Computer Algebra Systems and Representations Tadashi Takahashi Graduate School of Human Development and Environment Kobe University, Kobe, Japan Many proposals have already been made with regard to the effective use of computer algebra systems in mathematics education. If we hope to develop and improve what has already been achieved, we will need to take advantage of the research results from cognitive science. Computer algebra systems are powerful tools that allow learners to _run_ mathematical formulae. Powerful tools can become effective tools by finding effective ways to use them. In order to fully utilize computer algebra systems in mathematics education, teaching methods that are based on cognitive science will be needed, and these are clearly different from those used in _pen and paper_ teaching. This paper considers the use of computer algebra systems as _tools_ and analyzes how such tools can affect the thinking of learners. We report the practices in university mathematics by using computer algebra system.