Abstract
This work deals with the role of social practice in the construction of models related to advanced mathematical knowledge; specifically, with the way an individual uses the notion of variation in different phenomena while predictive thinking is the underlying principle in the mathematical process. The mathematical modelling of successive variation in mathematics and science is addressed through the interpretation of graphs in two cases of different nature: the diagnosis of a cardiologist on the health of a patient (a non-deterministic phenomenon) and the arguments of high school students facing the task of filling containers (a deterministic phenomenon). An emerging theory in the field of mathematics education—the socio-epistemological theory—explains the problem of construction of mathematical knowledge. The constructs of this theory are elaborated with an empirical basis; and the legitimacy of all forms of knowledge is assumed, be this knowledge popular, technical or scientific, since all of them constitute human wisdom. (In contrast, other contemporary approaches examine only one of the forms of knowledge).
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