Process Orientated Learning Environments For Interactive Geometry Lessons

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'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.