From New Technological Infrastructures to Curricular Activity Systems: Advanced Designs for Teaching and Learning



We suggest an “advanced design” for teaching and learning should offer a plan for bridging the gap between new technological affordances and what most teachers need and can use. We draw attention to three different foci of design: (a) design of representational and communicative infrastructure (b) design of curricular activity systems, and (c) design of new classroom practices and routines. Two different SimCalc projects are presented to illustrate these design foci; both concern the use of technology to democratize access to conceptually demanding mathematics among adolescents. We particularly emphasize curricular activity systems because we are finding that attention to this focus of design has been critically important in our ability to measure learning outcomes at the scale of hundreds of teachers.


Mathematics Technology Activities Representation Curriculum design Networks Scaling up 



We thank Corinne Singleton for her work on an earlier draft of this chapter. This material is based in part upon work supported by the National Science Foundation under Grant Numbers 0437861 and 033710. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


  1. Abu-Hilal, M. (2000). A structural model for predicting mathematics achievement: Its relation with anxiety and self-concept in mathematics. Psychological Reports, 86, 835-847.CrossRefGoogle Scholar
  2. Ames, C. (1992). Classrooms, goals, structures, and student motivation. Journal of Educational Psychology, 84, 261-271.CrossRefGoogle Scholar
  3. Ball, D. L. & Cohen, D. K. (1996). Reform by the book: What is - or might be - the role of curriculum materials in teacher learning and instructional reform. Educational Researcher, 25(9), 6-8.Google Scholar
  4. Ball, D., Roskam, A., Morris, A., Hiebert, J., Suzuka, K., Lewis, J., et al. (2009). Improving mathematics teaching and teacher education through “specification”. Paper presented at the National Council of Teachers of Mathematics Research Precession, Washington DC, April, 21, 2009.Google Scholar
  5. Barab, S. & Squire, K. (2004). Design-based research: Putting a stake in the ground. The Journal of the Learning Sciences, 13(1), 1-14.CrossRefGoogle Scholar
  6. Barron, B. (2000). Achieving coordination in collaborative problem-solving groups. The Journal of the Learning Sciences, 9(4), 403-436.CrossRefGoogle Scholar
  7. Bell, P., Hoadley, C. M., & Linn, M. C. (2004). Design-based research in education. In M. C. Linn, E. A. Davis & P. Bell (Eds.), Internet environments for science education (pp. 73-85). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  8. Boaler, J. (2002). Experiencing school mathematics. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  9. Cazden, C. B. & Beck, S. W. (2003). Classroom discourse. In A. C. Graesser, M. A. Gernsbacher & S. R. Goldman (Eds.), Handbook of discourse processes (pp. 165-197). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  10. Cobb, P., Yackel, E., & McClain, K. (eds). (2002). Communicating and symbolizing in mathematics: Perspectives on discourse, tools, and instructional design. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  11. Cohen, D. K., & Ball, D. L. (1999). Instruction, capacity, and improvement (No. CPRE Research Report No. RR-043). Philadelphia, PA: University of Pennsylvania, Consortium for Policy Research in Education.Google Scholar
  12. Cohen, D. K., Raudenbush, S., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 1-24.CrossRefGoogle Scholar
  13. Davidson, A. (1999). Negotiating social differences: Youth’s assessments of educators’ strategies. Urban Education, 34, 338-369.CrossRefGoogle Scholar
  14. Davidson, A. & Phelan, P. (1999). Students’ multiple worlds: An anthropological approach to understanding students’ engagement with school. In T. C. Urdan (Ed.), Advances in motivation and achievement: Role of context (Vol. 2, pp. 233-283). Stamford, CT: JAI Press.Google Scholar
  15. Dede, C. (2004). If design-based research is the answer, what is the question? A commentary on Collins, Joseph, and Bielaczyc; diSessa and Cobb; and Fishman, Marx, Blumenthal, Krajcik, and Soloway in the JLS special issue on design-based research. The Journal of the Learning Sciences, 13(1), 105-114.CrossRefGoogle Scholar
  16. diSessa, A. A. & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The Journal of the Learning Sciences, 13(1), 77-103.CrossRefGoogle Scholar
  17. Edelson, D. C. (2002). What we learn when we engage in design. Journal of the Learning Sciences, 11(1), 105-121.CrossRefGoogle Scholar
  18. Fishman, B. (2006). It’s not about the technology [Electronic Version]. Teachers College Record. Retrieved July 6, 2006 from
  19. Geary, D.C., Berch, D.B., Boykin, A.W., Embretson, S., Reyna, V., Siegler, R., et al. (2008). Report of the task group on learning processes. Retrived July 17, 2008 from
  20. Goldenberg, P. (1995). Multiple representations: A vehicle for understanding understandings. In D. N. Perkins, J. L. Schwartz, M. M. West & M. S. Wiske (Eds.), Software goes to school (pp. 155-171). New York, NY: Oxford University Press.Google Scholar
  21. Halverson, R., Shaffer, D., Squire, K., & Steinkuehler, C. (2006). Theorizing games in/and education. Bloomington, IN: Paper presented at the seventh International Conference on Learning Sciences.Google Scholar
  22. Harter, S. (1992). The relationship between perceived competence, affect, and motivational orientation within the classroom: Process and patterns of change. In A. Boggiano & T. Pittman (Eds.), Achievement and motivation: A social-developmental perspective (pp. 77-114). New York: Cambridge University Press.Google Scholar
  23. Hegedus, S., Dalton, S., Moniz, R., & Roschelle, J. (2007). SimCalc classroom connectivity project 2: Understanding classroom interactions among diverse, connected classroom technologies (No. 1:1). North Dartmouth, MA: University of Massachusetts.Google Scholar
  24. Hegedus, S., & Kaput, J. J. (2002). Exploring the phenomenon of classroom connectivity. Paper presented at the 24th Conference for the North American Chapter of the International Group for the Psychology of Mathematics Education, Athens, GA.Google Scholar
  25. Hegedus, S. J. & Kaput, J. (2003). The effect of a SimCalc connected classroom on students’ algebraic thinking. Honolulu, HI: Paper presented at the Psychology in Mathematics Education conference.Google Scholar
  26. Hegedus, S. J. & Kaput, J. J. (2004). An introduction to the profound potential of connected algebra activities: Issues of representation, engagement and pedagogy. Bergen, Norway: Paper presented at the Eighth Conference of the International Group for the Psychology of Mathematics Education.Google Scholar
  27. Hegedus, S., Moreno, L., & Dalton, S. (2007). Technology that mediates and participation in mathematical cognition. Paper presented at the 5th Congress of the European Society for Research in Mathematics Education (CERME), Larnaca, Cyprus.Google Scholar
  28. Hegedus, S. J. & Penuel, W. R. (2008). Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics, 68(2), 171-183.CrossRefGoogle Scholar
  29. Hicks, D. (1995). Discourse, learning, and teaching. Review of Research in Education, 21(1), 49-95.CrossRefGoogle Scholar
  30. Hiebert, J. & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, NC: Information Age Pub Inc.Google Scholar
  31. Johnson, M. K., Crosnoe, R., & Elder, G., Jr. (2001). Students’ attachment and academic engagement: The role of race and ethnicity. Sociology of Education, 74, 318-340.CrossRefGoogle Scholar
  32. Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), A handbook of research on mathematics teaching and learning (pp. 515-556). New York: Macmillan.Google Scholar
  33. Kaput, J. (1994). Democratizing access to calculus: New routes using old roots. In A. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 77-155). Hillsdale, NJ: Erlbaum.Google Scholar
  34. Kaput, J., & Hegedus, S. J. (2002). Exploiting classroom connectivity by aggregating student constructions to create new learning opportunities. Paper presented at the 26th Conference of the International Group for the Psychology of Mathematics Education, Norwich, UK.Google Scholar
  35. Kaput, J. & Hegedus, S. (2007). Technology becoming infrastructural in mathematics education. In R. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the Future in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  36. Kaput, J., Noss, R., & Hoyles, C. (2002). Developing new notations for a learnable mathematics in the computational era. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 51-75). Mahway, NJ: Lawrence Erlbaum Associates.Google Scholar
  37. Kaput, J. & Roschelle, J. (1998). The mathematics of change and variation from a millennial perspective: New content, new context. In C. Hoyles, C. Morgan & G. Woodhouse (Eds.), Rethinking the mathematics curriculum. London, UK: Falmer Press.Google Scholar
  38. Kaput, J. & Schorr, R. (2008). Changing representational infrastructures changes most everything: The case of SimCalc, Algebra, and Calculus. In K. Heid & G. W. Blume (Eds.), Research on the impact of technology on the teaching and learning of mathematics: Volume 2, cases and perspectives (pp. 211-253). Charlotte, NC: Information Age Publishing.Google Scholar
  39. Kaput, J. J. & Thompson, P. W. (1994). Technology in mathematics education research: The first 25 years in the JRME. Journal for Research in Mathematics Education, 25(6), 676-684.CrossRefGoogle Scholar
  40. Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465.Google Scholar
  41. Meece, J. (1991). The classroom context and student’s motivational goals. In M. Maehr & P. Pintrich (Eds.), Advances in motivation and achievement (Vol. 7, pp. 261-285). Greenwich, CT: JAI Press.Google Scholar
  42. Mitchell, M. (1993). Situational interest: Its multifaceted structure in the secondary school mathematics classroom. Journal of Educational Psychology, 85, 424-436.CrossRefGoogle Scholar
  43. Newman, R. & Goldin, L. (1990). Children’s reluctance to seek help with school work. Journal of Educational Psychology, 82, 92-100.CrossRefGoogle Scholar
  44. Papert, S. (2004). Will going digital improve or transform education? [Electronic Version]. New futures for learning in the digital age. Retrieved July 30, 2008 from
  45. Phelan, P., Davidson, A., & Yu, H. (1998). Adolescents’ worlds: Negotiating family, peers, and school. New York: Teachers College Press.Google Scholar
  46. Piaget, J. (1970). The child’s conception of movement and speed. New York, NY: Basic Books.Google Scholar
  47. Roschelle, J. & Jackiw, N. (2000). Technology design as educational research: Interweaving imagination, inquiry & impact. In A. Kelly & R. Lesh (Eds.), Research design in mathematics & science education (pp. 777-797). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  48. Roschelle, J. & Kaput, J. (1996). SimCalc MathWorlds for the mathematics of change. Communications of the ACM, 39(8), 97-99.CrossRefGoogle Scholar
  49. Roschelle, J., Kaput, J., & Stroup, W. (2000). SimCalc: Accelerating student engagement with the mathematics of change. In M. J. Jacobsen & R. B. Kozma (Eds.), Learning the sciences of the 21st century: Research, design, and implementing advanced technology learning environments (pp. 47-75). Hillsdale, NJ: Erlbaum.Google Scholar
  50. Roschelle, J., Penuel, W. R., & Abrahamson, L. (2004). The networked classroom. Educational Leadership, 61(5), 4.Google Scholar
  51. Roschelle, J., Tatar, D., Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., et al. (2008). Extending the SimCalc approach to grade 8 mathematics (SimCalc Technical Report 02). Menlo Park, CA: SRI International.Google Scholar
  52. Roschelle, J., Tatar, D., Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., et al. (2007). Can a technology-enhanced curriculum improve student learning of important mathematics? (SimCalc Technical Report 01). Menlo Park, CA: SRI International.Google Scholar
  53. Roschelle, J., Tatar, D., Shechtman, N., & Knudsen, J. (2008). The role of scaling up research in designing for and evaluating robustness. Educational Studies in Mathematics, 68(2), 149-170.CrossRefGoogle Scholar
  54. Ryan, A. & Pintrich, P. (1997). “Should I ask for help?” The role of motivation and attitudes in adolescents’ help seeking in math class. Journal of Educational Psychology, 89, 329-341.CrossRefGoogle Scholar
  55. Skinner, E. & Belmont, M. (1993). Motivation in the classroom: Reciprocal effects of teacher behavior and student engagement across the school year. Journal of Educational Psychology, 85, 571-581.CrossRefGoogle Scholar
  56. Stroup, W. M., Ares, N. M., & Hurford, A. C. (2005). A Dialectic analysis of generativity: Issues of network-supported design in mathematics and science. Mathematical Thinking and Learning, 7(3), 181-206.CrossRefGoogle Scholar
  57. Stroup, W. M., Kaput, J., Ares, N., Wilensky, U., Hegedus, S. J., Roschelle, J., et al. (2002). The nature and future of classroom connectivity: The dialectics of mathematics in the social space. Paper presented at the Psychology and Mathematics Education North America conference, Athens, GA.Google Scholar
  58. Tatar, D., Roschelle, J., Knudsen, J., Shechtman, N., Kaput, J., & Hopkins, B. (2008). Scaling up innovative technology-based mathematics. Journal of the Learning Sciences, 17(2), 248-286.CrossRefGoogle Scholar
  59. Treisman, U. & Fullilove, R. (1990). Mathematics achievement among African-American undergraduates at the University of California, Berkeley: An evaluation of the mathematics workshop program. Journal of Negro Education, 59(3), 463-478.Google Scholar
  60. Turner, J., Thorpe, P., & Meyer, D. (1998). Students’ reports of motivation and negative affect: A theoretical and empirical analysis. Journal of Educational Psychology, 90, 758-771.CrossRefGoogle Scholar
  61. Vahey, P., Roschelle, J., & Tatar, D. (2007). Using handheld technology to move between private and public interactions in the classroom. In M. van ‘t Hooft & K. Swan (Eds.), Ubiquitous computing in education: Invisible technology, visible impact. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.SRI InternationalMenlo ParkUSA
  2. 2.University of MassachusettsFairhavenUSA

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