Embracing Nepantla: Rethinking "Knowledge" and its Use in Mathematics Teaching
Downloads
Abstract
Although educational researchers are moving beyond purely psychological and cognitive models of learning to consider the ways in which mathematics teaching might reach a more diverse student population, this work remains in its infancy, and the concept of “knowledge” is rarely questioned. This paper begins with the idea that mathematics education has much to gain from perspectives in Latin@ studies. I draw on the work of Gloria Anzaldúa, specifically her concepts of “conocimiento” and “Nepantla” to bring a more holistic/connected perspective to the “knowledge” teachers may need for teaching and highlight how it might align with broader definitions of mathematics. I also offer examples from a partnership with a Chicago high school to show how pre-service teachers move through cycles of knowledge construction. Implications for teacher education, and teacher recruitment are discussed.Downloads
References
Alper, L., Fendel, D., Fraser, S., Resek, D. (1997). Interactive mathematics program, Year 1. Emeryville, CA: Key Curriculum. Anzaldúa, G. (1987). Borderlands/La Frontera: The new mestiza.
Google Scholar CrossrefSan Francisco, Aunt Lute Books.
Google Scholar CrossrefAnzaldúa, G. (ed.) (1990). Making face, making soul/Haciendo caras:
Google Scholar CrossrefCreative and critical perspectives by feminists of color. San
Google Scholar CrossrefFrancisco: Aunt Lute Books.
Google Scholar CrossrefAnzaldúa, G. (2000). Interviews/Entrevistas. New York: Routledge. Anzaldúa, G. and Keating, A. L. (2002). This bridge we call home:
Google Scholar CrossrefRadical visions for transformation. New York: Routledge. Aparicio. F. R. (1998). Listening to salsa: Gender, Latin popular music, and Puerto Rican cultures. Hanover, NH: Wesleyan
Google Scholar CrossrefUniversity Press.
Google Scholar CrossrefAscher, M. (2002). Mathematics elsewhere: An exploration of ideas
Google Scholar Crossrefacross cultures. Princeton, NJ: Princeton University Press. Barnett, J. & A. AmreinBeardsley. (2011). Actions over credentials: Moving from highly qualified to measurably effective. Teachers College Record. http://www.tcrecord.org. Accessed 9/27/2011. Bergioli, G. & McClosky, A. (2006, April). Building Models of Pre service Elementary Teachers’ Conceptions of Mathematics, Teaching and Learning Mathematics,and Children’s Mathematics: Implications for Cognitive Equity. Paper presented at the Annual meeting of the National Council of Teachers of Mathematics,
Google Scholar CrossrefResearch Presession, St. Louis, Missouri.
Google Scholar CrossrefREDIMAT Journal of Research in Mathematics Education, 1 (1) 49
Google Scholar CrossrefBoaler, J. (2002). Experiencing school mathematics. Mahwah, NJ: Lawrence Erlbaum.
Google Scholar CrossrefCastillo, A. (1994). Massacre of the dreamers: Essays on Xicanisma. New York: Plume.
Google Scholar CrossrefCinzia, B. (2005). How informal outofschool mathematics can help students make sense of formal inschool mathematics: the case of multiplying by decimal numbers. Mathematics Thinking and Learning, 7(4), 313344.
Google Scholar CrossrefCivil, M. & Andrade, R. (2002). Transitions between home and school mathematics: Rays of hope amidst the passing clouds. In G. de Abreu, A.J. Bishop, and N.C. Presmeg (Eds.), Transitions between contexts of mathematical practices (pp. 149169). Boston, MA: Kluwer.
Google Scholar CrossrefCivil, M., & Kahn, L. (2001). Mathematics instruction developed from a garden theme. Teaching Children Mathematics, 7, 400405. Civil, M., Planas, N., & Quintos, B. (2005). Immigrant parents’ perspectives on their children’s mathematics. Zentralblatt für
Google Scholar CrossrefDidaktik der Mathematik, 37(2), 8189.
Google Scholar CrossrefCobb, P. & Yackel, E. (1998). A constructivist perspective on the
Google Scholar Crossrefculture of the mathematics classroom. In Seeger, F., Voigt, J., & Waschescio, U. (Eds.), The culture of the mathematics classroom (pp. 158190). Cambridge, MA: Cambridge University Press.
Google Scholar CrossrefCobb, P. and Nasir, N. (Eds.) (2007). Diversity, equity, and access to mathematical ideas. New York: Teachers College Press.
Google Scholar CrossrefD’Ambrosio, U. (1985) Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 4448.
Google Scholar CrossrefD’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. Rotterdam, The Netherlands: Sense Publishers. Darder, A. (2002). Reinventing Paulo Freire: A pedagogy of love.
Google Scholar CrossrefBoulder, CO: Westview.
Google Scholar CrossrefDarlingHammond, L. & Bransford, J. (2005). Preparing teachers for
Google Scholar Crossrefa changing world: What teachers should learn and be able to do.
Google Scholar CrossrefSan Francisco: JosseyBass.
Google Scholar Crossrefde Abreu, G., Bishop, A. J., & Presmeg, N. C. (Eds.) (2002).
Google Scholar CrossrefTransitions between contexts of mathematical practices. Boston, MA: Kluwer.
Google Scholar Crossrefde Abreu, G. & Cline, T. (2005). Parents’ representations of their children’s mathematics learning in multiethnic primary schools. British Educational Research Journal, 31(6), 697722.
Google Scholar Crossrefde Abreu, G. and Cline, T. (2007). Social valorisation of mathematical practices: The implications for learners in multicultural schools. In Nasir, N. S. and Cobb, P. (Eds.) Improving Access to Mathematics: Diversity and Equity in the Classroom. New York: Teachers College Press.
Google Scholar CrossrefDiezPalomar, J., Simic, K., and Varley, M. (2008). “Math is everywhere:” Connecting mathematics to students’ lives. Adults Learning Mathematics International Journal, 1(8), 2036.
Google Scholar CrossrefEdwards, A., Gilroy, P., & Hartley, D. (2002). Rethinking teacher education: Collaborative responses to uncertainty. New York: Routledge.
Google Scholar CrossrefEnglish, L. D. (2002). Handbook of international research in mathematics education. Mahwah, NJ: Lawrence Erlbaum.
Google Scholar CrossrefEven, R. & Tirosh, D. (2002). Teacher knowledge and understanding of students’ mathematical learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 219240). Mahwah, NJ: Lawrence Erlbaum.
Google Scholar CrossrefErnest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 1333.
Google Scholar CrossrefFrankenstein, M. (1994). Understanding the politics of mathematical knowledge as an integral part of becoming critically numerate. Radical Statistics, 56, 2240.
Google Scholar CrossrefFrankenstein, M. (2009). Using real reallife problems in teaching critical mathematical literacy. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay, (Eds.) Words and worlds: Modeling verbal descriptions of situations. Rotterdam: The Netherlands: Sense Publications.
Google Scholar CrossrefGonzález, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging funds of distributed knowledge: Creating zones of practices in mathematics. Journal of Education for Students Placed At Risk, 6(1&2), 115132.
Google Scholar CrossrefGorgorió, N., Planas, N., & Vilella, X. (2002). Immigrant children learning mathematics in mainstream schools. In G. de Abreu, A. Bishop & N. Presmeg (Eds.), Transitions between contexts of mathematical practices (pp. 152). Boston: Kluwer.
Google Scholar CrossrefGreer, B., Mukhopadyay, S., Powell, A., & NelsonBarber, S. (2009). Culturally responsive mathematics education. New York: Routledge.
Google Scholar CrossrefGutierrez, K., BaquedanoLopez, P., & Tejeda, C. (1999). Rethinking diversity: Hybridity and hybrid language practices in the third space. Mind, Culture, & Activity, 41, 286303.
Google Scholar CrossrefGutiérrez, R. (1999a). Advancing urban, Latino youth in mathematics: Lessons from an effective high school mathematics department. Urban Review, 31(3), 263–281.
Google Scholar CrossrefGutiérrez, R. (1999b). Triumphs and trials of community membership: Mathematics teachers implementing reform. Paper presented at the Annual Meeting of the American Educational Research Association. Montreal, Quebec, Canada.
Google Scholar CrossrefGutiérrez, R. (2000b). Is the multiculturalization of mathematics doing us more harm than good? In Mahalingam, R. and McCarthy, C. (Eds.) Multicultural Curriculum: New Directions for Social Theory, Practice, and Policy (pp. 199219). New York: Routledge.
Google Scholar CrossrefGutiérrez, R. (2002a). Enabling the practice of mathematics teachers in context: Towards a new equity research agenda. Mathematical Thinking and Learning. 4(2&3), 145187.
Google Scholar CrossrefGutiérrez, R. (2002b). Beyond Essentialism: The Complexity of Language in Teaching Latina/o Students Mathematics. American Educational Research Journal, 39(4), 10471088.
Google Scholar CrossrefGutiérrez, R. (2007). (Re)defining equity: The importance of a critical perspective. In N. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas. New York: Teachers College Press.
Google Scholar CrossrefGutiérrez, R. (2008). Realizing the potential of Chicanas/os and Native Americans: Engaging identity and power issues in teaching students mathematics and science. SACNAS News, 11(1), 1011, 15.
Google Scholar CrossrefGutiérrez, R. (2009). Embracing the inherent tensions in teaching mathematics from an equity stance. Democracy and Education, 18(3), 916.
Google Scholar CrossrefGutiérrez, R. (2010). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education. Available online at http://www.nctm.org/eresources/article_summary.asp?from=B&ur i=JRME2010061a
Google Scholar CrossrefGutiérrez, R. (in press). Context matters: How should we conceptualize equity in mathematics education? In Choppin, J., HerbelEisenmann, B., & Wagner, D., (Eds.), Equity in discourse for mathematics education: Theories, practices, and policies. New York: Springer.
Google Scholar CrossrefGutiérrez, R. (in preparation). Mathematics teaching as subversive activity: Why teachers need political knowledge. Gutiérrez, R. and DixonRomán, E. (2011). Beyond gap gazing: How can thinking about education comprehensively help us (re)envision mathematics education? In Atweh, B., Graven, M., Secada, W., and Valero, P. (eds.), Mapping equity and quality in
Google Scholar Crossrefmathematics education (pp. 2134). New York: Springer. Gutstein, E., (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in
Google Scholar CrossrefMathematics Education, 34(1), 3773.
Google Scholar CrossrefGutstein, E. (2006). Reading and writing the world with mathematics:
Google Scholar CrossrefToward a pedagogy for social justice. New York: Teachers
Google Scholar CrossrefCollege Press.
Google Scholar CrossrefGutstein, E. (2007). “So one question leads to another:” Using
Google Scholar Crossrefmathematics to develop a pedagogy of questioning. In N.S. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas. New York: Teachers College Press.
Google Scholar CrossrefGutstein, E., Lipman, P., Hernandez, P., & de los Reyes, R. (1997). Culturally relevant mathematics teachers in a MexicanAmerican context. Journal for Research in Mathematics Education, 28(6), 709–737.
Google Scholar CrossrefHill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371406.
Google Scholar CrossrefKastberg, S. E. & D’Ambrosio, B. S. (2006, April). Knowledge Development for Constructivist Teaching with Implications for Equity Practice. A paper presented at the Annual meeting of the National Council of Teachers of Mathematics, Research Pre session, St. Louis, Missouri.
Google Scholar CrossrefKeating, A. L. (ed.) (2005). Entremundos/AmongWorlds: New perspectives on Gloria Anzaldúa. New York: Palgrave Macmillan.
Google Scholar CrossrefKoehler, M. S., & Grouws, D. A. (1992). Mathematics teaching practices and their effects. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 115126). New York: MacMillan Publishing Company.
Google Scholar CrossrefKhisty, L. L., & Viego, G. (1999). Challenging conventional wisdom: A case study. In L. OrtizFranco, N. G. Hernandez, & Y. De La Cruz (Eds.), Changing the faces of mathematics: Perspectives on Latinos (pp. 71–80). Reston, VA: NCTM.
Google Scholar CrossrefKnijnik, G. (July, 2011). An ethnomathematics perspective of mathematics education. A paper presented at the Mathematics Education in Contemporary Society conference. Manchester, United Kingdom. England.
Google Scholar CrossrefLadsonBillings, G. (1995). Making mathematics meaningful in multicultural contexts. In W. G. Secada, E. Fennema, & L. B. Adajian (Eds.), New directions for equity in mathematics education (pp. 126–145). Cambridge, UK: Cambridge University Press.
Google Scholar CrossrefLubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454482.
Google Scholar CrossrefMa, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.
Google Scholar CrossrefMartin, D. B. (2006). Mathematics learning as racialized experience: African American parents speak on the struggle for mathematics literacy. Mathematical Thinking and Learning, 8(3), 197229.
Google Scholar CrossrefMartin, D. B. (2007). Mathematics learning and participation in an African American context: The coconstruction of identity in two intersecting realms of experience. In N. Nasir & P. Cobb (Eds.),
Google Scholar CrossrefDiversity, equity, and access to mathematical ideas. New York:
Google Scholar CrossrefTeachers College Press.
Google Scholar CrossrefMartin, D. B. (2009). Mathematics teaching, learning, and liberation
Google Scholar Crossrefin the lives of black children. New York: Routledge. Mason, J. & Spence. M. (1999). Beyond mere knowledge of mathematics: The importance of knowing to act in the moment. Educational Studies in Mathematics, 38, 135161. McGinnis, J. R., Shama, G., Graeber, A., & Watanabe, T. (1997). Development of an instrument to measure teacher candidates' attitudes and beliefs about the nature of the teaching of mathematics and science. The National Association for Research
Google Scholar Crossrefin Science Teaching. Oak Brook, IL.
Google Scholar CrossrefMiller, M. (1986). Kollecktive lernprozesse Studien zur grundlegung
Google Scholar Crossrefeiner soziologischen lerntheorie. Frankfurt: Suhrkamp Verlag. Mukhopadhyah, S. & Greer, B.. (2001). Modeling with a purpose: Mathematics as a critical tool. In B. Atweh, H. Forgasz & B. Nebres (Eds.), Sociocultural research on mathematics education.
Google Scholar CrossrefMahwah: Lawrence Erlbaum.
Google Scholar CrossrefNasir, N. S. (2007). Identity, goals, and learning: Mathematics in
Google Scholar Crossrefcultural practice. In N.S. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas. New York: Teachers College Press.
Google Scholar CrossrefNasir, N. S. & Cobb, P. (2006). (Eds.). Diversity, equity, and access to mathematical ideas. New York: Teachers College Press. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Gutierrez, R.. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317328. Noddings, N. (1992). The challenge to care in schools: An alternative approach to education. New York: Teachers College
Google Scholar CrossrefPress.
Google Scholar CrossrefPieterse, J. N. (2004). Globazliation and culture: Global mélange.
Google Scholar CrossrefNew York: Rowman & Littlefield.
Google Scholar CrossrefSaldivar, J. D. (1997). Border matters: Remapping American cultural
Google Scholar Crossrefstudies. Berkeley, CA: University of California Press.
Google Scholar CrossrefSleeter, C. (1993) How white teachers construct race. In C. McCarthy & W. Crichlow (Eds.), Race, identity and representation in education (pp. 157171). New York: Routledge.
Google Scholar CrossrefSkovsmose, O. & Valero, P. (2001). Breaking political neutrality: The critical engagement of mathematics education with democracy. In B. Atweh, H. Forgasz & B. Nebres (Eds.), Sociocultural research in mathematics education: An international perspective (pp. 3755). Mahwah, NJ: Lawrence Erlbaum.
Google Scholar CrossrefSkovsmose, O. (July, 2011). Symbolic power, robotting, and surveilling. A paper presented at the Mathematics Education in Contemporary Society conference. Manchester, United Kingdom.
Google Scholar CrossrefSteinbring, H. (2005). The construction of new mathematical knowledge in classroom interaction: An epistemological perspective. New York: Springer.
Google Scholar CrossrefStrutchens, M. E., Quander, J. R., & Gutiérrez, R. (2011). Mathematics learning communities that foster reasoning and sense making for all high school students. In Strutchens, M. E. (Ed.) Focus in high school mathematics: Making mathematical reasoning and sense making a reality for all. Reston, VA: National Council of Teachers of Mathematics.
Google Scholar CrossrefThompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127146). New York, NY: MacMillan Publishing Company.
Google Scholar CrossrefTurner, E. E., Gutierrez, M. V., & DiezPalomar, J. (2011). Latina/o bilingual elementary students pose and investigate problems grounded in community settings. In Tellez, K., Moschkovich, J. N., and Civil, M. (eds). Latino/as and mathematics education: Research on learning and teaching in classrooms and communities (pp. 149174). New York: Information Age Publishing.
Google Scholar CrossrefValero, P., Kilpatrick, J., Hoyles, C., & Skovsmose, O. (2005). Meaning in mathematics education. New York: Springer.
Google Scholar CrossrefDownloads
Published
Almetric
Dimensions
Issue
Section
License
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.
