Book
Mathematics Education Atlas: Mapping the Field of Mathematics Education Research
The field of mathematics education is the product of many people writing around some (disparate) ideas that have congealed into the semblance of a thing that looks solid, that looks fixed. The field is, however, a foam: a volatile substance made from many bubbles (foci) emerging, popping, merging, and splitting. Following in the genealogical tradition of Michel Foucault, I look back at the emergence of this field called mathematics education research to trace the emergence of foci of study. By looking at those articles published between 1970 and 2019 in the Journal for Research in Mathematics Education (JRME), as well as those published since 2010 in for the learning of mathematics (flm) and Educational Studies in Mathematics (ESM), the results of this citation network analysis show that the foci of the field have not been fixed nor is there consensus around so-called proper foci today. This fluid and dissensual nature of our evolving field gives me hope. What mathematics education research is today is not a natural inevitability, but the product of human action, the collision of incident, orthogonal, and/or opposite forces, and while its trajectory is tied to its origins, it is not tied to it deterministically. The field of mathematics education research, as it has been, limits what we can say is mathematics education research, see as counting as mathematics education research, think as mathematics education, and do in the name of mathematics education research. These limits on what can be seen, said, thought, and done in the name of mathematics education research, what is (non)sensical, constitute a distribution of the sensible. This book serves as an outline and perturbation of those sensible limits.
Descriptions of individual chapters are listed below.
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Chapter 1: Introduction
My project is twofold: (1) to show and name the limits of mathematics education research as a field and (2) to consider what might be possible if what can be mathematics education research is severed from what is and has been mathematics education research. While I have presented my project as a duality, these two threads are intertwined and my methods for addressing each are necessarily entangled. In chapter 4, in the study of the JRME, I show that what has counted as mathematics education research in that journal has shifted across time. By bringing the findings of chapters 4, 5, and 6 together in the discussion (Chapter 7), I am able to show that what currently constitutes mathematics education research is different in different spaces. These two results together, then, suggest that there is not a fixed object that constitutes the proper object of mathematics education research. Instead, each of these views constitute partages of the sensible in mathematics education research—demarcations and delimitations of what is sensible as mathematics education research—what can be seen, said, or thought as mathematics education research. Since what has been has not been constant and there is not currently a consensus on what is mathematics education research, it is easier to think of alternatives.
Chapter 2: Theoretical Orientations
Chapter 2 briefly describes the four broad theoretical orientations that guide this analysis:
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Researching Research and Producing Multiple Knowledges
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Mirrors as Levers: Foucault on History
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Bubbles and Foam: Sloterdijkian Reading of Scientific Fields
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What can be seen, said, and thought: Rancière’s Distribution of the Sensible
Chapter 3: Citation Networks
Chapter 3 introduces citation networks, their use for mapping, software tools for their creation, algorithms for their analysis, and options for map generation and sharing.
Sections:
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What are graphs and how might graphs be used?
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Some Related Literature
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Software for Citation Network Analysis
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Methods for Network Analyses
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Example Analyses
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Cartography: Typical and extended use
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Practicalities of this method
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Choice of Data
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Acquisition and Processing of Data
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Map Creation: Analysis of Data
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Presentation of Maps
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Chapter 4: Partage I: The Journal for Research in Mathematics Education
Chapter 4 includes the citation network analysis of five decades of journal articles published in the Journal for Research in Mathematics Education (JRME). For each decade the JRME has been published, 1970s-2010s, a map is presented that shows the bubbles of research foci and their relative central/marginal position within the JRME at that time.
Chapter 5: Partage II: for the learning of mathematics
Chapter 5 includes the citation network analysis of articles published in for the learning of mathematics (flm) between 2010 and 2017. A map is presented that shows the bubbles of research foci and their relative central/marginal position within flm during the 2010s.
Chapter 6: Partage III: Educational Studies in Mathematics
Chapter 6 includes the citation network analysis the articles published in Educational Studies in Mathematics (ESM) between 2010 and 2017. A map is presented that shows the bubbles of research foci and their relative central/marginal position within ESM during the 2010s.
Chapter 7: Discussion and Implications
In the final chapter, I bring the bubbles from the 2010s of the JRME, flm, and ESM together. Afterwards, I revisit the findings for the JRME in the light of a similar study to understand the research foci of the JRME across the past five decades. The differences in our findings will emphasize the mixture/product chemical metaphor used to introduce Foucault’s power-knowledge in Chapther 2. I will also revisit the theories from chapter 2 to elaborate not only the connections between those theories and the analysis but also the implications for the field.
Sections:
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Comparisons Between Journals
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Comparison to Other Research
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Politics of Mathematics Education Research
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Looking Back at This Text
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Parting Thoughts