2009. In Bardini,, C. Fortin, P. Oldknow, A. & Vagost D. (Eds.). Proceedings of the 9 th International Conference on Technology in Mathematics Teaching, pp. XXX. Metz, France: ICTMT 9 1- 1 DEMONSTRATING, GUIDING, AND ANALYZING PROCESSES IN DYNAMIC GEOMETRY SYSTEMS Christian Spannagel University of Education Ludwigsburg, Germany Ulrich Kortenkamp University of Education Karlsruhe, Germany Process-oriented mathematics education focuses on learning processes rather than on their outcomes only. These processes should be monitored, guided and supported by the teacher. In addition, feedback should be given on the students’ activities, not only on their results. Groups of 30 (school) up to more than 600 (university) learners render it impossible to support processes without appropriate technology. This paper describes the tool CleverPHL that allows for designing process-oriented learning scenarios: processes can be recorded, replayed, completed, guided, and analyzed. These features are demonstrated with dynamic geometry systems (DGS). PROCESS-ORIENTED MATHEMATICS EDUCATION Process-oriented mathematics education focuses on processes in addition to mathematical content. For example, the NCTM standards consist of content standards as well as process standards including problem solving, reasoning, and communicating (NCTM, 2000). Students should not only acquire mathematical knowledge. They should also learn how to create and use this knowledge; they should learn to think mathematically (cf. the teaching thinking approach; Costa, 2001; Bowkett, 2006; Brady, 2008). Besides these thinking skills, students have to learn genuinely mathematical skills like calculating, reducing fractions, and constructing geometric figures. When computers are used in the classroom, students also have to learn how to use the tools like spreadsheet calculators and dynamic geometry systems (DGS) in order to solve mathematical problems. In process-oriented mathematics education, processes should be focused in instruction. That means that the teacher must demonstrate processes, he should support the processes of the students with scaffolds, and he should give feedback not only on the products (e.g. the solutions) but also on the way they were produced. Having 30 students in a class at school or even about 600 students in a lecture at university, supporting and monitoring the processes of all students individually cannot be accomplished without computer support. In this article, the tool CleverPHL is described which allows for demonstrating, observing, completing, guiding, and analyzing processes in computer-based mathematical tools like DGS. First, the basic principles of the tool are explained. Afterwards, its features are exemplified with the use of DGS in mathematics classes.