Otherwise, it wouldn{\textquoteright}t be possible to use the tiling, as there must be a concise description suitable for the workers who lay out the concrete tiles.}, keywords = {refereed}, url = {http://www.nexusjournal.com/the-nexus-conferences/nexus-2006/171-n2006-kortenkamp.html}, author = {Kortenkamp, Ulrich}, editor = {Duvernoy, Sylvie and Pedemonte, Orietta} }