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.} } @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 {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 {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} }