@inbook {LadKor-EML-2014, title = {Number concepts {\textendash}- processes of internalization and externalization by the use of multi-touch technology Silke Ladel and Ulrich Kortenkamp}, booktitle = {Early Mathematics Learning}, year = {Submitted}, chapter = {3-3}, keywords = {ACAT}, author = {Silke Ladel and Ulrich Kortenkamp} } @conference {535, title = {Collaborative Design of Educational Digital Resources for Promoting Creative Mathematical Thinking}, booktitle = {13th International Congress on Mathematical Education}, year = {2016}, month = {07/2016}, address = {Hamburg - Germany}, author = {Jana Trgalov{\'a} and Mohamed El-Demerdash and Oliver Labs and Jean-Fran{\c c}ois Nicaud} } @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} } @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} } @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} } @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 {LadKor-DTBLEPVUAAT-2013, title = {Designing a technology based learning environment for place value using artifact-centric activity theory}, booktitle = {Proceedings of the 37th conference of the International Group for the Psychology of Mathematics Education. Mathematics learning across the life span}, volume = {1}, year = {2013}, pages = {188-192}, keywords = {refereed}, author = {Silke Ladel and Ulrich Kortenkamp}, editor = {Anke M. Lindmeier and Aiso Heinze} } @conference {LibKor-RMDEA-2013, title = {The Role of Metadata in the Design of Educational Activities}, booktitle = {Proceedings of CERME 8, Antalya}, year = {2013}, keywords = {refereed}, author = {Paul Libbrecht and Ulrich Kortenkamp} } @conference {LibKorRebMul-TCTA-2013, title = {Tales of a Companion Teacher Analytics}, booktitle = {Proceedings of the 2nd International Workshop on Teaching Analytics (IWTA-2013)}, year = {2013}, keywords = {refereed}, url = {http://ceur-ws.org/Vol-985/paper4.pdf}, author = {Paul Libbrecht and Ulrich Kortenkamp and Sandra Rebholz and Wolfgang M{\"u}ller}, editor = {Ravi Vatrapu} } @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} } @proceedings {462, title = {Preservice teachers{\textquoteright} patterns of metacognitive behavior during mathematics problem solving in a dynamic geometry environment}, journal = {46. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik}, volume = {2}, year = {2012}, pages = {513{\textendash}516}, publisher = {WTM-Verlag.}, address = {Weingarten}, author = {Ana Kuzle}, editor = {Matthias Ludwig and Michael Kleine} } @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} } @proceedings {KorLamZei-CPATM-2011, title = {Computerwerkzeuge und Pr{\"u}fungen / Aufgaben mit Technologieeinsatz im Mathematikunterricht. Bericht {\"u}ber die 24. und 25. Arbeitstagung des Arbeitskreises Mathematikunterricht und Informatik}, year = {2011}, publisher = {Franzbecker}, address = {Hildesheim}, keywords = {herausgeber}, isbn = {978-3-88120-822-2}, editor = {Kortenkamp, Ulrich and Lambert, Anselm and Zeimetz, Antonia} } @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} } @booklet {TrgKorJahLibMerRecSou-IPSDGROE-2010, title = {I2Geo.net {\textendash} a platform for sharing dynamic geometry resources all over Europe}, year = {2011}, keywords = {poster}, author = {Trgalova, Jana and Kortenkamp, Ulrich and Jahn, Ana Paula and Libbrecht, Paul and Mercat, Christian and Recio, Tomas and Soury-Lavergne, Sophie} } @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 {KorLab-IIGEI-2011, title = {Interoperable {I}nteractive {G}eometry for {E}urope: an introduction}, journal = {ZDM {\textendash} The International Journal on Mathematics Education}, year = {2011}, note = {10.1007/s11858-011-0340-7}, pages = {1-3}, publisher = {Springer Berlin / Heidelberg}, keywords = {herausgeber}, issn = {1863-9690}, url = {http://dx.doi.org/10.1007/s11858-011-0340-7}, author = {Kortenkamp, Ulrich and Laborde, Colette} } @unpublished {LibKorMer-CCBWLTIGR-2010, title = {Crossing Cultural Boundaries with Long Term Interactive Geometry Resources}, year = {2010}, note = {Unpublished Manuscript}, keywords = {sonstige}, author = {Libbrecht, Paul and Kortenkamp, Ulrich 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 = {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 {LibKorMer-IWIG-2009, title = {I2Geo: a Web-Library of Interactive Geometry}, booktitle = {Proceedings of the 2nd Workshop Towards a Digital Mathematics Library (DML-2009)}, year = {2009}, publisher = {Masaryk University}, organization = {Masaryk University}, keywords = {refereed}, isbn = {978-80-210-4781-5}, author = {Paul Libbrecht and Ulrich Kortenkamp and Christian Mercat}, editor = {Petr Sojka} } @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} } @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} } @booklet {Kor-MUTATT-2008, title = {Math Unit Testing {\textendash} A New Approach to the Use of Technology in Teaching}, year = {2008}, keywords = {poster}, author = {Kortenkamp, Ulrich}, editor = {Laborde, Colette} } @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 {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} } @conference {FesKor-TGAWV-2007, title = {Teaching Graph Algorithms with {V}isage}, booktitle = {Proceedings of CADGME 2007 in P{\'e}cs}, year = {2007}, month = {6}, keywords = {invited}, author = {Fest, Andreas and Kortenkamp, Ulrich}, editor = {S{\'a}rv{\'a}ri, Csaba and Lavicza, Zsolt} } @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} } @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} }