The main focus of the LINGOT project is how to build systems that facilitate algebra learning. The starting point is to capture in a multi-dimensional way students knowledge from their behaviour when working with a computer on algebraic tasks. Once captured, this knowledge is used by humans teachers to propose to the students learning activities likely to help the evolution of their knowledge. The originality of this on going project is to be based on a mathematical education research that had set up a multi-dimensional model of competence in algebra. This model is first applied to analyse and design tasks given by teachers to students, paper-and-pencil tasks as well as computerised tasks. Secondly this model is used to analyse the students’ answers when performing those tasks. We have built a first prototype, PÉPITE, that helps teachers to assess students in elementary algebra, setting up students’ cognitive profiles. This system is yet tested in actual classrooms and yet used in teachers training. The research work on computer mediated remedial activities is just beginning. In this paper, we focus on the assessment system and we share our experience of designing classrooms tools in a participative way. The methodology adopted is a combination of work in mathematics education and user-centred design derived from Human-Computer Interaction research. Finally we discuss the validation process of such an assessment system and our research results.