A brief story of mathematics education
Abstract This manuscript presents a different way to look at history: rethinking history not as a lineal-chronological movement, but as flexible and rhizomatic, as a multidimensional network of entangled events. In doing so, it takes elements from the toolboxes of Michel Foucault and of Gilles Deleuze and Félix Guattari. It begins by thinking about the possible origins of mathematics education, in seeking for traces of its teaching and learning. Entry points of the rhizomatic network are located in Grecce, Mesopotamia, Prussia, even in Chile. Within this movement, diverse lines of flight that introduced some turns to the discipline are placed. The manuscript continues by recounting some episodes which elevated mathematics education to the category of a scientific field of inquiry and which positioned mathematics as a key element in educating the masses. This writing presents a brief glimpse to the rhizome that unfolds in historicizing mathematics education.
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Andrade-Molina, M.: (D)effecting the child: The scientifization of the self through school mathematics, Published doctoral dissertation, Aalborg, Aalborg University Press, 2017a.
Andrade-Molina, M.: «The Fabrication of Qualified Citizens: From the “Expert-Hand Worker” to the “Scientific Minded”», Perspectivas da Educação Matemática, 10(22) (2017b), pp. 29-44.
Barbin, E. y Menghini, M.: «History of teaching geometry», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 473-492.
Bass, H.: «Moments in the life of ICMI», en Menghini, M.; Furinghetti, F.; Giacardi, L. y Arzarello, F. (eds.): The first century of the International Commission of Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education, Roma, Istituto della Enciclopedia Italiana fondata da Giovanni Treccani, 2008, pp. 9-24.
Bernard, A.; Proust, C. y Ross, M.: «Mathematics Education in Antiquity», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 27-53.
Bishop, A. J.: Mathematical Enculturation. A Cultural Perspective on Mathematics Education, Dordrecht, Kluwer, 1988.
Bjarnadóttir, K.: «History of teaching arithmetic», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 431-457.
Bourdieu, P.: Leçon sur la leçon, Paris, Minuit, 1982.
Brown, T. y Heywood, D.: «Geometry, subjectivity and the seduction of language: the regulation of spatial perception», Educational Studies in Mathematics, 77(2-3) (2011), pp. 351-367.
Clements, M. A. K.; Keitel, C.; Bishop, A. J.; Kilpatrick, J. y Leung, F. K.: «From the few to the many: Historical perspectives on who should learn mathematics», en Clements, M. A. K.; Bishop, A.; Keitel, C.; Kilpatrick, J. y Leung, F. K. (eds.): Third international handbook of mathematics education, New York, Springer, 2013, pp. 7-40.
De Carvalho, J. B. P. y Dassie, B. A.: «The history of mathematics education in Brazil», ZDM, 44(4) (2012), pp. 499-511.
Del Barrio, P.: «Id. de don Paulino del Barrio sobre los de varios ramos de matemáticas del Instituto Nacional i los de física del Seminario Conciliar», Anales de la Universidad de Chile, 15(1) (1857), pp. 57-79. Doi:10.5354/0717-8883.2010.2278
Deleuze, G.: Essays critical and clinical (D. W. Smith y M. A. Greco, trads.), London-New York, Verso, 1998.
Deleuze, G. y Guattari, F.: A thousand plateaus: Capitalism and schizophrenia, Minneapolis, University of Minnesota Press, 1987.
Dussel, I.: «Profile of famous educators: Víctor Mercante (1870-1934)», Prospects, 26(2) (1996), pp. 415-431.
Ernest, P.: «A postmodern perspective on research in mathematics education», en Sierpinska, A. y Kilpatrick, J. (eds.): Mathematics Education as a research domain: A search for identity, Dordrecht, Kluwer, 1998, pp. 71-85.
Fisch, J.: «Der Mathematische Unterricht von 1800-1803», en Zur zweiten Säcularfeier des Königl. Laurentianums zu Arnsberg, Arnsberg, Buchdrucherei von Anton Düser, 1843, pp. 53-58.
Foucault, M.: «Who are you, Professor Foucault? (1967)», en Carrette, J. (ed.): Religion and Culture, New York, Routledge, 1999, pp. 87-103.
Furinghetti, F.: Matos, J. M. y Menghini, M.: «From mathematics and education, to mathematics education», en Clements, M. A. K.; Bishop, A.; Keitel, C.; Kilpatrick, J. y Leung, F. K. (eds.): Third international handbook of mathematics education, New York, Springer, 2013, pp. 273-302.
Gates, P. y Vistro-Yu, C. P.: «Is mathematics for all?», en Bishop, A.; Clements, M. A. K.; Keitel, C.; Kilpatrick, J. y Leung, F. K. (eds.): Second international handbook of mathematics education, Dordrecht, Springer, 2003, pp. 31-73.
Gibson, S.: Statuta antiqua Universitatis Oxoniensis Oxford The Clarendon, 1931.
Gispert, H.: «Mathematics education in France: 1800-1980», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 229-240.
Guevara-Casanova, I. y Burgués-Flamarich, C.: «Geometry and Visual Reasoning. Introducing algebraic language in the manner of Liu Hui and al-Khwãrizmî», en Clark, K.; Hoff Kjeldsen, T.; Schorcht, S. y Tzanakis, C. (eds.): Mathematics, Education and History. Towards a harmonious partnership, Cham, Springer, 2018, pp. 165-192.
Gutiérrez, R.: «The sociopolitical turn in mathematics education», Journal for Research in Mathematics Education, 44 (2013), pp. 37-68.
Karp, A.: «History of Mathematics Education – Personal perspectives», en Karp, A. (ed.): Leaders in Mathematics Education: Experience and Vision, Rotterdam, Sense Publishers, 2014a, pp. 1-9.
Karp, A.: «Mathematics education in Russia», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014b, pp. 303-322.
Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014a.
Karp, A. y Schubring, G.: «Mathematics Education in Europe in the Premodern Times», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014b, pp. 129-151.
Katz, V. y Barton, B. J.: «Stages in the history of algebra with implications for teaching», Educational Studies in Mathematics, 66(2) (2007), pp. 185-201.
Kilpatrick, J.: «A History of Research in Mathematics Education», en Grouws, D. A. (ed.): Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 1992, pp. 3-38.
Kilpatrick, J.: «The new math as an international phenomenon», ZDM, 44(4) (2012), pp. 563-571.
Lawrence, S.: «Balkan mathematics before the First World War», BSHM Bulletin: Journal of the British Society for the History of Mathematics, 20(1) (2005), pp. 28-36.
Lerman, S.: «The social turn in mathematics education research», en Boaler, J. (ed.): Multiple perspectives on mathematics teaching and learning, Westport, CT, Ablex, 2000, pp. 19-44.
Lesh, R. y Sriraman, B.: «Mathematics Education as a Design Science», ZDM, 37(6) (2005), pp. 490-505.
Mellin-Olsen, S.: The politics of mathematics education, Boston, MA, Kluwer Academic Publishers, 1987.
Mercante, V.: Psicología de la Aptitud Matemática del Niño, Buenos Aires, Cabaut y Cía., 1904.
Nctm: «The Second Report of the Commission on Post-War Plans», en Bidwell, J. y Clason, R. (eds.): Readings in the history of Mathematic Education, Washington, National Council of Teachers of Mathematics, 1970, pp. 618-654.
Nykänen, A.: Alkeisgeometrian opetuksesta Suomessa, erityisesti oppikirjojen kehitystä silmällä pitäen, Jyväskylä, K. J. Gummerus, 1945.
Oece: Mathématiques nouvelles, Paris, OECE, 1961.
Ordóñez, M.: «Trigonometría general rectilínea y esférica», Revista de Ciencias Económicas, VIII(74) (1919), pp. 568-570.
Pais, A.: «Economy: The absent centre of mathematics education», ZDM, 46(7) (2014), pp. 1085-1093.
Pepe, L.: «A cosa serve la storia degli insegnamenti Matematici?», Lettera Matematica Pristem, 101(1) (2017), pp. 40-48.
Pólya, G.: How to solve it, Princeton, NJ, Princeton University Press, 1945.
Schubring, G.: «On historiography of teaching and learning mathematics», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 3-8.
Schubring, G.; Furinghetti, F. y Siu, M. K.: «Introduction: the history of mathematics teaching. Indicators for modernization process in societies», ZDM, 44(4) (2012), pp. 457-459.
Skovsmose, O.: Towards a philosophy of critical mathematics education, Dordrecht, Kluwer Academic Publishers, 1994.
Valero, P.: «Mathematics education as a network of social practices», en Durand-Guerrier, V.; Soury-Lavergne, S. y Arzarello, F. (eds.): Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, Lyon, Institut National de Récherche Pédagogique, 2010, pp. LIV-LXXX.
Van Oers, B.: «Educational forms of initiation in mathematical culture», Educational Studies in Mathematics, 46 (2001), pp. 59-85.
Andrade-Molina, M.: «The Fabrication of Qualified Citizens: From the “Expert-Hand Worker” to the “Scientific Minded”», Perspectivas da Educação Matemática, 10(22) (2017b), pp. 29-44.
Barbin, E. y Menghini, M.: «History of teaching geometry», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 473-492.
Bass, H.: «Moments in the life of ICMI», en Menghini, M.; Furinghetti, F.; Giacardi, L. y Arzarello, F. (eds.): The first century of the International Commission of Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education, Roma, Istituto della Enciclopedia Italiana fondata da Giovanni Treccani, 2008, pp. 9-24.
Bernard, A.; Proust, C. y Ross, M.: «Mathematics Education in Antiquity», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 27-53.
Bishop, A. J.: Mathematical Enculturation. A Cultural Perspective on Mathematics Education, Dordrecht, Kluwer, 1988.
Bjarnadóttir, K.: «History of teaching arithmetic», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 431-457.
Bourdieu, P.: Leçon sur la leçon, Paris, Minuit, 1982.
Brown, T. y Heywood, D.: «Geometry, subjectivity and the seduction of language: the regulation of spatial perception», Educational Studies in Mathematics, 77(2-3) (2011), pp. 351-367.
Clements, M. A. K.; Keitel, C.; Bishop, A. J.; Kilpatrick, J. y Leung, F. K.: «From the few to the many: Historical perspectives on who should learn mathematics», en Clements, M. A. K.; Bishop, A.; Keitel, C.; Kilpatrick, J. y Leung, F. K. (eds.): Third international handbook of mathematics education, New York, Springer, 2013, pp. 7-40.
De Carvalho, J. B. P. y Dassie, B. A.: «The history of mathematics education in Brazil», ZDM, 44(4) (2012), pp. 499-511.
Del Barrio, P.: «Id. de don Paulino del Barrio sobre los de varios ramos de matemáticas del Instituto Nacional i los de física del Seminario Conciliar», Anales de la Universidad de Chile, 15(1) (1857), pp. 57-79. Doi:10.5354/0717-8883.2010.2278
Deleuze, G.: Essays critical and clinical (D. W. Smith y M. A. Greco, trads.), London-New York, Verso, 1998.
Deleuze, G. y Guattari, F.: A thousand plateaus: Capitalism and schizophrenia, Minneapolis, University of Minnesota Press, 1987.
Dussel, I.: «Profile of famous educators: Víctor Mercante (1870-1934)», Prospects, 26(2) (1996), pp. 415-431.
Ernest, P.: «A postmodern perspective on research in mathematics education», en Sierpinska, A. y Kilpatrick, J. (eds.): Mathematics Education as a research domain: A search for identity, Dordrecht, Kluwer, 1998, pp. 71-85.
Fisch, J.: «Der Mathematische Unterricht von 1800-1803», en Zur zweiten Säcularfeier des Königl. Laurentianums zu Arnsberg, Arnsberg, Buchdrucherei von Anton Düser, 1843, pp. 53-58.
Foucault, M.: «Who are you, Professor Foucault? (1967)», en Carrette, J. (ed.): Religion and Culture, New York, Routledge, 1999, pp. 87-103.
Furinghetti, F.: Matos, J. M. y Menghini, M.: «From mathematics and education, to mathematics education», en Clements, M. A. K.; Bishop, A.; Keitel, C.; Kilpatrick, J. y Leung, F. K. (eds.): Third international handbook of mathematics education, New York, Springer, 2013, pp. 273-302.
Gates, P. y Vistro-Yu, C. P.: «Is mathematics for all?», en Bishop, A.; Clements, M. A. K.; Keitel, C.; Kilpatrick, J. y Leung, F. K. (eds.): Second international handbook of mathematics education, Dordrecht, Springer, 2003, pp. 31-73.
Gibson, S.: Statuta antiqua Universitatis Oxoniensis Oxford The Clarendon, 1931.
Gispert, H.: «Mathematics education in France: 1800-1980», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 229-240.
Guevara-Casanova, I. y Burgués-Flamarich, C.: «Geometry and Visual Reasoning. Introducing algebraic language in the manner of Liu Hui and al-Khwãrizmî», en Clark, K.; Hoff Kjeldsen, T.; Schorcht, S. y Tzanakis, C. (eds.): Mathematics, Education and History. Towards a harmonious partnership, Cham, Springer, 2018, pp. 165-192.
Gutiérrez, R.: «The sociopolitical turn in mathematics education», Journal for Research in Mathematics Education, 44 (2013), pp. 37-68.
Karp, A.: «History of Mathematics Education – Personal perspectives», en Karp, A. (ed.): Leaders in Mathematics Education: Experience and Vision, Rotterdam, Sense Publishers, 2014a, pp. 1-9.
Karp, A.: «Mathematics education in Russia», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014b, pp. 303-322.
Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014a.
Karp, A. y Schubring, G.: «Mathematics Education in Europe in the Premodern Times», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014b, pp. 129-151.
Katz, V. y Barton, B. J.: «Stages in the history of algebra with implications for teaching», Educational Studies in Mathematics, 66(2) (2007), pp. 185-201.
Kilpatrick, J.: «A History of Research in Mathematics Education», en Grouws, D. A. (ed.): Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 1992, pp. 3-38.
Kilpatrick, J.: «The new math as an international phenomenon», ZDM, 44(4) (2012), pp. 563-571.
Lawrence, S.: «Balkan mathematics before the First World War», BSHM Bulletin: Journal of the British Society for the History of Mathematics, 20(1) (2005), pp. 28-36.
Lerman, S.: «The social turn in mathematics education research», en Boaler, J. (ed.): Multiple perspectives on mathematics teaching and learning, Westport, CT, Ablex, 2000, pp. 19-44.
Lesh, R. y Sriraman, B.: «Mathematics Education as a Design Science», ZDM, 37(6) (2005), pp. 490-505.
Mellin-Olsen, S.: The politics of mathematics education, Boston, MA, Kluwer Academic Publishers, 1987.
Mercante, V.: Psicología de la Aptitud Matemática del Niño, Buenos Aires, Cabaut y Cía., 1904.
Nctm: «The Second Report of the Commission on Post-War Plans», en Bidwell, J. y Clason, R. (eds.): Readings in the history of Mathematic Education, Washington, National Council of Teachers of Mathematics, 1970, pp. 618-654.
Nykänen, A.: Alkeisgeometrian opetuksesta Suomessa, erityisesti oppikirjojen kehitystä silmällä pitäen, Jyväskylä, K. J. Gummerus, 1945.
Oece: Mathématiques nouvelles, Paris, OECE, 1961.
Ordóñez, M.: «Trigonometría general rectilínea y esférica», Revista de Ciencias Económicas, VIII(74) (1919), pp. 568-570.
Pais, A.: «Economy: The absent centre of mathematics education», ZDM, 46(7) (2014), pp. 1085-1093.
Pepe, L.: «A cosa serve la storia degli insegnamenti Matematici?», Lettera Matematica Pristem, 101(1) (2017), pp. 40-48.
Pólya, G.: How to solve it, Princeton, NJ, Princeton University Press, 1945.
Schubring, G.: «On historiography of teaching and learning mathematics», en Karp, A. y Schubring, G. (eds.): Handbook on the history of mathematics education, New York, Springer, 2014, pp. 3-8.
Schubring, G.; Furinghetti, F. y Siu, M. K.: «Introduction: the history of mathematics teaching. Indicators for modernization process in societies», ZDM, 44(4) (2012), pp. 457-459.
Skovsmose, O.: Towards a philosophy of critical mathematics education, Dordrecht, Kluwer Academic Publishers, 1994.
Valero, P.: «Mathematics education as a network of social practices», en Durand-Guerrier, V.; Soury-Lavergne, S. y Arzarello, F. (eds.): Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, Lyon, Institut National de Récherche Pédagogique, 2010, pp. LIV-LXXX.
Van Oers, B.: «Educational forms of initiation in mathematical culture», Educational Studies in Mathematics, 46 (2001), pp. 59-85.
Andrade-Molina, M. (2022). A brief story of mathematics education. Historia De La Educación, 40(1), 139–156. https://doi.org/10.14201/hedu202140139156
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