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

• This article analyzes a meeting in which a scientific research team presents its results to an informed audience.
• With hindsight, there are unnoticed contradictions in the mathematical models that the scientists use and the interpretations that they produce.
• Because scientists are not aware of contradictions, these do not drive the unfolding research process.
• This study calls into question any deficit approaches to the interpretation of data from school-based studies of mathematical learning.

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.