Previous investigations demonstrate that many preservice teachers do not acquire adequately the concepts of ratio and proportion (Ben-Chaim, Keret and Ilany, 2012; Valverde, 2012). These students seem not to have constituted well certain mental objects that, in agreement with Fernandez (2009), can consider predecessors of these concepts. This can be due to the fact that this topic is not taught well, that seems to settle with a precarious, poor and brief approach disconnected of the reality (Streefland, 1985). In this respect, this doctoral thesis studies the test of a didactic experience with preservice teachers, centred on the resolution of a task which contains implicitly the mental object "relatively" in order that they are capable of re-constitute it. In our case, we design a numerical comparison task of the type " which is the best buy? " (Ben-Chaim et to., 2012; Lamon, 2007) involving the mental object "relatively". In the first phase, the task is submitted to an analysis to distinguish the study of what the students do (empirical analysis) of the examination of the task mathematical content (rational analysis). Of the theoretical frame as well as of the rational analysis, there stem the dimensions of analyses that allow us to interpret the resolutions of the students. The obtained results have been organized in schemes of categories and subcategories that give detailed account of the cognitive bosses of response to the task. Once observed the forms of thought that makes emerge this type of tasks in the preservice teachers and which are the difficulties that they resolutions show, we have raised a didactic experience structured around maieutical principles. This experience uses the cognitive bosses of response categorized in the first phase, because it has been designed used different archetypical examples that sustain the diverse possible resolutions, in order to there be able to anticipate the answers of a any group of preservice teachers. Hereby there are planned the cognitive conflicts that it is interested in promoting in those students with difficulties of agreement with the maieutical method. The last end is to guide the students in the need to re-constitute the mental object "relatively". Once raised, the experience was implemented in a group of preservice teachers of the University of Valencia and it was analyzed later. This shapes the second phase of our study. The results of the first phase point that the majority of the students have a limited development of the relative thought. Also, there is obtained that between the students which compare relative quantities there exists an important number of them who have difficulties with the interpretation of the discount referent. The didactic experience carried out in the second phase has allowed us to obtain evidences of that some students have realized metacognitive processes that have allowed them to change from an absolute thought to the relative thought. These happened in a first stage in which the preservice teachers noticed his mistake and in a second stage in which they constructed a new efficient solution, re-constituting the mental object "relatively".
