Teaching Mathematics for Spatial Justice: An Investigation of the Lottery

References

• ACCLAIM Center for Learning & Teaching. (2010). Community and place in mathematics instruction in selected rural schools. Athens, OH: Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM).
   Google Scholar
• Ariyabuddhiphongs, V. (2011). Lottery gambling: A review. Journal of Gambling Studies, 27, 15–33.
   Google Scholar
• Bartell, T. (2013). Learning to teach mathematics for social justice: Negotiating social justice and mathematics goals [Special issue]. Journal for Research in Mathematics Education, 41, 129–163. Retrieved from http://www.nctm.org/uploadedFiles/Journals_and_Books/JRME/articles/JRME_Special_Equity_Issue/Bartell.pdf.
   Google Scholar
• Batanero, C., Navarro-Pelayo, V., & Godino, J. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics, 32, 181–199.
   Google Scholar
• Battista, M. (2007). The development of geometric and spatial thinking. In D. Grouws (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Beckert, J., & Lutter, M. (2013). Why the poor play the lottery: Sociological approaches to explaining class-based lottery play. Sociology, 47(6), 1152–1170.
   Google Scholar
• Best, J. (2001). Damned lies and statistics. Berkeley, CA: University of California Press.
   Google Scholar
• Blalock, G., Just, D. R., & Simon, D. H. (2007). Hitting the jackpot or hitting the skids. Entertainment, poverty, and the demand for state lotteries. American Journal of Economics and Sociology, 66, 545–570.
   Google Scholar
• Brantlinger, A. (2005). The geometry of inequality. In E. Gutstein and B. Peterson (Eds.), Rethinking mathematics: Teaching social justice by the numbers. Milwaukee, WI: Rethinking Schools.
   Google Scholar
• Brantlinger, A. (2013). Between politics and equations: Teaching critical mathematics in a remedial secondary classroom. American Educational Research Journal, 50(5), 1050–1080.
   Google Scholar
• Bright, N. G., Manchester, H., & Allendyke, S. (2013). Space, place, and social justice in education: Growing a bigger entanglement: Editors' introduction. Qualitative Inquiry, 19(10), 747–755.
   Google Scholar
• Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43.
   Google Scholar
• Cohen, E., & Lotan, R. (1995). Producing equal status interaction in the heterogeneous classroom. American Educational Research Journal, 32(1), 99–120.
   Google Scholar
• Design Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.
   Google Scholar
• Dewey, J. (1900/1959). School and society. In M. Dworkin (Ed.), Dewey on education (pp. 76–78). New York, NY: Teachers College Press.
   Google Scholar
• Diversity in Mathematics Education. (2007). Culture, race, power, and mathematics education. In D. Grouws (Ed.), Second handbook of research on mathematics teaching and learning (pp. 405–434). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• English, L. D. (1993). Children's strategies for solving two- and three-dimensional combinatorial problems. Journal for Research in Mathematics Education, 24(3), 225–273.
   Google Scholar
• Enyedy, N., Danish, J., & Fields, D. (2011). Negotiating the “relevant” in culturally relevant mathematics. Mathematical Thinking & Learning, 11(3), 273–291.
   Google Scholar
• Enyedy, N. & Mukhophadyay, S. (2007). They don't show nothing I didn't know: Emergent tensions between culturally relevant pedagogy and mathematics pedagogy. Journal of the Learning Sciences, 16(2), 139–174.
   Google Scholar
• Esmonde, I. (2014). “Nobody's rich and nobody's poor… It sounds good, but it's actually not”: Affluent students learning mathematics and social justice. Journal of the Learning Sciences, 23(3), 348–391.
   Google Scholar
• Fischbein, E., & Gazit, A. (1988). The combinatorial solving capacity in children and adolescents. ZDM International Journal on Mathematics Education, 5, 193–198.
   Google Scholar
• Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96–106.
   Google Scholar
• Florida, R. (2012, October 9). The high inequality of U.S. metro areas compared to countries. City Lab. Retrieved from www.citylab.com/work/2012/10/high-inequality-us-metro-areas-compared-countries/3079/.
   Google Scholar
• Frankenstein, M. (1989). Relearning mathematics: A different third R, radical maths. London, UK: Free Association.
   Google Scholar
• Frankenstein, M. (1995). Equity in mathematics education: Class in the world outside the class. In W. Secada, E. Fennema, & L. Adajian (Eds.), New directions for equity in mathematics education (pp. 165–190). Cambridge, UK: Cambridge University Press.
   Google Scholar
• Friel, S., Curcio, F., & Bright, G. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional Implications. Journal for Research in Mathematics Education, 32(2), 124–158.
   Google Scholar
• Gallese, V., & Lakoff, G. (2005). The brain's concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22(3–4), 455–479.
   Google Scholar
• Gonnerman, J. (2004, November 9). Million dollar blocks. The village voice. Retrieved from http://www.villagevoice.com/news/million-dollar-blocks-6398537
   Google Scholar
• Gruenewald, D. (2003a). The best of both worlds: A critical pedagogy of place. Educational Researcher, 32(4), 3–12.
   Google Scholar
• Gruenewald, D. (2003b). Foundations of place: A multi-disciplinary framework for place-conscious education. American Educational Research Journal, 40(3), 619–654.
   Google Scholar
• Gruenewald, D. & Smith, G. (2010). Place-based education in the global age. New York, NY: Routledge.
   Google Scholar
• Gutiérrez, K., Baquedano-López, P., & Tejeda, C. (1999). Rethinking diversity: Hybridity and hybrid language practices in the third space. Mind, Culture, and Activity, 6(4), 286–303.
   Google Scholar
• Gutiérrez, M. V. (2012). Community spaces as a part of hybrid math learning spaces: Integrating multiple funds of knowledge. In E. Tan & A. Calabrese Barton (Eds.), Empowering science and mathematics education in urban schools (pp. 145–165). Chicago, IL: University of Chicago Press.
   Google Scholar
• Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37–73.
   Google Scholar
• Gutstein, E. (2006). Reading and writing the world with mathematics. New York, NY: Routledge.
   Google Scholar
• Gutstein, E. (2013). Whose community is this? Mathematics of neighborhood displacement. Rethinking Schools, 27(3), 11–17.
   Google Scholar
• Hall-Wieckert, M., Rubel, L., & Lim, V. (2016, accepted). Making space for place: Embodied distribution on a walkable map surface. Paper to be presented at the Annual Meeting of the American Educational Research Association. Washington, DC.
   Google Scholar
• Harvey, D. (1973). Social justice and the city. Baltimore, MD: Johns Hopkins University Press.
   Google Scholar
• Harvey, D. (1996). Justice, nature, and the geography of difference. Malden, MA: Blackwell.
   Google Scholar
• Horn, I. (2007). Fast kids, slow kids, lazy kids: Classification of students and conceptions of subject matter in math teachers' conversations. Journal of the Learning Sciences, 16, 37–79.
   Google Scholar
• Horn, I. (2012). Strength in numbers: Collaborative learning in secondary mathematics. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Howley, A., Showalter, D., Howley, M. D., Howley, C. B., Klein, R., & Johnson, J. (2011). Challenges for place-based mathematics pedagogy in rural schools and communities in the United States. Children, Youth, and Environments, 21(1), 101–127.
   Google Scholar
• Jackson, K. (2009). The social construction of youth and mathematics: The case of a fifth-grade classroom. In D. Martin (Ed.), Mathematics teaching, learning, and liberation in the lives of black children (pp. 175–199). New York, NY: Routledge.
   Google Scholar
• Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30(5), 487–519.
   Google Scholar
• Kurgan, L., Cadora, E., Reinfurt, D., & Williams, S. (2006). Million dollar blocks. Retrieved from http://spatialinformationdesignlab.org/projects.php%3Fid%3D16
   Google Scholar
• Kurti, A., Spikol, D., & Milrad, M. (2008). Bridging outdoors and indoors educational activities in schools with the support of mobile and positioning technologies. International Journal of Mobile Learning and Organization: Special Issue on Current Learning Technologies and Applications, 2, 166–186.
   Google Scholar
• Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465–491.
   Google Scholar
• Ladson-Billings, G., & Tate, W. F. (1995). Toward a critical race theory of education. Teachers College Record, 97(1), 47–68.
   Google Scholar
• Leander, K. M., & Sheehy, M. (2004). Spatializing literacy research and practice. New York, NY: Peter Lang.
   Google Scholar
• Leander, K., Phillips, N., & Taylor, K. H. (2010). The changing social spaces of learning: Mapping new mobilities. Review of Research in Education, 34, 329–394.
   Google Scholar
• Lefebvre, H. (1968). Le droit ala ville. Paris, France: Anthropos.
   Google Scholar
• Lim, M., & Barton, A. C. (2006). Science learning and a sense of place in an urban middle school. Cultural Studies of Science Education, 1, 107–142.
   Google Scholar
• Lim, V., Rubel, L., Deahl, E., & Williams, S. (2015). Local Lotto: Mathematics and mobile technologies to study the lottery. In D. Polly (Ed.), Cases on technology and common core mathematics standards (pp. 43–67). Hershey, PA: IGI Global.
   Google Scholar
• Lim, V., Rubel, L., Shookhoff, L., Sullivan, M., & Williams, S. (in press). The lottery is a mathematics powerball. Mathematics Teaching in the Middle School, 21.
   Google Scholar
• Lincoln, Y. S., & Guba, E. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.
   Google Scholar
• Literat, I. (2013). Participatory mapping with urban youth: The visual elicitation of socio-spatial research data. Learning, Media and Technology, 38(2), 198–216.
   Google Scholar
• Monmeier, M. (1991). How to lie with maps. Chicago, IL: The University of Chicago Press.
   Google Scholar
• Morris, K. (2013). Map reading framework ( Unpublished manuscript in preparation). Department of Teaching, Learning, Policy, & Leadership, University of Maryland, College Park, Maryland.
   Google Scholar
• Moses, R., & Cobb, C. (2002). Radical equations: Civil rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press.
   Google Scholar
• National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for mathematics. Washington, DC: Authors.
   Google Scholar
• National Research Council. (2006). Learning to think spatially: GIS as a support system in the K–12 curriculum. Washington, DC: National Academies Press.
   Google Scholar
• New York Civil Liberties Union. (2007). Criminalizing the classroom: The over policing of New York City schools. Retrieved from www.nyclu.org/pdfs/criminalizing_the_classroom_report.pdf
   Google Scholar
• Philip, T. M., Schuler-Brown, S., & Way, W. (2013). A framework for learning about big data with mobile technologies for democratic participation: Possibilities, limitations, and unanticipated obstacles. Technology, Knowledge and Learning, 18(3), 103–120.
   Google Scholar
• Philip, T. M., & Garcia, A. D. (2013). The importance of still teaching the iGeneration: New technologies and the centrality of pedagogy. Harvard Educational Review, 83(2), 300–319.
   Google Scholar
• Philip, T. M., Way, W., Garcia, A. D., Schuler-Brown, S., & Navarro, O. (2013). When educators attempt to make “community” a part of classroom learning: The dangers of (mis)appropriating students' communities into schools. Teaching and Teacher Education, 34, 174–183.
   Google Scholar
• Pickles, J. (2004). A history of spaces: Cartographic reason, mapping, and the geo-coded world. New York, NY: Routledge.
   Google Scholar
• Povey, H. (2003). Teaching and learning mathematics: can the concept of citizenship be reclaimed for social justice? In L. Burton (Ed.), Which way social justice in mathematics education? (pp. 51–64). Westport, CT: Praeger Publishers.
   Google Scholar
• Quintana, C. (2012). Pervasive science: Using mobile devices and the cloud to support science education anytime, anyplace. Interactions, 19(4), 76–80.
   Google Scholar
• Radinsky, J. (2008). Students' roles in group-work with visual data: A site of science learning. Cognition & Instruction, 26(2), 145–194.
   Google Scholar
• Raudenbush, S., Rowan, B., & Cheong, Y.F. (1993). The pursuit of higher order instructional goals in secondary schools: Class, teacher, and school influences. American Educational Research Journal, 30(3), 523–553.
   Google Scholar
• Rubel, L. (2005/2013). The mathematics of lotteries: Going beyond probability. In E. Gutstein & B. Peterson (Eds.), Rethinking mathematics: Teaching mathematics for social justice. 2nd edition (pp. 236–237). Milwaukee, WI: Rethinking Schools.
   Google Scholar
• Rubel, L., Driskill, M., & Lesser, L. (2012). Decennial redistricting: Rich mathematics in context. Mathematics Teacher, 106(3), 206–211.
   Google Scholar
• Rubel, L., Lim, V., Candace Full, M., & Hall-Wieckert, M. (2015). “Critical pedagogy of place” in mathematics: Texts, tools, and talk. In B. Greer & S. Mukhophadyay (Eds.), Proceedings of Mathematics Education & Society 8 (pp. 912–924). Portland, Oregon.
   Google Scholar
• Shaughnessy, J. M. (1992). Research on probability and statistics. In D. Grouws (Ed.), First handbook of research on mathematics teaching and learning (pp. 465–494). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1011). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Showalter, D. A. (2013). Place-based mathematics education: A conflated pedagogy? Journal of Research in Rural Education, 28(6), 1–13. Retrieved from http://jrre.psu.edu/articles/28-6.pdf
   Google Scholar
• Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht, Netherlands: Kluwer Academic Publishers.
   Google Scholar
• Smith, G. (2002). Place-based education: Learning to be where we are. Phi Delta Kappan, 83, 584–594.
   Google Scholar
• Sobel, D. (1998). Mapmaking with children. Portsmouth, NH: Heinemann.
   Google Scholar
• Sobel, D. (2004). Place-based education: Connecting classrooms & communities. Great Barrington, MA: Orion Society.
   Google Scholar
• Soja, E. W. (1996). Thirdspace: Journeys to Los Angeles and other real-and-imagined places. Cambridge, MA: Blackwell.
   Google Scholar
• Soja, E. W. (2010). Seeking spatial justice. Minneapolis, MN: University of Minnesota Press.
   Google Scholar
• Staples, M. (2005). Integrals and Equity. In E. Gutstein & B. Peterson (Eds.), Rethinking mathematics: Teaching social justice by the numbers (pp. 103–106). Milwaukee, WI: Rethinking Schools, Ltd.
   Google Scholar
• Stinson, D., & Wager, A. (2013). Teaching mathematics for social justice: Conversations with educators. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Strauss, A. (1987). Qualitative analysis for social scientists. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Tan, E., & Barton, A. (2012). Empowering science and mathematics education in urban schools. Chicago, IL: University of Chicago Press.
   Google Scholar
• Tate, W. F. & Hogrebe, M. (2011). From visuals to vision: Using GIS to inform civic dialogue about African American males. Race, Ethnicity and Education, 14(1), 51–71.
   Google Scholar
• Taylor, K. H. (2013). Counting mapping the neighborhood: A social design experiment for spatial justice (Doctoral dissertation). Retrieved from ProQuest Dissertation and Theses. (Accession Order No. AAT 3575572)
   Google Scholar
• Trouche, L., & Drijvers, P. (2010). Handheld technology: Flashback into the future. ZDM, The International Journal on Mathematics Education, 42, 667–681.
   Google Scholar
• Tuan, Y. F. (1975). Place: An experiential perspective. Geographical Review, 65(2), 151–165.
   Google Scholar
• Tuan, Y. F. (1977). Space and place: The perspective of experience. Minneapolis, MN: University of Minnesota Press.
   Google Scholar
• Turner, E. (2012). Critical mathematical agency in the Francis Middle School Overcrowding Project. In E. Tan & A.C. Barton (Eds.), Empowering science & mathematics education in urban schools (pp. 51–76). Chicago, IL: University of Chicago Press.
   Google Scholar
• Tversky, A., & Kahneman, D. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430–454.
   Google Scholar
• Van Wart, S., Tsai, K., & Parikh, T. (2010). Local Ground: A paper-based toolkit for documenting local geo-spatial knowledge. In A. Dearden (Ed.), Proceedings of the First ACM Symposium on Computing for Development. London, UK: ACM.
   Google Scholar
• Veletsianos, G. (2011). Designing opportunities for transformation with emerging technologies. Educational Technology, 51(2), 41–46.
   Google Scholar
• Vithal, R. (2003). In search of a pedagogy of conflict and dialogue for mathematics education. Dordrecht, The Netherlands: Kluwer.
   Google Scholar
• Whitin, D. (2006). Learning to talk back to a statistic. In G. Burrill & P. Elliott (Eds.), Thinking and reasoning with data and chance (pp. 31–40). Reston: VA: National Council of Teachers of Mathematics.
   Google Scholar
• Wijers, M., Jonkers, V., Drijvers, P. (2010). Mobile math: Exploring mathematics outside of the classroom. ZDM International Journal of Mathematics Education, 42, 789–799.
   Google Scholar
• Wilkerson-Jerde, M., & Laina, V. (2015). Stories of our city: Coordinating youths' mathematical, representational, and community knowledge through data visualization. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.
   Google Scholar
• Williams, S., Deahl, E., Rubel, L., & Lim, V. (2014). City Digits Local Lotto: Developing youth data literacy by investigating the lottery. Journal of Digital and Media Literacy, 2(2). Retrieved from http://www.jodml.org/2014/12/15/city-digits-local-lotto-developing-youth-data-literacy-by-investigating-the-lottery/
   Google Scholar
• Winter, D. (2007). Infusing mathematics with culture: Teaching technical subjects for social justice. New Directions for Teaching and Learning, 111, 97–106.
   Google Scholar
• Wisman, J. D. (2006). State lotteries: Using state power to fleece the poor. Journal of Economic Issues, XL(4), 955–966.
   Google Scholar
• Wood, D., Fels, J., & Krygier, J. (2010). Rethinking the power of maps. New York, NY: Guilford Press.
   Google Scholar
• Wood, D., Kaiser, W., & Abramms, B. (2006). Seeing through maps: Many ways to see the world. Amherst, MA: ODT.
   Google Scholar