# Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying

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## Abstract

This article describes emerging perspectives on contextualizing, complementizing, and complexifying—three processes involved when individuals ascribe meaning to mathematical objects of their thinking. The article is oriented toward a dialectic between theory and empirical research and is structured in two parts. The first part focuses on an evolving theoretical framing that acknowledges the significance of these three processes in mathematical cognition. In the second part, the evolving theoretical framing is used to analyze one student’s knowing of the limit concept of a sequence. This analysis directs one’s attention to the emergence and function of this student’s knowledge resource, which was generic in usage and complex in structure, allowing the activation of productive ideas and contextual meaning-making as needed. Through this analysis, theoretical and interpretative possibilities were generated that inform research on mathematical cognition and elucidate the emerging theoretical perspectives of contextualizing, complementizing, and complexifying.

## Keywords

Mathematical cognition Meaning-making Theory advancement Giving meaning Limit concept## Notes

### Acknowledgments

We are grateful to Annie Selden for her thoughtful comments and helpful suggestions given throughout the development of this paper. The first author wants to thank for support of this work both the Foundation of German Business through the Klaus Murmann Fellowship and Macquarie University through the Research Excellence Scholarship.

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