For the past 12 years we have been interested in the foundations for Mathematics Education Research (Batanero, Godino, Steiner, & Wenzelburger, 1994),and we have developed diverse theoretical tools to deal with some of the mentioned questions. These tools were based on several theoretical antecedents, which are described and analysed in Godino (2003, Chap. 2).These tools have been developed in three stages, in each of which the object of inquiry was progressively
refined. Next, we succinctly describe these three stages and the issues dealt with in each of them.