Mathematics Teaching and Learning: humans and non-humans

Abstract

The text presents the third part of the research project Epistemology of the Mathematics Teacher in which the data were collected from interviews conducted with 17 teachers in Peru, Chile and Uruguay. The objective is to identify the teachers' epistemological conceptions that underlie the teaching of Mathematics and to assess the extent to which they are similar to those found in Brazil: empiricist, based on aprioristic and rarely constructivist. The specific objectives are to know how teachers explain the learning capacities of their students, comparing them with those of non-human mammals, learning difficulties and the functions of teacher and student in the classroom. To do so, the answers to items 9 to 11 of a 24-item questionnaire presented to teachers at all educational levels are analysed. As in the previous analyses, the responses obtained are similar to those from Brazilian teachers with regards the predominance of empiricist conceptions, underpinned by aprioristic conceptions, while constructivist epistemological conceptions scarcely appear. The claim that rational capacities are innate and teaching, formal or informal, perfects them is recurrent; there is no dialectical debate regarding genetic inheritance and environment. This context is conducive to the confusion of reason and perception, attributing to the former what pertains to the latter. Hence the difficulty in distinguishing human mathematics from non-human mammalian “mathematics”. Concepts of learning that value the constitutive action of the epistemic subject and of the teaching that attends its postulates fall apart. The evidence found shows the hegemony of teaching over learning. The basic theoretical reference is the Genetic Epistemology.