Urban Mathematics Education Research

Using Citation Cartography to Map Bubbles and Foams in Mathematics Education Research

Authors

DOI:

https://doi.org/10.21423/jume-v14i2a425

Keywords:

bubbles, Bullock, cartography, citation network, foam, Foucault, ghettoes, history, Larnell, metaphor, philosophy, theory, Rancière, Sloterdijk

Abstract

As Foucault’s ironic approach to history is to suggest that looking at our past can help us to change the future, I contend that connections make the best disruptions. To wit, I introduce citation networks to make connections between articles and citations as a way of disrupting assumptions about what has been and can be done in the name of mathematics education research. The purpose of this paper is to introduce citation networks, a novel method for identifying field connections, and a theory of spatiality that deploys the metaphors of bubbles and foams to imagine disruptions. After introducing the method and theory that guide this investigation, I introduce and describe the foams of the research published in the Journal for Research in Mathematics Education and Educational Studies in Mathematics during the 2010s. In doing so, I show what topics of inquiry constitute the dominant research foci of our field, or at least of our field as it is published in these mainstream mathematics education journals. Later, I read these maps with a critical lens towards the foci to discern what is marginalized and excluded, namely the urban. This research builds on earlier work that names the ghettoization of urban mathematics education research and provides a critical interrogation of the ways that urban research is marked and marginalized within dominant mathematics education research journals. I conclude by situating the role of the Journal of Urban Mathematics Education as a place to blow bubbles, a place to reconfigure what we can see, say, think, and do in the name of (urban) mathematics education research.

References

Aria, M., & Cuccurullo, C. (2017). Bibliometrix: An R-tool for comprehensive science mapping analysis. Journal of Informetrics, 11(4), 959–975. https://doi.org/10.1016/j.joi.2017.08.007

Bastian, M., Heymann, S., & Jacomy, M. (2009). Gephi: An open source software for exploring and manipulating networks. In E. Adar, M. Hurst, T. Finin, N. Glance, N. Nicolov, & B. Tseng (Eds.), Proceedings of the Third International Association for the Advancement of Artificial Intelligence Conference on Weblogs and Social Media (pp. 361–362). AAAI Press.

Blondel, V. D., Guillaume, J. L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of com-munities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), Article P10008. https://doi.org/10.1088/1742-5468/2008/10/P10008

Borch, C. (2009). Organizational atmospheres: Foam, affect and architecture. Organization, 17(2), 223–241. https://doi.org/10.1177/1350508409337168

Bruce, C. D., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., Francis, K., Hawes, Z., Moss, J., Mulligan, J., Okamoto, Y., Whiteley, W., & Woolcott, G. (2017). Understanding gaps in research networks: Using “spatial reasoning” as a window into the importance of networked educational research. Educational Studies in Mathematics, 95, 143–161. https://doi.org/10.1007/s10649-016-9743-2

Bullock, E. C. (2014). Danger: Ghetto Ahead? Journal of Urban Mathematics Education, 7(1), 1–6. https://doi.org/10.21423/jume-v7i1a234

Bullock, E. C., & Larnell, G. V. (2015). Reframing urban mathematics education: The spatial politics of opportunity. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th Annual Meeting of the North American Chap-ter of the International Group for the Psychology of Mathematics Education (pp. 1285–1290). Michigan State University.

Chen, C. (2006). CiteSpace II: Detecting and visualizing emerging trends and transient patterns in scientific literature. Journal of the American Society for information Science and Technol-ogy, 57(3), 359–377. https://doi.org/10.1002/asi.20317

Chen, C. (2013). Mapping scientific frontiers: The quest for knowledge visualization. Springer.

Clarivate. (2021, June 5). HistCite: No longer in active development or officially supported. https://support.clarivate.com/ScientificandAcademicResearch/s/article/HistCite-No-longer-in-active-development-or-officially-supported

Clements, D. H., & Sarama, J. (2017). Valid issues but limited scope: A response to Kitchen and Berk's research commentary on educational technology. Journal for Research in Mathemat-ics Education, 48(5), 474–482.

Cobo, M. J., López-Herrera, A. G., Herrera-Viedma, E., & Herrera, F. (2011). An approach for detecting, quantifying, and visualizing the evolution of a research field: A practical applica-tion to the Fuzzy Sets Theory field. Journal of Informetrics, 5(1), 146–166. https://doi.org/10.1016/j.joi.2010.10.002

Cohen, D. K., & Ball, D. L. (2000). Instructional innovation: Reconsidering the story [Working paper]. University of Michigan. http://sii.soe.umich.edu/newsite/documents/InstructionalInnovation.pdf

Dubbs, C. (2020). Whose ethics? Toward clarifying ethics in mathematics education research. Journal of Philosophy of Education, 54(3), 521–540.

Dubbs, C. H. (2021a). Mapping JUME: Identifying clusters in urban mathematics education re-search [Manuscript in preparation]. Department of Mathematics, East Stroudsburg Univer-sity.

Dubbs, C. H. (2021b). Mathematics education atlas: Mapping the field of mathematics education research. Crave Press.

Engelsman, E. C., & van Raan, A. F. J. (1994). A patent-based cartography of technology. Re-search Policy, 23(1), 1–26.

Fendler, L. (2010). Michel Foucault. Bloomsbury.

Foucault, M. (1972). The archaeology of knowledge & the discourse on language (A. M. Sheri-dan Smith, Trans.). Pantheon Books. (Original work published 1969)

Foucault, M. (1983). On the genealogy of ethics: An overview of work in progress. In H. L. Dreyfus & P. Rabinow (Eds.), Michel Foucault: Beyond structuralism and hermeneutics. 229–252. University of Chicago Press.

Foucault, M. (1988). Truth, power, self: An interview with Michel Foucault. In L. H. Martin, H. Gutman, & P. H. Hutton (Eds.), Technologies of the self: A seminar with Michel Foucault (pp. 9¬–15). University of Massachusetts Press.

Funcke, B. (2005). Against gravity: Bettina Funcke talks with Peter Sloterdijk. BookForum, 11(5), 27–29.

Garfield, E. (2009). From the science of science to Scientometrics visualizing the history of sci-ence with HistCite software. Journal of Informetrics, 3(3), 173–179. https://doi.org/10.1016/j.joi.2009.03.009

Gray, L., Thomas, N., & Lewis, L. (2010). Teachers’ use of educational technology in U.S. pub-lic schools: 2009: First look (NCES 2010-040). U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. Retrieved from http://nces.ed.gov/pubs2010/2010040.pdf

Gutiérrez, R. (2008). A “gap-gazing” fetish in mathematics education? Problematizing research on the achievement gap. Journal for Research in Mathematics Education, 39(4), 357–364.

Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37–68.

Heid, M. K. (1997). The technological revolution and the reform of school mathematics. Ameri-can Journal of Education, 106(1), 5–61.

Heid, M. K. (2010). Where’s the math (in mathematics education research)? Journal for Research in Mathematics Education, 41(2), 102–103.

Hinze, S. (1994). Bibliographical cartography of an emerging interdisciplinary discipline: The case of bioelectronics. Scientometrics, 29(3), 353–376. https://doi.org/10.1007/BF02033445

Inglis, M., & Foster, C. (2018). Five decades of mathematics education research. Journal for Research in Mathematics Education, 49(4), 462–500. https://doi.org/10.5951/jresematheduc.49.4.0462

Institute for Scientific Information. (1981). ISI atlas of science: Biochemistry and molecular biol-ogy, 1978/80.

Jacomy, M., Venturini, T., Heymann, S., & Bastian, M. (2014). ForceAtlas2, a continuous graph layout algorithm for handy network visualization designed for the Gephi software. PLOS ONE, 9(6), Article e98679. https://doi.org/10.1371/journal.pone.0098679

Kajikawa, Y., Ohno, J., Takeda, Y., Matsushima, K., & Komiyama, H. (2007). Creating an aca-demic landscape of sustainability science: An analysis of the citation network. Sustainabil-ity Science, 2(2), 221–231.

Kieren, T. E. (2000). Dichotomies or binoculars: Reflections on the papers by Steffe and Thomp-son and by Lerman. Journal for Research in Mathematics Education, 31(2), 228–233.

Kitchen, R., & Berk, S. (2016). Educational technology: An equity challenge to the Common Core. Journal for Research in Mathematics Education, 47(1), 3–16.

Kitchen, R., & Berk, S. (2017). Keeping the focus on underserved students, privilege, and power: A reaction to Clements and Sarama. Journal for Research in Mathematics Education, 48(5), 483–487.

Larnell, G. V., & Bullock, E. C. (2018). A socio-spatial framework for urban mathematics educa-tion: Considering equity, social justice, and the spatial turn. In T. G. Bartell (Ed.), To-ward equity and social justice in mathematics education (pp. 43–57). Springer.

Lester, F. K., & Kerr, D. R. (1979). Some ideas about research methodologies in mathematics education. Journal for Research in Mathematics Education, 10(3), 228–232.

Latour, B. (2009). Spheres and networks: Two ways to reinterpret globalization. Harvard Design Magazine, 30(1), 138–144.

Lubienski, S. T. (2008). On “gap gazing” in mathematics education: The need for gaps analyses. Journal for Research in Mathematics Education, 39(4), 350–356.

Lubienski, S. T., & Gutiérrez, R. (2008). Bridging the gaps in perspectives on equity in mathe-matics education. Journal for Research in Mathematics Education, 39(4), 365–371.

Muñoz, J. E. (1999). Disidentifications: Queers of color and the performance of politics. Univer-sity of Minnesota Press.

Narin, F., Carpenter, M., & Berlt, N. C. (1972). Interrelationships of scientific journals. Journal of the American Society for Information Science, 23(5), 323–331. https://doi.org/10.1002/asi.4630230508

Nivens, R. A., & Otten, S. (2017). Assessing journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 348–368. https://doi.org/10.5951/jresematheduc.48.4.0348

Noack, A. (2009). Modularity clustering is force-directed layout. Physical Review E, 79(2), Arti-cle 026102.

Noyons, E. C. M., & van Raan, A. F. J. (1994). Bibliometric cartography of scientific and tech-nological developments of an R & D field: The case of optomechatronics. Scientometrics, 30(1), 157–173. https://doi.org/10.1007/BF02017220

Nylander, E., Österlund, L., & Fejes, A. (2018). Exploring the adult learning research field by analysing who cites whom. Vocations and Learning, 11(1), 113–131. https://doi.org/10.1007/s12186-017-9181-z

Özkaya, A. (2018). Bibliometric analysis of the studies in the field of mathematics education. Educational Research and Reviews, 13(22), 723–734. https://doi.org/10.5897/ERR2018.3603

Pan, X., Yan, E., Cui, M., & Hua, W. (2018). Examining the usage, citation, and diffusion pat-terns of bibliometric mapping software: A comparative study of three tools. Journal of In-formetrics, 12(2), 481–493. https://doi.org/10.1016/j.joi.2018.03.005

Parks, A. N., & Schmeichel, M. (2012). Obstacles to addressing race and ethnicity in the mathe-matics education literature. Journal for Research in Mathematics Education, 43(3), 238–252. https://doi.org/10.5951/jresematheduc.43.3.0238

Price, D. J. D. S. (1965, July 30). Networks of scientific papers: The pattern of bibliographic references indicates the nature of the scientific research front. Science, 149(3683) 510–515. https://doi.org/10.1126/science.149.3683.510

Rancière, J. (2000). History and the art system (interview with Yan Ciret). Art Press, 258, 18–23.

Rancière, J. (2004). The politics of aesthetics: The distribution of the sensible (G. Rockhill, Trans.). Bloomsbury. (Original work published 2000)

Rancière, J. (2009). The emancipated spectator (G. Elliott, Trans.). Verso Books. (Original work published 2008)

Scharnhorst, A., Börner, K., & van den Besselaar, P. (Eds.). (2012). Models of science dynamics: Encounters between complexity theory and information sciences. Springer.

Skovsmose, O., & Penteado, M. G. (2011). Ghettoes in the classroom and the construction of possibilities. In B. Atweh, M. Graven, W. G. Secada, & P. Valero (Eds.), Mapping equity and quality in mathematics education (pp. 77–90). Springer.

Slavin, R. E., & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78(3), 427–515. https://doi.org/10.3102%2F0034654308317473

Sloterdijk, P. (2011). Bubbles (W. Hoban, Trans.). Semiotext(e). (Original work published 1998)

Sloterdijk, P. (2014). Globes (W. Hoban, Trans.). Semiotext(e). (Original work published 1999)

Sloterdijk, P. (2016). Foams (W. Hoban, Trans.). Semiotext(e). (Original work published 2004)

Snow, D. R. (2011). The teacher’s role in effective computer-assisted instruction intervention. Mathematics Teacher, 104(7), 532–536.

Stinson, D. W. (2010). The Sixth International Mathematics Education and Society Conference: Finding freedom in a mathematics education ghetto. Journal of Urban Mathematics Educa-tion. 3(1), 1–8. https://doi.org/10.21423/jume-v3i1a91

Thrift, N. (2003). Space: The fundamental stuff of geography. In S. L. Holloway, S. P. Rice, & G. Valentine (Eds.), Key concepts in geography (pp. 95–107). Sage.

van Eck, N. J., & Waltman, L. (2014). CitNetExplorer: A new software tool for analyzing and visualizing citation networks. Journal of Informetrics, 8(4), 802–823. https://doi.org/10.1016/j.joi.2014.07.006

van Eck, N. J., & Waltman, L. (2017). Citation-based clustering of publications using CitNetEx-plorer and VOSviewer. Scientometrics, 111(2), 1053–1070. https://doi.org/10.1007/s11192-017-2300-7

Wang, Y., & Bowers, A. J. (2016). Mapping the field of educational administration research: A journal citation network analysis. Journal of Educational Administration, 54(3), 242–269. https://doi.org/10.1108/JEA-02-2015-0013

Weller, M., Jordan, K., DeVries, I., & Rolfe, V. (2018). Mapping the open education landscape: Citation network analysis of historical open and distance education research. Open Praxis, 10(2), 109–126.

Williams, S. R., & Leatham, K. R. (2017). Journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 369–396. https://doi.org./10.5951/jresematheduc.48.4.0369

Downloads

Published

2021-12-21

Issue

Section

FIELD DISRUPTIONS AND FIELD CONNECTIONS