@conference {LadKor-EMWMAA-2012, title = {Early maths with multi-touch {\textendash} an activity-theoretic approach}, booktitle = {Proceedings of POEM 2012}, year = {2012}, keywords = {invited}, url = {http://cermat.org/poem2012/main/proceedings_files/Ladel-Kortenkamp-POEM2012.pdf}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @inbook {BesHerKorMulZim-ETWIAF-2012, title = {E-learning Tools with Intelligent Assessment and Feedback}, booktitle = {Intelligent and Adaptive Learning Systems: Technology Enhanced Support for Learners and Teachers}, year = {2012}, publisher = {IGI Global}, organization = {IGI Global}, keywords = {refereed}, author = {Bescherer, Christine and Herding, Daniel and Kortenkamp, Ulrich and M{\"u}ller, Wolfgang and Zimmermann, Marc}, editor = {Graf, Sabine and Lin, Fuhua and Kinshuk and McGreal, Rory} } @conference {El-Kor-EEPUDGSDMGSGC-2009, title = {The Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students{\textquoteright} Geometric Creativity}, booktitle = {Proceedings of the 9th International Conference on Technology in Mathematics Teaching}, year = {2009}, publisher = {ICTMT-9}, organization = {ICTMT-9}, address = {Metz}, abstract = {

The research work presented in this paper was guided by three goals: First, to identify the principles of preparing an enrichment program in Euclidean geometry using Dynamic Geometry Software to develop the mathematically gifted students{\textquoteright} geometric creativity in high schools, second, to develop an enrichment program based on the identified principles, and third, to investigate its effectiveness by testing it with high school students. The enrichment program was administered to 7 mathematically gifted students in 12 weekly 90-minute sessions. Results of a pre-post measurements revealed the effectiveness of the program in developing the subjects{\textquoteright} geometric creativity as a whole ability and its four sub-components (fluency, flexibility, originality, and elaboration).

}, keywords = {refereed}, author = {El-Demerdash, Mohamed and Kortenkamp, Ulrich}, editor = {Bardini, C. and Fortin, C. and Oldknow, Adrian and Vagost, D.} } @conference {Kor-EP-2005, title = {Experimentieren und Publizieren}, booktitle = {WWW und Mathematik - Lehren und Lernen im Internet, Tagungsband der 21. Arbeitstagung des Arbeitskreis Mathematikunterricht und Informatik in Dillingen/Donau}, year = {2005}, pages = {120-126}, publisher = {Franzbecker}, organization = {Franzbecker}, address = {Hildesheim}, abstract = {

In diesem Artikel werden zwei Erweiterungen Dynamischer Geometrie-Software (DGS) vorgestellt, die bisher vorhandene L{\"u}cken schlie{\ss}en und neue didaktische Impulse geben k{\"o}nnen. Zum einen wird die Unterst{\"u}tzung von Algorithmen in DGS und die Erweiterung durch selbst geschriebene Module beschrieben, wie sie bereits prototypisch in Cinderella implementiert ist. Zum anderen wird CINErella vorgestellt, eine Kombination aus Interaktion und Film, die sich zum Beispiel f{\"u}r die Dokumentation von Forschungsarbeit mit der DGS eignet.

}, keywords = {invited}, url = {http://kortenkamps.net/papers/2005/Dillingen03.pdf}, author = {Kortenkamp, Ulrich}, editor = {Bender, Peter and Herget, Wilfried and Weigand, Hans-Georg and Weth, Thomas} } @article {Kor-EMPWSMK-2004, title = {Experimental mathematics and proofs {\textendash} what is secure mathematical knowledge?}, journal = {Zentralblatt f{\"u}r Didaktik der Mathematik}, volume = {36}, number = {2}, year = {2004}, pages = {61{\textendash}66}, abstract = {

Experimental mathematics is a serious branch of mathematics that starts gaining attention both in mathematics education and research. We give examples of using experimental techniques (not only) in the classroom. At first sight it seems that introducing experiments will weaken the formal rules and the abstractness of mathematics that are considered a valuable contribution to education as a whole. By putting proof and experiment side by side we show how this can be avoided. We also highlight consequences of experimentation for educational computer software. Experimentelle Mathematik hat sich zu einem ernst zu nehmenden Teil der mathematischen Forschung und Ausbildung entwickelt, der immer mehr Beachtung findet. Wir geben Beispiele, wie solche experimentellen Techniken nicht nur, aber auch im Unterricht eingesetzt werden k{\"o}nnen. Zun{\"a}chst scheint es so, als w{\"u}rden Experimente die formalen Regeln und Abstraktionen der Mathematik schw{\"a}chen, die ein eigentliches Ziel des Mathematikunterrichts darstellen. Im Vergleich von Beweis und Experiment stellen wir dar, wie diese Schw{\"a}chung vermieden werden kann. Weiterhin betonen wir die Auswirkungen dieser Methoden auf Lern- und Lehrsoftware.

}, keywords = {refereed}, url = {http://subs.emis.de/journals/ZDM/zdm042a4.pdf}, author = {Kortenkamp, Ulrich} } @article {RicKor-ENGC-2000, title = {Euklidische und nicht-{E}uklidische {G}eometrie in {C}inderella}, journal = {Journal f{\"u}r Mathematikdidaktik}, volume = {22}, year = {2000}, pages = {303{\textendash}324}, abstract = {

Zusammenfassung: Wir erinnern an die Konzeption euklidischer und nicht-euklidischer Geometrie durch Klein und Cayley und weisen auf ihre Bedeutung fu ̈r moderne Software zur interaktiven (oder dynamischen) Geometrie hin. Insbesondere zeigt es sich, dass sich komplexe Zahlen vorzu ̈glich zu einer allgemein Behandlung hyperbolischer, elliptischer, euklidischer und anderer Geometrie eignen. Summary: We recall the concepts of Euclidean and non-Euclidean Geometry in the sense of Klein and Cayley and illustrate their importance for modern interactive (dynamic) geometry software. In particular, the use of complex numbers turns out to be the key to the most general approach to measurements in hyperbolic, elliptic, Euclidean and other geometries.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2000/Euklidisch-NichtEuklidisch.pdf}, author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich} } @article {Kor-ESPWMVQNP-1997, title = {Every simplicial polytope with at most d+4 vertices is a quotient of a neighborly polytope}, journal = {Discrete \& Computational Geometry}, volume = {18}, year = {1997}, pages = {455{\textendash}462}, abstract = {

We show that every simplicial d-polytope with d + 4 vertices is a quotient of a neighborly (2d + 4)-polytope with 2d + 8 vertices, using the technique of affine Gale diagrams. The result is extended to matroid polytopes.

}, keywords = {refereed}, url = {http://link.springer.de/link/service/journals/00454/htabst/18n4p455.html}, author = {Kortenkamp, Ulrich} } @article {KorRicSarZie-EP0-1997, title = {Extremal properties of 0/1-polytopes}, journal = {Discrete \& Computational Geometry}, volume = {17}, year = {1997}, pages = {439{\textendash}448}, abstract = {

We provide lower and upper bounds for the maximal number of facets of a d-dimensional 0/1-polytope, and for the maximal number of vertices that can appear in a two-dimensional projection ("shadow") of such a polytope.

}, keywords = {refereed}, url = {http://link.springer.de/link/service/journals/00454/htabst/17n4p439.html}, author = {Kortenkamp, Ulrich and Richter-Gebert, J{\"u}rgen and Sarangarajan, A. and Ziegler, G{\"u}nter M.} }