The field of mathematics education does not exist per se, but rather 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, but really is a foam: a volatile substance made from many bubbles 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 (foam) to trace the emergence of foci of study (bubbles). From the focus on teaching and learning and achievement differences in the 1970s to issues of inclusion, racial equity, and critical research methods in the 2010s, the foci of the field have not been fixed. This shift, the fluid nature of an evolving field gives me hope. What mathematics education research is is not a natural inevitability, but the product of human action, the collision of incident, orthogonal, and/or opposite forces, and its trajectory is tied to its origins, yet not deterministically.What has been done in the name of mathematics education research is not its natural inevitability but the product of these collisions of forces, this popping, merging, and splitting of bubbles, and those certain foci have merely gained dominance, imbuing them with a state of presumed inevitability. Since there is no natural start/origin, there is no naturally inevitable conclusion/destination and the field can grow in new/different/unexpected ways. 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), I provide a tracing of a field called mathematics education research. By mapping the citation relationships of these articles and their references in their entirety, I will identify the bubbles of research in each decade of interest (five from the JRME and one from each of flm and ESM). In addition, I will identify the bubbles that together constitute the foam of the field: the bubbles correspond to the different foci that, put together, share borders.Borrowing on Jacques Ranciere's distribution of the sensible, I believe that the field, 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 dissertation serves as a perturbation of those sensible limits.What follows in this dissertation is an elaboration of my theoretical orientations towards the field of mathematics education research itself: what constitutes the (im)possible, the (non)sensical, and the (im)proper. Then, I introduce graph theory though an introduction of citation network research methods, coupling both theories on the development of fields of research and computational methods for implementing citation network research. The methods, while I include their mathematical roots, will be presented by way of practicality: what software can accomplish which tasks with relative ease. Then, once the theories and methods are unpacked, the maps, the citation networks, will be presented at both bubble (micro-perspective of research foci) and foam (macro-perspective of what the bubbles together constitute) levels. These maps of the bubbles and foams (1970s-2010s JRME, 2000s flm, 2000s ESM) together constitute an atlas of mathematics education research as it has been and how it has evolved from the 1970s to today. Drawing on the genealogic process of Foucault, I conclude by celebrating the fact that what has been, and what currently is, is neither natural nor inevitable. Therefore, what can be in mathematics education research is limited only by our imaginations as a field.
Read
