Contradictions and uncertainty in scientists’ mathematical modeling and interpretation of data

Abstract

Contradictions have been recognized as important factors in learning (conceptual change), because they require students to engage in deep reflection that leads to accommodation and learning. However, in the face of uncertainty, confirmation bias and the theory-laden nature of observation may not allow the recognition of a situation as harboring a contradiction. In the present study, I analyze a meeting in which a scientific research team presents its results to an informed audience. I show that with hindsight, there are contradictions in the mathematical models that the scientists use and the graph interpretations that they produce. Because the contradictions went unnoticed, they could not become a determinant factor in the process. This has implications for thinking about the role of uncertainty and contradiction as factors in and of mathematical learning.