The role of theory in research and practice: Characterizing cognition and context within mathematics education

This chapter explores how cognition and context are theoretically defined within mathematics education. To identify how discipline-specific theoretical models implicitly influence research and practice, we contrast these definitions with those adopted in cognitive science. We observe that mathematics education research is increasingly moving towards situated models. There is extensive documentation of the kinds of contexts in which individuals can complete mathematics, which is interpreted as children are engaging in different cognitive processes in different contexts. By contrast, cognitive approaches aim to identify universal aspects of cognition across contexts by explicitly controlling for effects of context as “error” terms in cognitive learning models. To resolve these conflicts, we put forward a model which argues that although the underlying knowledge representation and cognitive processes involved in mathematics thinking are invariant across context, how this cognition is manifested (i.e., what the cognition looks like) is mediated by context. This model emphasizes the classroom, assessments, and mathematics “in the wild,” as all unique contexts. We call for researchers systematically to explore the variability across contexts to build more complete learning models. Understanding the mediating role of context on mathematics reasoning will allow for the development of targeted and effective intervention across contexts and population.