Mathematical interaction shaped by communication, epistemological constraints and enactivism

On the surface, mathematical interaction often appears as an immediately transparent event that could be directly understood by careful observation. Theoretical considerations, however, clearly show that mathematical speaking and conversation in teaching-learning situations are highly complex social structures comprising many preconditions. Communication does not generate direct understanding and the object of communication-mathematics-is, as knowledge of abstract relations, not directly accessible. The learning agents-the teacher and students in the mathematics classroom-have to cope with these difficulties in a way of reciprocal actions between social communication and individual consciousness.