@article {466, title = {Problem solving as an instructional method: The case of strategy-open problem {\textquotedblleft}The treasure island problem{\textquotedblright}}, journal = {LUMAT {\textendash} Research and Practice in Math, Science and Technology Education}, year = {Submitted}, author = {Ana Kuzle} } @proceedings {411, title = {Past-Present-Future: Winkel anschaulich unterrichten!}, journal = {47. Jahrestagung der Gesellschaft f{\"u}r Didaktik der Mathematik}, year = {2013}, address = {M{\"u}nster}, abstract = {

Der Winkelbegriff und das Messen von Winkeln sind von zentraler Bedeu- tung f{\"u}r die ebene Geometrie und Raumgeometrie. Im Alltag begegnet man vielf{\"a}ltigen Winkelsituationen, wie z.B. beim Autofahren oder in Orientie- rungssituationen. Dar{\"u}ber hinaus ist die Winkelmessung in vielen Berufs- zweigen von gr{\"o}{\ss}ter Bedeutung, wie z.B. bei Architekten, (Bau-) Ingenieu- ren, Schreinern oder Piloten (Berry III \& Wiggins, 2001). Der Winkelbe- griff ist aufgrund vielf{\"a}ltiger Aspekte und Definitionen ein komplexer Ge- genstand des Geometrieunterrichts.

Im Mathematikunterricht sind S{\"a}tze {\"u}ber Gleichheit, Summen und Diffe- renzen von Winkeln in der gesamten Geometrie relevant. Sch{\"u}lerInnen zeigen Schwierigkeiten bei der operativen und konzeptuellen Winkelbe- griffsentwicklung (z.B. Krainer, 1989; Mitchelmore \& White, 2000). Im Beitrag werden Schulbuchanalysen mit typischen Fehlermustern und Fehl- konzepten kontrastiert und Schlussfolgerungen f{\"u}r eine anschauliche Be- griffsbildung diskutiert.

}, keywords = {angle}, author = {Dohrmann, Christian and Kuzle, Ana} } @article {459, title = {Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment}, journal = {International Electronic Journal of Mathematics Education}, volume = {8}, year = {2013}, pages = {20{\textendash}40}, author = {Ana Kuzle} } @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} } @mastersthesis {463, title = {Preservice teachers{\textquoteright} patterns of metacognitive behavior during mathematics problem solving in a dynamic geometry environment}, year = {2011}, school = {University of Georgia{\textendash}Athens}, type = {Doctoral dissertation}, address = {Athens, GA}, author = {Ana Kuzle} } @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} } @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 {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} } @booklet {Kor-PA-2006, title = {{P}unkt- und {A}chsenspiegelungen}, year = {2006}, note = {Beitrag auf Lehrer-Online}, keywords = {lehrer}, url = {http://www.lehrer-online.de/url/spiegelungen}, author = {Kortenkamp, Ulrich} } @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} } @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} } @booklet {Hun-POM-1995, title = {Pseudosph{\"a}renarrangements zu {O}rientierten {M}atroiden}, year = {1995}, publisher = {Westf{\"a}lische Wilhelms-Universit{\"a}t}, type = {Diplomarbeit}, address = {M{\"u}nster}, keywords = {qualifikation}, author = {Hund, Ulrich} }