@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 {401, title = {Funktionales Denken mit dem Computer unterst{\"u}tzen - Empirische Untersuchungen im Rahmen des prop{\"a}deutischen Unterrichts der Analysis}, booktitle = {27. Arbeitstagung des Arbeitskreises "Mathematikunterricht und Informatik" in der GDM}, year = {2009}, address = {Soest}, keywords = {2009, 27., Arbeitstagung, Denken, Funktionales, GDM, Soest}, author = {Andrea Hoffkamp} } @booklet {400, title = {Funktionales Denken und Analysisprop{\"a}deutik - Ein Beitrag zu einem qualitativen Einstieg in die Schulanalysis durch Computereinsatz}, year = {2009}, abstract = {

"Funktionales Denken beginnt bei intuitiven Vorstellungen {\"u}ber funktionale Zusammenh{\"a}nge wie {\textquoteright}Wenn man\ die eine Gr{\"o}{\ss}e {\"a}ndert, dann {\"a}ndert sich die andere" oder "Je mehr..., desto mehr", und es ist voll entwickelt bei\ Denkweisen der Analysis"(Vollrath [6]). Die Realit{\"a}t ist aber ein kalk{\"u}lorientierter Analysisunterricht mit wenig\ inhaltlichen Vorstellungen. Deswegen pl{\"a}dieren viele Didaktiker f{\"u}r einen qualitativen Zugang zur Differential und\ Integralrechnung. Basierend auf der DGS Cinderella wurden interaktive Lernumgebungen entworfen, die\ die dynamische Komponente funktionalen Denkens durch eine zweistufige dynamische Visualisierung akzentuieren.\ Sie zielen darauf ab, inhaltliche Vorstellungen von {\"A}nderungsverhalten funktionaler Abh{\"a}ngigkeiten\ zu entwickeln, bevor das Kalk{\textasciidieresis}ul im Unterricht entwickelt wird. Im Artikel wird exemplarisch an einer Lernumgebung\ gezeigt, wie dies aussehen kann.

}, keywords = {Analysis, Denken, Funktionales}, author = {Andrea Hoffkamp} } @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-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} } @article {Kor-FDG-2000, title = {Foundations of {D}ynamic {G}eometry}, journal = {Journal f{\"u}r Mathematikdidaktik}, volume = {21}, number = {2}, year = {2000}, pages = {161{\textendash}162}, keywords = {sonstige}, author = {Kortenkamp, Ulrich} } @mastersthesis {Kor-FDG-1999, title = {Foundations of Dynamic Geometry}, year = {1999}, month = {11}, school = {ETH Z{\"u}rich, Institut f{\"u}r Theoretische Informatik}, type = {phdDissertation}, address = {Z{\"u}rich}, keywords = {qualifikation}, url = {http://kortenkamps.net/papers/1999/diss.pdf}, author = {Kortenkamp, Ulrich} }