A tale of two researchers: Commonalities, complementarities, and contrasts in an examination of mental computation and relational thinking

Helena P Osana,Jérôme Proulx

doi:10.5964/jnc.v4i1.89

Abstract

This paper describes a research collaboration between an educational psychologist and a mathematics education researcher, namely a didacticien des mathématiques. Our joint project aimed to explore the mental computation strategies of preservice teachers in an elementary mathematics methods course and to investigate the relationship between mental computation and relational thinking. The primary objective of the paper, however, is to go beyond the data and their interpretation. We describe the commonalities, complementarities, and points of contrast that emerged between us as researchers who hail from different disciplines, but who have the same overarching interests in mathematical thinking. In particular, we untangle issues we encountered during our collaboration related to our research questions, methodologies, and epistemological stances. We detail the ways in which we navigated these issues in the context of the research and describe what we learned about our own disciplinary perspectives and each other’s. We conclude by discussing what our story offers as a means of reflecting on our individual fields and potential interactions between them.

Highlights

This paper describes a research collaboration between an educational psychologist and a mathematics education researcher, namely a didacticien des mathématiques
Central questions for HPO were: Did the preservice teachers engage in computational strategies to determine the truth value of mathematical equations or were they able to think about the relationships among the quantities in the equations? Can we find evidence to support the claim that the mental computation intervention facilitated their relational thinking? If the research generates such evidence, what can be said of the theoretical overlap between mental computation and relational thinking? Such questions make evident that HPO was driven by the search for evidence that would make recommendations for teaching practice credible
Given that HPO was primarily interested in determining the increase in relational thinking from pretest to posttest, all justifications on the Relational Thinking Test (RTT) that were coded C and OT were collapsed into one non-relational category (NR)

Summary

Introduction

This paper describes a research collaboration between an educational psychologist and a mathematics education researcher, namely a didacticien des mathématiques. This paper describes a collaborative effort between two researchers from different fields with common interests in the nature of mathematical thinking. (2016) conducted a collaborative exercise with a number of researchers in the fields of mathematics education, psychology, and neuroscience to identify themes and key research directions that could serve to unify the three disciplines. They presented somewhat caricatural profiles by describing typical backgrounds and activities of the researchers from the three fields. Gauvrit’s (2012) analysis supplements these depictions He argued that a primary difference between the disciplines is that studies conducted by didacticiens des mathématiques are grounded in mathematics, which can be explained by their initial training with and in mathematics. Historical or sociological layers are not necessarily discarded; when taken into account, these layers are grounded in mathematical explanations and rationales

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