On the pregnance of bodily movement and geometrical objects: A post-constructivist account of the origin of mathematical knowledge

Abstract

Traditional (e.g., constructivist) accounts of knowledge ground its origin in the intentional construction on the part of the learner. Such accounts are blind to the fact that learners, by the fact that they do not know the knowledge to be learned, cannot orient toward it as an object to be constructed. In this study, I provide a phenomenological account of the naissance (birth) of knowledge, two words that both have their etymological origin in the same, homonymic Proto-Indo-European syllable ʇen-, ʇen∂-, ʇne¯-, ʇno¯-. Accordingly, the things of the world and the bodily movements they shape, following Merleau-Ponty (1964), are pregnant with new knowledge that cannot foresee itself, and that no existing knowledge can anticipate. I draw on a study of learning in a second-grade mathematics classroom, where children (6-7 years) learned geometry by classifying and modeling 3-dimensional objects. The data clearly show that the children did not foresee, and therefore did not intentionally construct, the knowledge that emerged from the movements of their hands, arms, and bodies that comply with the forms of things. Implications are drawn for classroom instruction.