@inbook {Kor-EAVA-2011, title = {Die etwas andere Vorlesung: AnOrMaL}, booktitle = {Mathematik f{\"u}r alle - Wege zum {\"O}ffnen von Mathematik. Mathematikdidaktische Ans{\"a}tze. Festschrift f{\"u}r Wilfried Herget}, year = {2011}, publisher = {Franzbecker}, organization = {Franzbecker}, address = {Hildesheim}, keywords = {invited}, author = {Kortenkamp, Ulrich}, editor = {Krohn, Thomas and Malitte, Eva and Richter, Gerd and Richter, Karin and Sch{\"o}neburg, Silvia and Sommer, Rolf} } @conference {SpaKor-DGAPDGS-2009, title = {Demonstrating, Guiding, and Analyzing Processes in Dynamic Geometry Systems}, booktitle = {Proceedings of the 9th International Conference on Technology in Mathematics Teaching}, year = {2009}, publisher = {ICTMT-9}, organization = {ICTMT-9}, address = {Metz}, abstract = {

Process-oriented mathematics education focuses on learning processes rather than on their outcomes only. These processes should be monitored, guided and supported by the teacher. In addition, feedback should be given on the students{\textquoteright} activities, not only on their results. Groups of 30 (school) up to more than 600 (university) learners render it impossible to support processes without appropriate technology. This paper describes the tool CleverPHL that allows for designing process-oriented learning scenarios: processes can be recorded, replayed, completed, guided, and analyzed. These features are demonstrated with dynamic geometry systems (DGS).

}, keywords = {refereed}, author = {Spannagel, Christian and Kortenkamp, Ulrich}, editor = {Bardini, C. and Fortin, C. and Oldknow, Adrian and Vagost, D.} } @conference {KorRol-GBEWAGDDCS-2009, title = {"Der Boxplot ist nur von einzelnen Werten abh{\"a}ngig" {\textendash} Dateninterpretation durch Computereinsatz schulen}, booktitle = {Beitr{\"a}ge zum Mathematikunterricht. Vortr{\"a}ge auf der 43. Tagung f{\"u}r Didaktik der Mathematik in Oldenburg}, year = {2009}, abstract = {

Mit Hilfe von Boxplots lassen sich Datenreihen in aufschlussreicher Form visualisieren. Allerdings sind die Informationen, die in der grafischen Dar- stellung als Boxplot {\"u}bermittelt werden, auf gewisse Aspekte beschr{\"a}nkt. Bakker, Biehler und Konold (2004) stellen beispielsweise fest, dass der Umgang mit und das Verst{\"a}ndnis von Boxplots insbesondere f{\"u}r j{\"u}ngere Sch{\"u}lerinnen und Sch{\"u}ler mit nicht unerheblichen Schwierigkeiten verbun- den ist. Ziel unserer Arbeit ist es nicht, dass die Sch{\"u}lerinnen und Sch{\"u}ler Boxplots besser oder einfacher erstellen k{\"o}nnen. Durch die Vereinfachung der Erstellung von Boxplots mit Hilfe eines Applets1 und die darauf abge- stimmten {\"U}bungen sollen die Sch{\"u}lerinnen und Sch{\"u}ler vielmehr in die Lage versetzt werden, Boxplots zu interpretieren und dadurch Informatio- nen {\"u}ber die Verteilung der zugrunde liegenden Datenmenge erschlie{\ss}en zu k{\"o}nnen.

}, keywords = {invited}, url = {http://www.mathematik.tu-dortmund.de/ieem/cms/media/BzMU/BzMU2009/Beitraege/KORTENKAMP_Ulrich_ROLKA_Katrin_2009_Boxplots.pdf}, author = {Kortenkamp, Ulrich and Rolka, Katrin} } @conference {BleKor-EVM-2008, title = {Der {E}insatz von {V}ideo{C}lip{Q}uests in {M}oodle}, booktitle = {Vortr{\"a}ge auf der 5. Internationalen Moodle Konferenz 2008 in Klagenfurt}, year = {2008}, address = {Klagenfurt}, keywords = {refereed}, url = {http://moodlemoot.at/moodle/mod/data/view.php?d=2\&rid=22}, author = {Blessing, Axel M. and Kortenkamp, Ulrich} } @inbook {Kor-DDPWKGI-2005, title = {Dokumentation, Diskussion und Protokolle: Wie kommuniziert man Geometrie im Internetzeitalter?}, booktitle = {Strukturieren {\textendash} Modellieren {\textendash} Kommunizieren. Leitbilder mathematischer und informatischer Aktivit{\"a}ten}, year = {2005}, pages = {141-150}, publisher = {Franzbecker}, organization = {Franzbecker}, type = {{Festschrift f{\"u}r Karl-Dieter Klose, Siegfried Krauter, Herbert L{\"o}the und Heinrich W{\"o}lpert.}}, address = {Hildesheim}, abstract = {

Neue Medien sind nicht nur technisches Spielzeug, sondern bieten auch die Gelegenheit, {\"u}ber Kommunikation nachzudenken. Protokolle, Kodierungen, Spezifizierungen sind Beitr{\"a}ge der Informatik zur Wissensstrukturierung; Netzwerke und Datenbanken oder Kombinationen davon (also zum Beispiel das Internet) dienen der Kommunikation dieser Strukturen {\"u}ber kurze und weite Strecken, aber auch {\"u}ber die Dimension der Zeit hinweg. Im Schulunterricht sind genau solche F{\"a}higkeiten gefragt; Gruppen- oder Projektarbeit oder auch Lerntageb{\"u}cher sind schon l{\"a}nger wirksame Mittel zum "besseren" Lehren und Lernen. Im Mathematikunterricht, speziell in der Geometrie, k{\"o}nnen nun neue Medien, in diesem Fall Lehr-/Lernsoftware, mit den informationstechnischen Methoden verkn{\"u}pft werden; in diesem Artikel versuchen wir allgemeine Richtlinien herzuleiten und stellen kurz einige durch diese Richtlinien motivierten Projekte vor.

}, keywords = {invited}, url = {http://kortenkamps.net/papers/2005/DDP-LB.pdf}, author = {Kortenkamp, Ulrich}, editor = {Engel, Joachim and Vogel, Rose and Wessolowski, Silvia} } @conference {RicKor-DGGM-2002, title = {Dynamische {G}eometrie: {G}rundlagen und {M}{\"o}glichkeiten}, booktitle = {Tagungsband zum N{\"u}rnberger Kolloquium zur Didaktik der Mathematik 2002}, year = {2002}, pages = {369-372}, keywords = {invited}, url = {http://www.cinderella.de/papers/DG\_GM.pdf}, author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich}, editor = {Weth, Thomas} } @conference {KorRic-DCDG-2001, title = {Decision complexity in {D}ynamic {G}eometry}, booktitle = {Proceedings of ADG 2000}, series = {Lecture Notes in Artificial Intelligence}, number = {2061}, year = {2001}, pages = {167{\textendash}172}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, address = {Heidelberg}, abstract = {

Geometric straight-line programs [5,8] can be used to model geometric constructions and their implicit ambiguities. In this paper we discuss the complexity of deciding whether two instances of the same geometric straight-line program are connected by a continuous path, the Complex Reachability Problem.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2001/36_DecisionComplexity.pdf}, author = {Kortenkamp, Ulrich and Richter-Gebert, J{\"u}rgen}, editor = {Wang, Dongming} } @conference {Kor-IGC-2001, title = {Die interaktive {G}eometrie-{S}oftware {C}inderella}, booktitle = {Tagungsband Learntec 2001}, volume = {2}, year = {2001}, pages = {525{\textendash}532}, address = {Karlsruhe}, keywords = {refereed}, author = {Kortenkamp, Ulrich}, editor = {Beck, Uwe and Sommer, Winfried} } @conference {RicKor-DSEG-2001, title = {A dynamic setup for elementary geometry}, booktitle = {Proceedings of MTCM 2000}, year = {2001}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, abstract = {

In this article we survey the theoretical background that is required to build a consistent and continuous setup of dynamic elementary geometry. Unlike in static elementary geometry in dynamic elementary geometry the elements of a construction are allowed to move around as long as the geometric constraints intended by the construction are not violated. A typical problem in such a scenario is to resolve ambiguous situations that arise from geometric operations like intersecting a circle and a line. After introducing a formal framework for dealing with dynamic geometric constructions, we will demonstrate that a suitable resolution of these ambiguities requires the consideration of complex projective spaces. We will discuss several aspects where one can benefit from such a rather general approach. Finally, we will sketch some proofs that show that several fundamental algorithmic problems arising in such a context are NP-hard or even harder.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2001/35\_DynamicSetup.pdf}, author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich} } @article {Kor-DG-2001, title = {Dynamische {G}eometrie}, journal = {Mitteilungen der DMV}, volume = {3}, year = {2001}, pages = {33{\textendash}40}, keywords = {invited}, author = {Kortenkamp, Ulrich} } @conference {KorRic-DCDG-2000, title = {Decision complexity in {D}ynamic {G}eometry}, booktitle = {Proceedings of ADG 2000}, series = {International Workshop on Automatic Deduction in Geometry}, volume = {3}, year = {2000}, note = {Extended Abstract}, pages = {216{\textendash}220}, abstract = {

Geometric straight-line programs [6, 10] can be used to model geo- metric constructions and their implicit ambiguities. In this paper we discuss the complexity of deciding whether two instances of the same geometric straight-line program are connected by a continuous path, the Complex Reachability Problem.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2000/ADG2000_UK.pdf}, author = {Kortenkamp, Ulrich and Richter-Gebert, J{\"u}rgen}, editor = {Wang, Dongming} } @conference {RicKor-DACG-2000, title = {Dynamic aspects in computational geometry}, booktitle = {Proceedings of the EACA 2000}, year = {2000}, pages = {51{\textendash}61}, address = {Barcelona}, abstract = {

Computational Geometry very often focuses on static problems, like computing the convex hull or Voronoi complex of a given set of points. Fundamentally new questions arise when the objects under consideration are no longer static, but may move around with respect to certain constraints. This scenario is not unusual, for instance every mechanism can be considered as a dynamic geometry entity. Here we focus on the new areas of problems that arise from genuinely dynamic effects. Constructions from elementary geometry play a crucial role in this context, since they form first natural instances of non-trivial examples where it is reasonable to study the dynamic behaviour. One of the most fundamental problems arises when one considers one point of an intersection of a line and a circle and allows the line to move around. Since the point of intersection is not unique, a computer program has to decide for every "discrete snapshot" which of the two intersection points is meant. If this decision is not made correctly a "path-jumping" of the point may occur. A careful analysis of the situation shows that for a satisfactory resolution of the problem one has to embed the configuration in an ambient complex projective space. One even has to take monodromy effects and underlying Riemann surfaces into account. We will develop a theory for the study of these phenomena. After this, we will investigate the algorithmic complexity of "making the right decision". It will turn out that even in very weak versions this problem is NP-hard. In some stronger versions it is PSPACE hard or even undecidable.

}, keywords = {refereed}, author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich}, editor = {Montes, Antonio} }