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Designing for Generative Activities: Expanding Spaces for Learning and Teaching

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The SimCalc Vision and Contributions

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

The focus of this chapter is on issues of equity in generative activities and in SimCalc’s goal of democratizing access to rigorous mathematics. Changes in content, opportunities to participate, and avenues for students to draw on the varied cultural and linguistic resources they bring to learning are explored. They are also theorized in light of research findings from SimCalc and other network-supported activities. I explore expansion in classroom social spaces resulting from the multiplicity of ways that students can participate and contribute. The expansion that emerges via engaging varieties of students’ backgrounds and cultural displays is central to efforts to pursue equity through generative design of networked classrooms.

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Notes

  1. 1.

    This extended excerpt is also included in Ares, 2008, p. 32.

References

  • Anderson, E. (1999). Code of the street: decency, violence, and the moral life of the inner city. New York: Norton.

    Google Scholar 

  • Ares, N. (2008). Cultural relevance in design and use of networked classroom technologies. International Journal of Computer Supported Collaborative Learning, 3(3), 301–326.

    Article  Google Scholar 

  • Ares, N., & Stroup, W. M. (2004). Drawing on diverse social, cultural, and academic resources in technology-mediated classrooms. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th annual meeting of the international group for the psychology in mathematics education (pp. 837–844). Norwich, England: University of East Anglia.

    Google Scholar 

  • Ares, N., Stroup, W. M, & Schademan, A. R. (2009). The power of mediating artifacts in group-level development of mathematical discourses. Cognition & Instruction, 27(1), 1–24.

    Article  Google Scholar 

  • Au, K. H. (1980). Participation structures in a reading lesson with Hawaiian children: analysis of a culturally appropriate instructional event. Anthropology and Education Quarterly, 11(2), 91–115.

    Article  Google Scholar 

  • Barton, D. (2007). Literacy: an introduction to the ecology of written language. New York: Wiley.

    Google Scholar 

  • Boykin, A. W. (1986). The triple quandary and the schooling of Afro-American children. In U. Neisser (Ed.), The school achievement of minority children: new perspectives (pp. 57–91). Hillsdale: Erlbaum.

    Google Scholar 

  • Boykin, A. W., & Ellison, C. M. (1995). The multiple ecologies of Black youth socialization: an Afrographic analysis. In R. T. Taylor (Ed.), African-American youth: their social and economic status in the United States (pp. 93–128). Westport: Praeger.

    Google Scholar 

  • Boykin, A. W., Tyler, K. M., & Miller, O. (2005). In search of cultural themes and their expressions in the dynamics of classroom life. Urban Education, 40(5), 521–549.

    Article  Google Scholar 

  • Bu, L., Spector, J. M., & Haciomeroglu, E. S. (2011). Toward model-centered mathematics learning and instruction using GeoGebra: a theoretical framework for learning mathematics with understanding. In L. Bu & R. Schoen (Eds.), Model-centered learning: pathways to mathematical understanding using GeoGebra (pp. 13–40). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Cole, M. (1996). Cultural psychology: a once and future discipline. Cambridge: Harvard University Press.

    Google Scholar 

  • Cole, M., & Engeström, Y. (1993). A cultural-historical approach to distributed cognition. In G. Salomon (Ed.), Distributed cognitions: psychological and educational considerations (pp. 1–46). New York: Cambridge University Press.

    Google Scholar 

  • Dance, L. J. (2002). Tough fronts: the impact of street culture on schooling. New York: Routledge.

    Google Scholar 

  • de Certeau, M. (1997). Culture in the plural. Minneapolis: University of Minnesota Press.

    Google Scholar 

  • Dienes, Z. P. (1964). The power of mathematics. London: Hutchinson.

    Google Scholar 

  • Flores, J. (1993). Divided borders: essays on Puerto Rican identity. Houston: Arte PĂşblico Press.

    Google Scholar 

  • González, 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), 115–132.

    Article  Google Scholar 

  • Hart, B., & Risley, T. R. (1995). Meaningful differences in the everyday experiences of young American children. Baltimore: Paul Brookes.

    Google Scholar 

  • Harvey, D. (1973/2009). Social justice and the city. Athens: The University of Georgia Press.

    Google Scholar 

  • Hegedus, S., & Kaput, J. (2003). The effect of SimCalc connected classrooms on students’ algebraic thinking. In N. A. Pateman, B. J. Dougherty, & J. Zillox (Eds.), Proceedings of the 27th conference of the international group for the psychology of mathematics education held jointly with the 25th conference of the North American chapter of the international group for the psychology of mathematics education (Vol. 3, pp. 47–54). Honolulu: College of Education, University of Hawaii.

    Google Scholar 

  • Hegedus, S., & Moreno-Armella, L. (2009). Intersecting representation and communication infrastructures. ZDM: The International Journal on Mathematics Education: Transforming Mathematics Education Through the Use of Dynamic Mathematics, 41(4), 399–412.

    Google Scholar 

  • Hegedus, S., Moreno, L., & Dalton, S. (2007). Technology that mediates and participation in mathematical cognition. In Proceedings of the fifth congress of the European society for research in mathematics education (CERME) conference, Larnaca, Cyprus.

    Google Scholar 

  • Hegedus, S., & Penuel, W. (2008). Studying new forms of participation and classroom identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics, 68(2), 171–184.

    Article  Google Scholar 

  • Kaput, J. J. (1998). Representations, inscriptions, descriptions, and learning: a kaleidoscope of windows. Journal of Mathematical Behaviour, 17(2), 256–281.

    Article  Google Scholar 

  • Kaput, J. J., & Hegedus, S. (2002). Exploiting classroom connectivity by aggregating student constructions to create new learning opportunities. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th annual conference of the international group for the psychology of mathematics education (Vol. 3, pp. 177–184). Norwich: University of East Anglia.

    Google Scholar 

  • Kaput, J., & Roschelle, J. (1996). Connecting the connectivity and the component revolutions to deep curriculum reform. Washington: Department of Education.

    Google Scholar 

  • Kaput, J., Roschelle, J., Tatar, D., & Hegedus, S. (2002). Enacted representations and performances in connected SimCalc classrooms. Paper presented at the American Educational Research Association meeting, New Orleans.

    Google Scholar 

  • Ladson-Billings, G. (1997). It doesn’t add up: African American students’ mathematics achievement. Journal for Research in Mathematics Education, 28(6), 697–708.

    Article  Google Scholar 

  • Lee, C. D. (2003). Toward a framework for culturally responsive design in multimedia computer environments: cultural modeling as a case. Mind, Culture, and Activity, 10(1), 42–61.

    Article  Google Scholar 

  • Lee, O., & Fradd, S. H. (1998). Science for all, including students from non-English-language backgrounds. Educational Researcher, 37(4), 12–21.

    Google Scholar 

  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Research design in mathematics and science education (pp. 591–646). Mahwah: Erlbaum.

    Google Scholar 

  • Moll, L. C., & Greenberg, J. B. (1990). Creating zones of possibilities: combining social contexts for instruction. In L. C. Moll (Ed.), Vygotsky and education: instructional implications of sociohistorical psychology (pp. 319–348). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Moreno-Armella, L., & Hegedus, S. (2009). Co-action with digital technologies. ZDM, 41(4), 505–519.

    Article  Google Scholar 

  • Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: historical and representational perspectives. Educational Studies in Mathematics, 68(2), 99–111.

    Article  Google Scholar 

  • Moss, B. J. (1994). Creating a community: literacy events in African American churches. In B. J. Moss (Ed.), Literacy across communities (pp. 147–178). Cresskill: Hampton Press.

    Google Scholar 

  • Noble, T., Nemirovsky, R., Wright, T., & Tierney, C. (2001). Experiencing change: the mathematics of change in multiple environments. Journal for Research in Mathematics Education, 32(2), 85–108.

    Article  Google Scholar 

  • Pogrow, S. (2004). The missing element in reducing the learning gap: eliminating the “blank stare”. Teachers College Record, 106(10), 11381. http://www.tcrecord.org.

    Google Scholar 

  • Schorr, R. Y., & Goldin, G. A. (2008). Students’ expression of affect in an inner-city SimCalc classroom. Educational Studies in Mathematics, 68(2), 131–148.

    Article  Google Scholar 

  • Smitherman, G. (1977). Talkin and testifyin: the language of Black America. Detroit: Wayne State University Press.

    Google Scholar 

  • Soja, E. W. (1996). Thirdspace: journeys to Los Angeles and other real-and-imagined places. Cambridge: Blackwell Publishers.

    Google Scholar 

  • Sollervall, H. (2011). Affordances and their mediating artifacts as instruments for the collaborative design of innovative mathematical learning activities. In Proceedings of the 8th Swedish mathematics education research seminar. http://www.mai.liu.se/SMDF/madif8/Sollervall.pdf.

  • Stroup, W. M., Ares, N., & Hurford, A. (2004). A taxonomy of generative activity design supported by next-generation classroom networks. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the 26th annual conference of psychology in mathematics education North America (pp. 837–846). Toronto, Canada: OISE/UT.

    Google Scholar 

  • Stroup, W., Ares, N., & Hurford, A. (2005). A dialectical analysis of generativity: issues of network supported design in mathematics and science. Mathematical Thinking and Learning, 7(3), 181–206.

    Article  Google Scholar 

  • Stroup, W. M., Kaput, J. J., Ares, N. M., Wilensky, U., Hegedus, S., Roschelle, J., et al. (2002). The nature and future of classroom connectivity: the dialectics of mathematics in the social space. In D. Mewborn et al. (Eds.), Proceedings of the 24th annual meeting of the North American chapter of the international group for the psychology of mathematics education (Vol. 1, pp. 195–243). Columbus: ERIC Clearinghouse for Science, Mathematics, & Environmental Education.

    Google Scholar 

  • Vahey, P., Roschelle, J., & Tatar, D. (2007). Using handhelds to link private cognition and public interaction. Educational Technology, 47(3), 13–16.

    Google Scholar 

  • Vygotsky, L. S. (1987). Thinking and speech. In R. W. Reiber & A. S. Carton (Eds.), The collected works of L. S. Vygotsky (Vol. 1, pp. 39–285). New York: Plenum.

    Google Scholar 

  • Wertsch, J. V. (1995). The need for action in sociocultural research. In J. V. Wertsch, P. d. Rio, & A. Alvarez (Eds.), Sociocultural studies of minds (pp. 56–74). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Wilensky, U., & Stroup, W. (1999). Learning through participatory simulations: network-based design for systems learning in classrooms. In Proceedings of the conference on computer-supported collaborative learning, CSCL’99. Stanford: Stanford University.

    Google Scholar 

  • Wittrock, M. C. (1974). A generative model of mathematics education. Journal for Research in Mathematics Education, 5(4), 181–196.

    Article  Google Scholar 

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Correspondence to Nancy Ares .

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Ares, N. (2013). Designing for Generative Activities: Expanding Spaces for Learning and Teaching. In: Hegedus, S., Roschelle, J. (eds) The SimCalc Vision and Contributions. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5696-0_6

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