@book {KorBraBenKruLadVog-EML-2014, title = {Early Mathematics Learning}, year = {2014}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, keywords = {submitted}, isbn = {978-1-4614-4677-4}, url = {http://www.springer.com/education+\%26+language/mathematics+education/book/978-1-4614-4677-4}, editor = {Ulrich Kortenkamp and Birgit Brandt and Christiane Benz and G{\"o}tz Krummheuer and Silke Ladel and Rose Vogel} } @article {KisBurVolKor-ESSMSPS-2013a, title = {An Explorative Study of Search of Model Space in Problem Solving}, year = {2013}, note = {Submitted for publication}, keywords = {submitted}, author = {Saskia Kistener and Bruce Burns and Regina Vollmeyer and Ulrich Kortenkamp} } @booklet {KisBurVolKor-ESSMSPS-2013, title = {An Explorative Study of Search of Model Space in Problem Solving}, year = {2013}, abstract = {Building on dual-space theories, the three-space theory of problem solving suggests to add search of a model space in addition to search of experiment and hypothesis space. This study aimed at exploring the three postulated spaces, especially model space, by means of verbal protocols. Participants (n=32) were asked to think aloud while working with a computer based learning program. With this program they could learn about torques in physics using interactive graphics in which experiments with levers and forces could be conducted. Their knowledge about torques was tested before and after working with the program. Verbal protocols were analyzed with regard to the amount of search of the three spaces and regarding the quality of the participants{\textquoteright} models for torques. The three postulated spaces could be reliably identified in the protocols. For validity, the model quality score was related to performance and predicted final knowledge beyond prior knowledge. Our results add to the validity of model space and allow us to derive more specific hypotheses from the three-space theory.}, keywords = {poster}, url = {http://www.academia.edu/4237499}, author = {Saskia Kistener and Bruce Burns and Regina Vollmeyer and Ulrich Kortenkamp} } @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} } @mastersthesis {402, title = {The Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students{\textquoteright} Geometric Creativity in High Schools}, volume = {Ph.D.}, year = {2010}, pages = {523}, school = {Universit{\"a}t Schw{\"a}bisch-Gm{\"u}nd}, address = {Schw{\"a}bisch-Gm{\"u}nd}, abstract = {

It goes without saying that students can learn and develop their creative potential if\ appropriate programs are used that successfully teach them the creative skills and operationsnecessary. However, mathematics in general and geometry in particular, by their\ own nature, have a lot of possibilities that can be used in developing creativity. The\ purpose of the present study was threefold: First, to identify the principles of preparing\ a suggested 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 identi ed principles;\ third, to investigate the e ectiveness of this program by testing it with high school\ students.\ By reviewing the prior literature and studies related to the subject of the study, the\ principles of developing the suggested enrichment program were identi ed. Then, a\ suggested enrichment program based on these identi ed principles using the Interactive\ Geometry Software, Cinderella was developed. Moreover, within the present study an\ instrument, a geometric creativity test (GCT), was developed and a grading method for\ assessing the mathematically gifted students geometric creativity was established.\ The material was tested with a group of 7 mathematically gifted students in the Landesgymnasium\ fur Hochbegabte (LGH), a public high school for highly gifted and talented\ students in Schwabisch Gmund { Baden-Wurttemberg, Germany. The students came\ from 11th (5), 10th (1) and 9th (1) grade, two of them were male, ve female.\ In the study, the researcher used a one-group pretest { intervention { posttest preexperimental\ design. In this context the GCT was administered to students as a pretest\ at the beginning of the study; then the suggested enrichment program was introduced\ to them in 12 weekly 90-minutes sessions during the rst semester of the academic year\ 2008/09. The students retook the GCT as a posttest at the end of the study.\ 

The results indicated there were statistically signi cant di erences between the mean\ ranks of the subjects{\textquoteright} scores on the pre-post measurements of the geometric creativity\ test and its subscales in favor of the post measurement. The results also revealed that\ the suggested enrichment program was signi cantly e ective in developing geometric\ creativity as a whole ability and its four sub-components uency,\ exibility, originality,\ and elaboration.\ The results of the study suggest that the prepared enrichment program using DGS\ has a positive impact on the mathematically gifted students{\textquoteright} geometric creativity. The\ positive impact can be traced back to the content of the suggested enrichment program\ and its open-ended and divergent-production geometric situations and problems. Also,\ the positive impact can be attributed to the use of DGS along the program sessions\ that provide the subjects with not only many opportunities to explore, experiment,\ and make new mathematical conjectures, but also to solve problems and pose related\ problems.\ However, the study requires replication and improvements before any rm conclusions\ can be made. One of the biggest improvements would be to have more subjects so\ that the results become more generalized and meaningful. Moreover, pertaining to the\ experimental design, further studies are needed to investigate the e ectiveness of the\ suggested enrichment program using both quasi-experimental and true-experimental\ designs.\ Other avenues for research may focus on students{\textquoteright} a ective and emotional domains\ (e.g. self con dence, attitudes, and achievement motivation, among others), and might\ as well include an analysis of gender-related individual di erences.

}, url = {https://dl.dropboxusercontent.com/u/5761672/dissertation.pdf}, author = {El-Demerdash, Mohamed} } @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.} } @proceedings {398, title = {Enhancing Functional Thinking Using the Computer for Representational Transfer}, journal = {Proceedings of CERME 6}, year = {2009}, address = {Lyon (France)}, abstract = {

The area of functional thinking is complex and has many facets. There are several\ studies that describe the specific difficulties of functional thinking. They show that the\ main difficulties are the transfer between the various representations of functions,\ e.g. graph, words, table, real situation or formula, and the dynamic view of\ functional dependencies (process concept of a function). Interactive Geometry\ Software allows the visualization of the dynamic aspect of functional dependencies\ simultaneously in different representations and offers the opportunity to experiment\ with them. The author presents and discusses the potential of two interactive learning\ activities that focus on the dynamic aspect of functional thinking in a special way.\ Some preliminary results from a first adoption of the activities in class are presented.\ Resulting research questions and plans for further research are stated.

}, keywords = {empirical study, Functional thinking, Interactive Geometry Software, Interactive learning activity, representational transfer}, author = {Andrea Hoffkamp} } @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} } @booklet {KirNorRudSabUlr-EAFMNU-2003, title = {Empfehlungen zur {A}usstattung von {F}achraum-{M}edieninseln f{\"u}r den mathematischen und naturwissenschaftlichen {U}nterricht}, year = {2003}, month = {11}, publisher = {Senatsverwaltung Bildung, Jugend Sport, Berlin}, keywords = {invited}, author = {Kirstein, J{\"u}rgen and Nordmeier, Volkhard and Rudolf, Rass and Sabina, Jeschke and Ulrich, Kortenkamp} } @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} } @conference {KorRic-ENGC-1999, title = {Euklidische und {N}icht-{E}uklidische {G}eometrie mit {C}inderella}, booktitle = {Tagungsband zum N{\"u}rnberger Kolloquium zur Didaktik der Mathematik 1999}, year = {1999}, keywords = {invited}, url = {http://www.inf.fu-berlin.de/~kortenka/Papers/nichtEuklidisch.pdf}, author = {Kortenkamp, Ulrich H. and Richter-Gebert, J{\"u}rgen}, editor = {Weth, Thomas} } @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.} }