@article {LadKor-AAMTEML-2012, title = {An activity-theoretic approach to multi-touch tools in early maths learning}, journal = {The International Journal for Technology in Mathematics Education}, volume = {20}, number = {1}, year = {2013}, abstract = {

In this article we present an activity theory based framework that can capture the complex situations that arise when modern technology like multi-touch devices are introduced in classroom situations. As these devices are able to cover more activities than traditional technologies, even computer-based, media, we have to accept that they now take a larger role in the model of interactions. We reflect this fact by moving the artefact into the centre of our observations, leading to an artefact-centric activity theory (ACAT). The theory was developed in the need of analysing learning environments for primary maths education.

}, keywords = {refereed}, url = {http://www.tech.plym.ac.uk/research/mathematics_education/field\%20of\%20work/ijtme/volume_20/number_one.html$\#$one}, 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 {LadKor-AAMTEML-2011, title = {An activity-theoretic approach to multi-touch tools in early maths learning}, booktitle = {Proceedings of ATATEMLO 2011 in Paris}, year = {2011}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @conference {LadKor-FMBUNO-2011, title = {Finger-Symbol-Sets and Multi-Touch for a better understanding of numbers and operations}, booktitle = {Proceedings of CERME 7, Rzeszow}, year = {2011}, abstract = {

Basic concepts of numbers and operations are fundamental for mathematical learning. Suitable materials for developing such basic concepts are hands and fingers. Among other things, this is because of their natural structure of 5 and 10. To support the development of concepts and the process of internalization a linking between different forms of representations by the computer can be helpful. To benefit of both, the advantages of the hands and fingers and the automatically linking, we suggest using multi-touch-technology, i.e. computer input devices that are able to recognize several touch gestures at the same time. Here, children can present numbers with their fingers that produce virtual objects. These objects can be automatically linked with the symbolic form of representation.

}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @conference {LadKor-IMSFSS-2011, title = {Implementation of a multi-touch-environment supporting finger symbol sets}, booktitle = {Proceedings of CERME 7, Rzeszow}, year = {2011}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @article {Kor-IIGE-2011, title = {Interoperable {I}nteractive {G}eometry for {E}urope}, journal = {The Electronic Journal of Mathematics and Technology}, volume = {5}, number = {1}, year = {2011}, abstract = {The Intergeo project is driven by a consortium of commercial, semi-commercial and open- source software producers as well as mathematics educators from all over Europe. The primary goal is to make mathematics driven by interactive resources more accessible to all teachers and learners, by facilitating the search, use and quality assurance of them. In this article I will highlight the main obstacles we faced and how we approached them and give an outlook on the future of interactive geometry and the project. Furthermore, I will raise some didactical and research questions that should be answered if we really want to integrate computer-based teaching, learning and assessment into our curricula. This article is a written version of the keynote held at the CADGME 2010 conference in Hluboka, Czech Republic. It does not, cannot and should not contain references for all claims made, but rather summarize the Intergeo project and serve as an introduction to the various publi- cations of the project that are available on its website http://i2geo.net. We refer to those for a much deeper description of each of the issues raised, as well as proper references to existing work.}, keywords = {Intergeo, refereed}, url = {http://www.radford.edu/ejmt}, author = {Kortenkamp, Ulrich} } @article {Kor-IIGE-2011, title = {Interoperable {I}nteractive {G}eometry for {E}urope}, journal = {The Electronic Journal of Mathematics and Technology}, volume = {5}, number = {1}, year = {2011}, abstract = {

The Intergeo project is driven by a consortium of commercial, semi-commercial and open- source software producers as well as mathematics educators from all over Europe. The primary goal is to make mathematics driven by interactive resources more accessible to all teachers and learners, by facilitating the search, use and quality assurance of them. In this article I will highlight the main obstacles we faced and how we approached them and give an outlook on the future of interactive geometry and the project. Furthermore, I will raise some didactical and research questions that should be answered if we really want to integrate computer-based teaching, learning and assessment into our curricula. This article is a written version of the keynote held at the CADGME 2010 conference in Hluboka, Czech Republic. It does not, cannot and should not contain references for all claims made, but rather summarize the Intergeo project and serve as an introduction to the various publi- cations of the project that are available on its website http://i2geo.net. We refer to those for a much deeper description of each of the issues raised, as well as proper references to existing work.

}, keywords = {Intergeo, refereed}, url = {http://www.radford.edu/ejmt}, author = {Kortenkamp, Ulrich} } @inbook {KorBle-VEP-2011, title = {VideoClipQuests as an E-Learning Pattern}, booktitle = {Investigations on E-Learning Patterns: Context Factors, Problems, and Solutions}, year = {2011}, pages = {237-248}, publisher = {Information Science Reference}, organization = {Information Science Reference}, chapter = {15}, address = {Hershey, PA}, keywords = {refereed}, doi = {10.4018/978-1-60960-144-7.ch015}, author = {Kortenkamp, Ulrich and Blessing, Axel M.}, editor = {Kohls, Christian and Wedekind, Joachim} } @conference {MulKor-LPWR-2010, title = {Learning Programming with {Ruby}}, booktitle = {Proceedings of the IFIP Workshop "New developments in ICT and Informatics education{\textquoteright}{\textquoteright}}, year = {2010}, publisher = {IFIP TC3}, organization = {IFIP TC3}, abstract = {

Introducing students into the fundamentals of programming can still be considered as a real challenge. The choice of the right programming language seems to play a major role. In this paper we present our experiences with the programming language Ruby in introductory programming classes. Ruby is a relatively young programming language, which provides some very interesting aspects and seems like a very good candidate as a beginner{\textquoteright}s programming language, integrating the advantages of other languages with respect to learning programming, while still being professional enough to support open-ended learning. We discuss several aspects of Ruby that distinguish it from other languages and which make it a good choice for a beginner{\textquoteright}s course in programming. In addition, we discuss the approaches applied at two different universities in teaching programming with Ruby. We present in some detail the individual programming exercises and present student results. Finally, we discuss the pros and cons for applying Ruby as a first programming language.

}, keywords = {refereed}, author = {M{\"u}ller, Wolfgang and Kortenkamp, Ulrich} } @article {RicKor-PSMP-2010, title = {The power of scripting: {DGS} meets programming}, journal = {Acta Didactica Napocensia}, volume = {3}, number = {2}, year = {2010}, pages = {67-78}, abstract = {

In this article we demonstrate how the combination of a system for dynamic geometry with a freely programmable scripting environment can be advantageously used in teaching and research. We explain the reasons behind various design decisions that were made by us when designing the language CindyScript and give examples that proof how they lead to easy and understandable code that can be used in education. We give several concrete application scenarios of the language that was developed by the authors and seamlessly interacts with the dynamic geometry system Cinderella.

}, keywords = {refereed}, url = {http://dppd.ubbcluj.ro/adn/article_3_2_7.pdf}, author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich} } @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} } @inbook {BleKor-VSL-2010, title = {VideoClipQuests as a New Setup For Learning}, booktitle = {Learning and Instruction in the Digital Age: Making a Difference through Cognitive Approaches, Technology-facilitated Collaboration and Assessment, and Personalized Communications}, year = {2010}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, chapter = {11}, abstract = {

VideoClipQuests (VCQs) are a teaching-learning approach focussed on the learner{\textquoteright}s self-activity while information is collected by searching the Internet, similar to the well- established concept of WebQuests. VCQs can be one element to sensibly integrate the possi- bilities and advantages of the virtual world into teaching. Some of the advantages of VCQs are that they allow the teachers great latitude, they can be created very easily, they are com- patible with a multitude of learning platforms, and they can be used both in e-Learning and traditional lectures. Moreover, they appear to inherently motivate the learners and thus be- come highly accepted. In this chapter we present the concept of a VCQ as well as first evalu- ation results of their influence in learning.

}, keywords = {refereed}, author = {Blessing, Axel M. and Kortenkamp, Ulrich}, editor = {Spector, J. Michael and Ifenthaler, Dirk and Isa{\'\i}as, Pedro and Kinshuk and Sampson, Demetrios G.} } @conference {KorRic-BEW-2009, title = {Blended Experimentation with DGS}, booktitle = {Proceedings of CADGME 2009}, year = {2009}, abstract = {

Experimentation is an important element of science teaching. Students should experience real-world phenomena, and support or disprove their hypotheses about the world by setting up appropriate situations, conducting the experiments, gathering data and drawing conclusions. Unfortunately, many experiments are unsuitable for school teaching out of various reasons. They might be too dangerous, too expensive, too complex, too unreliable, or they take too much time to complete. Using simulation software, many experiments can be replaced by safer, cheaper, easier, more reliable or sped-up virtual counterparts. Such simulations range from showing videos of repeated runs of the real experiment, together with interaction facilities, to mathematical simulations using numerical solutions of partial differential equations. However, there is a pedagogical drawback of the simulation approach: The connection to the real world situation is (at least partially) lost. This might harm both the motivation of the students and their belief in the conclusions. In this paper we describe the approach of blended experimentation, where simulations and the real world are connected via sensors and actors. The sensors are able to influence the simulation, while the actors can change the real world. We show first implementations and examples using Dynamic Geometry Software and other Mathematical Software as simulation environments.

}, keywords = {refereed}, url = {http://www.risc.jku.at/conferences/cadgme2009/?content=proceedings}, author = {Kortenkamp, Ulrich and Richter-Gebert, J{\"u}rgen} } @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 {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 {AbaBotEscHenKorKreLibMarMer-IFFP-2009, title = {The {I}ntergeo File Format in Progress}, booktitle = {Proceedings of the 22nd OpenMath Meeting}, year = {2009}, abstract = {In this paper we describe the ongoing effort to specify a com- mon file format for Interactive or Dynamic Geometry Systems (DGS). Our approach is based on the OpenMath standard, and uses its flexible extension mechanisms like Content Dictionaries. We discuss the various design decisions, the Content Dictionaries that have been defined, as well as open questions to be resolved.}, keywords = {Intergeo, refereed}, author = {Ab{\'a}nades, Miguel and Botana, Francisco and Escribano, Jes{\'u}s and Hendriks, Maxim and Kortenkamp, Ulrich and Kreis, Yves and Libbrecht, Paul and Marques, Daniel and Mercat, Christian} } @conference {AbaBotEscHenKorKreLibMarMer-IFFP-2009, title = {The {I}ntergeo File Format in Progress}, booktitle = {Proceedings of the 22nd OpenMath Meeting}, year = {2009}, abstract = {

In this paper we describe the ongoing effort to specify a com- mon file format for Interactive or Dynamic Geometry Systems (DGS). Our approach is based on the OpenMath standard, and uses its flexible extension mechanisms like Content Dictionaries. We discuss the various design decisions, the Content Dictionaries that have been defined, as well as open questions to be resolved.

}, keywords = {refereed}, author = {Ab{\'a}nades, Miguel and Botana, Francisco and Escribano, Jes{\'u}s and Hendriks, Maxim and Kortenkamp, Ulrich and Kreis, Yves and Libbrecht, Paul and Marques, Daniel 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 {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 {FesKor-POLEIGL-2009, title = {Process Orientated Learning Environments For Interactive Geometry Lessons}, booktitle = {Proceedings of the 9th International Conference on Technology in Mathematics Teachingh International Conference on Technology in Mathematics Teaching}, year = {2009}, publisher = {ICTMT-9}, organization = {ICTMT-9}, address = {Metz}, abstract = {

Based on the interactive geometry software Cinderella we developed a learning environment to be used for teaching geometry at university level. Following the ideas of the constructivist learning theory the software allows for learning by discovery. The activities are implemented in a process-oriented design. Our software supports both the learning of mathematical processes by the students and analysing their process of learning mathematics. In this paper we focus on a particular learning unit on congruencies and line reflections. By varying the axes of reflection, students can study the reduction theorems for geometric transformations. Different directly given or subliminal hints help the students to understand the mathematical principles behind these theorems. Our tool analyses the student{\textquoteright}s solution processes automatically and generates feedback on demand to the students. This learning environment can be used in conjunction with the recording of user actions. Our final goal is to be able to analyse learning processes of students using the tool semi- automatically and use this information to improve teaching and learning.

}, keywords = {refereed}, author = {Fest, Andreas and Kortenkamp, Ulrich}, editor = {Bardini, C. and Fortin, C. and Oldknow, Adrian and Vagost, D.} } @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} } @article {FesKor-TGAWV-2009, title = {Teaching Graph Algorithms with Visage}, journal = {Teaching Mathematics and Computer Science}, volume = {7}, number = {1}, year = {2009}, pages = {35-50}, abstract = {

Combinatorial optimization is a substantial pool for teaching authentic mathematics. Studying topics in combinatorial optimization practice different mathematical skills, and because of this have been integrated into the new Berlin curriculum for secondary schools. In addition, teachers are encouraged to use adequate teaching software. The presented software package "Visage" is a visualization tool for graph algorithms. Using the intuitive user interface of an interactive geometry system (Cinderella), graphs and networks can be drawn very easily and different textbook algorithms can be visualized on the graphs. An authoring tool for interactive worksheets and the usage of the build-in programming interface offer new ways for teaching graphs and algorithms in a classroom.

}, keywords = {refereed}, url = {http://tmcs.math.klte.hu/Contents/2009-Vol-VII-Issue-I.html}, author = {Fest, Andreas and Kortenkamp, Ulrich} } @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 {BleKor-VEP-2009, title = {VideoClipQuests as an E-Learning Pattern}, booktitle = {Proceedings of the E-Learning Patterns Workshop 2009}, year = {2009}, keywords = {refereed}, author = {Blessing, Axel and Kortenkamp, Ulrich} } @article {LadKor-VAGKF-2009, title = {Virtuell-enaktives Arbeiten mit der {\quotedblbase}Kraft der F{\"u}nf{\textquoteright}{\textquoteright}}, journal = {MNUprimar}, year = {2009}, abstract = {

Der {\"U}bergang von einem ordinalen Zahlkonzept zu einem strukturierten Zahlbegriff f{\"a}llt manchen Kindern schwer. Wir stellen vor, wie diesen Kindern mit Hilfe des Computers die {\guillemotright}Kraft der F{\"u}nf{\guillemotleft} n{\"a}hergebracht werden kann. Dabei stellt sich als entscheidender Vorteil heraus, dass die Kinder F{\"u}nferp{\"a}ckchen virtueller Pl{\"a}ttchen mit einem {\guillemotright}Griff{\guillemotleft} nehmen k{\"o}nnen, ohne die Pl{\"a}ttchen einzeln abz{\"a}hlen zu m{\"u}ssen, diese aber dennoch auch wieder einzeln gegriffen werden k{\"o}nnen.

}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @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} } @conference {KorFes-FCIAEMS-2008, title = {From {CAS/DGS} Integration to Algorithms in Educational Math Software}, booktitle = {Proceedings of ATCM 08}, year = {2008}, abstract = {

The standard triumvirate of \ "New Media" in the mathematics curriculum {\textendash} CAS, DGS and spreadsheet {\textendash} is establishing its secured position in teaching. This article illustrates, using the evolution of the software Cinderella as a guiding example, how a further integration of these products will allow for new teaching approaches. These will support the formation of important mathematical competencies, such as the ability to find and rate mathematical models for real world problems. A central observation is the algorithmic nature of userdefined functions and that it is crucial for the learning process to be able to execute algorithms step by step.

}, keywords = {refereed}, author = {Kortenkamp, Ulrich and Fest, Andreas} } @conference {Kor-TBADMC-2008, title = {A Technology Based Approach to Discrete Mathematics in the Classroom}, booktitle = {Proceedings of ICME-11, TSG 15}, year = {2008}, address = {Monterrey, Mexico}, abstract = {In this article we describe a new approach to teaching discrete mathematics, in particular graph theory and graph algorithms, using interactive geometry software. Students are encouraged to use the computer to explore and verify their theories using a computer, and use it as a tool for modeling real-life situations.}, keywords = {refereed}, url = {http://tsg.icme11.org/document/get/765}, author = {Kortenkamp, Ulrich}, editor = {Campbell, Stephen and Grenier, Denise} } @conference {BleKor-VSL-2008, title = {VideoClipQuests as a New Setup For Learning}, booktitle = {Proceedings of the IADIS International Conference on Cognition and Exploratory Learning in Digital Age (CELDA 2008)}, year = {2008}, month = {10}, pages = {343{\textendash}346}, publisher = {IADIS}, organization = {IADIS}, address = {Freiburg}, abstract = {

VideoClipQuests {\textendash} in short: VCQs {\textendash} are a teaching-learning-approach focussed on the learner{\textquoteright}s self-activity while information is collected by searching the Internet, similar to the well-established concept of WebQuests. VCQs can be one element to sensibly integrate the possibilities and advantages of the virtual world into teaching. Some of the advantages of VCQs are that they allow the teacher great latitude, they can be created very easily, they are compatible with a multitude of learning platforms, and they can be used both in e-learning and traditional lectures. Moreover, they appear to inherently motivate the learners and thus become highly accepted. In this paper we present the concept of a VCQ as well as first evaluation results of their influence to learning.

}, keywords = {refereed}, author = {Blessing, Axel and Kortenkamp, Ulrich}, editor = {Kinshuk and Sampson, Demetrios G. and Spector, J. Michael and Isa{\'\i}as, Pedro and Ifenthaler, Dirk} } @inbook {Kor-CTAT-2007, title = {Combining {CAS} and {DGS} {\textendash} {T}owards {A}lgorithmic {T}hinking}, booktitle = {Symbolic Computation and Education}, year = {2007}, pages = {150-173}, publisher = {World Scientific}, organization = {World Scientific}, address = {Singapore}, abstract = {This article discusses some ways to combine software for interactive geometry and computer algebra, with an emphasis on using this software in teaching. Some arising mathematical problems and necessary software specific paradigms that have to be adjusted are considered, and solutions to these problems are presented. The article also highlights some of the aspects that drove the development of the mathematics software Cinderella.2, which integrates an interactive geometry software package, a physics simulation engine, and an all-purpose functional programming language.}, keywords = {refereed}, author = {Kortenkamp, Ulrich}, editor = {Li, Shangzhi and Wang, Dongming and Zhang, Jing-Zhong} } @conference {Kor-GUCCME-2007, title = {Guidelines for Using Computers Creatively in Mathematics Education}, booktitle = {Enhancing University Mathematics: Proceedings of the First KAIST International Symposium on Teaching}, series = {CBMS Issues in Mathematics Education}, volume = {14}, year = {2007}, pages = {129{\textendash}138}, publisher = {AMS}, organization = {AMS}, abstract = {

Computers are the ultimate tool for teaching: They provide mi- croworlds that can be explored; they can be forgiving and strict; they take account of everything that{\textquoteright}s happening; they can create maps of what the learner knows or still has to learn; they are fun to use; they provide interactive illustrations that enlighten those who use them {\textendash} or at least, that{\textquoteright}s what they could be or do. There are significant drawbacks: many people do not know what they could do with them; if they know it, they probably do not know how to make them do it; and, finally, it is not validated whether it is of any didactic value to use them in the way they are used. In this text, we present some basic guidelines that can help in designing and evaluating electronic material. Starting from an example, we identify some roles the computer can take and discuss their implications for the development of mathematics tools.

}, keywords = {refereed}, url = {http://www.ams.org/bookstore?fn=20\&arg1=cbmathseries\&item=CBMATH-14}, author = {Kortenkamp, Ulrich}, editor = {Ko, Ki Hyoung and Arganbright, Deane} } @conference {SpaKor-PBLAWA-2007, title = {Prozesse beim {L}ernen mit {DGS}: {A}ufzeichnung, {W}iedergabe, {A}nalyse}, booktitle = {Tagungsband des Arbeitskreis Geometrie der GDM}, year = {2007}, publisher = {Franzbecker}, organization = {Franzbecker}, address = {Hildesheim, Berlin}, keywords = {refereed}, author = {Spannagel, Christian and Kortenkamp, Ulrich}, editor = {Ludwig, Matthias} } @inbook {Kor-PA-2007, title = {Punkt- und {A}chsenspiegelungen mit {DGS}}, booktitle = {Lernen mit Dynamischen Geometriesystemen}, series = {Ausgew{\"a}hlte Unterrichtskonzepte im Mathematikunterricht in unterrichtlicher Erprobung}, volume = {3}, year = {2007}, pages = {5-28}, publisher = {Franzbecker}, organization = {Franzbecker}, address = {Hildesheim}, keywords = {refereed}, author = {Kortenkamp, Ulrich}, editor = {Beckmann, Astrid} } @article {Kor-AGU-2006, title = {Algorithmische {G}eometrie im {U}nterricht}, journal = {Der Mathematikunterricht}, volume = {52}, number = {1}, year = {2006}, pages = {32-39}, publisher = {Friedrich Verlag}, address = {Hannover}, keywords = {refereed}, author = {Kortenkamp, Ulrich} } @conference {MulBesKorSpa-ICAMCSP-2006, title = {Intelligent Computer-aided Assessment in the Math Classroom: State-of-the-art and Perspectives}, booktitle = {Proceedings of the IFIP WG 3.1, 3.3, \& 3.5 Joint Conference Imagining the future for ICT and Education, Alesund, Norway}, year = {2006}, publisher = {IFIP}, organization = {IFIP}, address = {Alesund}, keywords = {refereed}, author = {M{\"u}ller, Wolfgang and Bescherer, Christine and Kortenkamp, Ulrich and Spannagel, Christian} } @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} } @article {GesKorLutMat-VVADM-2005, title = {Visage {\textendash} Visualization of Algorithms in Discrete Mathematics}, journal = {Zentralblatt f{\"u}r Didaktik der Mathematik}, volume = {37}, number = {5}, year = {2005}, pages = {395-401}, abstract = {

Abstract: Which route should the garbage collectors{\textquoteright} truck take? Just a simple question, but also the starting point of an exciting mathematics class. The only "hardware" you need is a city map, given on a sheet of paper or on the computer screen. Then lively discussions will take place in the classroom on how to find an optimal routing for the truck. The aim of this activity is to develop an algorithm that constructs Eulerian tours in graphs and to learn about graphs and their properties. This teaching sequence, and those stemming from discrete mathematics, in particular combinatorial optimization, are ideal for training problem solving skills and modeling {\textendash} general competencies that, influenced by the German National Standards, are finding their way into curricula. In this article, we investigate how computers can help in providing individual teaching tools for students. Within the Visage project we focus on electronic activities that can enhance explorations with graphs and guide students even if the teacher is not available {\textendash} without taking away freedom and creativity. The software package is embedded into a standard DGS, and it offers many pre-built and teacher-customizable tools in the area of graph algorithms. Until now, there are no complete didactical concepts for teaching graph algorithms, in particular using new media. We see a huge potential in our methods, and the topic is highly requested on part of the teachers, as it introduces a modern and highly relevant part of mathematics into the curriculum.

}, keywords = {refereed}, author = {Geschke, Anne and Kortenkamp, Ulrich and Lutz-Westphal, Brigitte and Materlik, Dirk} } @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 {KorMat-GTWCEUJJ-2004, title = {Geometry teaching in wireless classroom environments using {Java} and {J2ME}}, journal = {Science of Computer Programming}, volume = {53}, number = {1}, year = {2004}, month = {10}, pages = {71{\textendash}85}, abstract = {

Interactive geometry software is established as an important tool in geometry and math education. We present our research on possible ways to use such software in wireless classroom environments. In particular, we address user interface issues on portable devices and describe how we maintain a common code base for both desktop and mobile environments, thus increasing the stability of the application. We also report on our empirical data comparing different Java virtual machines that are available for portable devices using a prototype implementation of the Interactive Geometry Software Cinderella for J2ME.

}, keywords = {refereed}, doi = {10.1016/j.scico.2004.02.006}, url = {http://kortenkamps.net/papers/2004/wirelessj2me-final.pdf}, author = {Kortenkamp, Ulrich and Materlik, Dirk} } @conference {KorMat-PIGC-2004, title = {Pen-based input of geometric constructions}, booktitle = {Proceedings of MathUI 2004}, year = {2004}, abstract = {

Pen-based input is the classical approach to drawing. Without computers, using a pen was the natural approach to do drawings, and the simplicity of this "device" always called for similar electronic solutions. Today, a broad range of electronic input devices is available that try to pair the simplicity of input with the power of computing. They come in all sizes: from small touch-screens with stylus in personal digital assistants, via desktop-size input tablets or interactive displays, to electronic whiteboards with rear- or front-projection. These devices all share a direct interaction paradigm. The challenge in using these devices for geometric constructions is to automatically annotate the drawn objects with their relations to the other objects. A basic example is the drawing of a right-angled triangle: How can we automatically recognize the user{\textquoteright}s intention to have a right angle? Can we do that at all? Do we really want to do that? If not {\textendash} what is the easiest pen-compatible way to have the user add this information? We will demonstrate several approaches to these problems, implemented in a development version of Cinderella. Another interesting issue is the presentation of hand-drawn figures: Is it possible to preserve the look of a sketch while still guaranteeing mathematically correct figures? Using the additional information gathered by automatic theorem proving we show some solutions.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2004/Scribbling-article.pdf}, author = {Kortenkamp, Ulrich and Materlik, Dirk}, editor = {Libbrecht, Paul} } @conference {KorRic-UATPIUGS-2004, title = {Using Automatic Theorem Proving to Improve the Usability of Geometry Software}, booktitle = {Proceedings of MathUI 2004}, year = {2004}, abstract = {

Dynamic or interactive Geometry software (DGS) is the mathematical version of vector based drawing software: the objects (points, lines, circles, conics, polygons, etc.) are both graphical and mathematical entities. This allows adding relations between the objects that govern their behavior. Thus, DGS is used as an input tool for constructions, as opposed to simple drawings. The additional information that is present in a construction can be used to greatly enhance the usability of DGS. We show how automatic theorem proving can be used to remove redundant elements in a construction that obstruct a smooth work flow clarify the semantics of user actions, and improve the graphical rendering of elements. Finally we discuss the various possibilities of transforming the mathematical tool DGS into an educational tool. Here, automatic theorem proving is used to analyze user actions and to react properly.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2004/ATP-UI-article.pdf}, author = {Kortenkamp, Ulrich and Richter-Gebert, J{\"u}rgen}, editor = {Libbrecht, Paul} } @conference {KorMat-VLLM-2004, title = {Vernetztes Lehren und Lernen im Mathematikunterricht}, booktitle = {Grundfragen multimedialen Lehrens und Lernens. Tagungsband des 2. Workshops GML2004}, year = {2004}, publisher = {Alcatel SEL}, organization = {Alcatel SEL}, keywords = {refereed}, author = {Kortenkamp, Ulrich and Materlik, Dirk}, editor = {Fellbaum, Klaus and Rebensburg, Klaus and Schwill, Andreas} } @conference {Kor-MMTNVC-2002, title = {Making the move: {T}he next version of {C}inderella}, booktitle = {Proceedings of the First International Congress of Mathematical Software}, year = {2002}, note = {A slightly modified version appeared in the proceedings of CCCG 02.}, pages = {208{\textendash}216}, publisher = {World Scientific}, organization = {World Scientific}, abstract = {

Cinderella is a software package for interactive or dynamic geometry. Its first version was published in 1999 and was the first geometry software to be based on the theory of complex tracing3, thus avoiding mathematical inconsistencies and unmotivated discontinuities (modulo numerical errors). At the ICMS 2002 we will introduce the next major version of Cinderella and highlight its new features and new concepts.

}, keywords = {refereed}, url = {http://www.cs.uleth.ca/~wismath/cccg/papers/ulrich.pdf}, author = {Kortenkamp, Ulrich}, editor = {Cohen, Arjeh M. and Gao, Xiao-Shan and Takayama, Nobuki} } @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} } @conference {Kor-FMS-2001, title = {The future of mathematical software}, booktitle = {Proceedings of MTCM 2000}, year = {2001}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2001/future.pdf}, author = {Kortenkamp, Ulrich} } @inbook {RicKor-GDG-2001, title = {Grundlagen Dynamischer Geometrie}, booktitle = {Zeichnung {\textendash} Figur {\textendash} Zugfigur}, year = {2001}, pages = {123{\textendash}144}, publisher = {Franzbecker}, organization = {Franzbecker}, address = {Hildesheim, Berlin}, abstract = {

In this article we present fundamental definitions that can be used to introduce a mathematical model for dynamic geometry. Starting from reasonable expectations that such a model should meet we will formalize the terms (dynamic) construction, instance of a construction and Dynamic-Geometry-System (DGS). The behavior of a DGS will be described by the terms conservatism and continuity. One of the main results of this article is that we can find a continuous DGS for any construction Z that is built up using algebraic basic construction steps only.

}, keywords = {refereed}, url = {http://kortenkamps.net/papers/2001/DG_OW1.pdf}, author = {Richter-Gebert, J{\"u}rgen and Kortenkamp, Ulrich}, editor = {Henn, Hans-Wolfgang and Elschenbroich, Hans-J{\"u}rgen and Gawlick, Thomas} } @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} } @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.} }