Skip to main content

Advertisement

SpringerLink
Log in

The embodiment of cases as alternative perspective in a mathematics hypermedia learning environment

  • Development Article
  • Published:
Educational Technology Research and Development Aims and scope Submit manuscript

Abstract

This paper presents a design framework for cases as alternative perspectives (Jonassen in Learning to solve problems: a handbook for designing problem-solving learning environments, 2011a) in the context of K-12 mathematics. Using the design-based research strategy of conjecture mapping, the design of cases for a hypermedia site is described through embodiments of the learning environment (e.g., tools, materials, structures, practices), mediating processes these embodiments are conjectured to support, and outcomes relating to these processes. Considerations from cognitive flexibility theory and Realistic Mathematics Education are integrated into the framework as well as principles from hypermedia design. Cases are conceptualized beyond the traditional structure of cases as human experience and include phenomena pertinent to understanding complex concepts about space and perspective. In this way, cases are depicted as phenomena to be investigated with the goal of supporting learners’ construction of multiple and alternative perspectives. Data are provided to elucidate the design conjecture associated with learners investigating the variability of real-world geometric phenomena by visiting, revisiting, and juxtaposing cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Aamodt, A., & Plaza, E. (1994). Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications, 7(1), 39–59.

    Google Scholar 

  • Abbott, E. A. (1992). Flatland: A romance of many dimensions. New York, NY: Dover Publications Inc.

    Google Scholar 

  • Brown, D. E., & Hammer, D. (2008). Conceptual change in physics. In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 127–154). New York, NY: Routledge.

    Google Scholar 

  • Caplan, S., Wallace, W. (Producers), Travis, J., & Johnson, D. (Directors) (2007). Flatland: The movie [DVD]. Washington, DC: Flat World Productions.

  • Carroll, W. M. (1998). Geometric knowledge of middle school students in a reform-based mathematics curriculum. School Science and Mathematics, 98(4), 188–197.

    Article  Google Scholar 

  • Cilliers, P. (1998). Complexity and postmodernism: Understanding complex systems. New York, NY: Routledge.

    Google Scholar 

  • Clark, R. C., Nguyen, F., & Sweller, J. (2006). Efficiency in learning: Evidence-based guidelines to manage cognitive load. San Francisco, CA: Wiley.

    Google Scholar 

  • Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 151–178). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3–4), 175–190.

    Article  Google Scholar 

  • Cobb, P., Zhao, Q., & Visnovska, J. (2008). Learning from and adapting the theory of realistic mathematics education. Éducation & Didactique, 2(1), 105–124.

    Article  Google Scholar 

  • Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167. doi:10.2307/30034903.

    Article  Google Scholar 

  • Davis, B., & Sumara, D. (2006). Complexity and education: Inquiries into learning, teaching, and research. Mahwah: Lawrence Erlbaum Associates, Inc.

    Google Scholar 

  • Dick, W., Carey, L., & Carey, J. O. (2009). The systematic design of instruction (7th ed.). Glenview, IL: Scott, Foresman and Company.

    Google Scholar 

  • Driscoll, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Edwards, L. D. (1991). Children’s learning in a computer microworld for transformation geometry. Journal for Research in Mathematics Education, 22(2), 122–137.

    Article  Google Scholar 

  • Figueiredo, N., van Galen, F., & Gravemeijer, K. (2009). The actor’s and observer’s point of view: A geometry applet as an example. Educational Designer, 1(3), 1–20.

    Google Scholar 

  • Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: D. Reidel.

    Google Scholar 

  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: D. Reidel.

    Google Scholar 

  • Goeze, A., Zottmann, J. M., Vogel, F., Fischer, F., & Schrader, J. (2014). Getting immersed in teacher and student perspectives? Facilitating analytical competence using video cases in teacher education. Instructional Science, 42(1), 91–114.

    Article  Google Scholar 

  • Goldenberg, E. P., Cuoco, A. A., & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 3–44). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Goldstone, R. L. (2006). The complex systems see-change in education. Journal of the Learning Sciences, 15(1), 35–43.

    Article  Google Scholar 

  • Grant, D. A., & Berg, E. (1948). A behavioral analysis of degree of reinforcement and ease of shifting to new responses in a Weigl-type card-sorting problem. Journal of Experimental Psychology, 38(4), 404.

    Article  Google Scholar 

  • Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17–51). New York, NY: Routledge.

    Google Scholar 

  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. doi:10.2307/749690.

    Article  Google Scholar 

  • Herrington, J., Reeves, T. C., & Oliver, R. (2014). Authentic learning environments. New York, NY: Springer. http://link.springer.com/chapter/10.1007/978-1-4614-3185-5_32.

  • Ionescu, T. (2012). Exploring the nature of cognitive flexibility. New Ideas in Psychology, 30, 190–200.

    Article  Google Scholar 

  • Jacobson, M. J. (2008). A design framework for educational hypermedia systems: Theory, research, and learning emerging scientific conceptual perspectives. Educational Technology Research and Development, 56(1), 5–28.

    Article  Google Scholar 

  • Jacobson, M. J., & Archodidou, A. (2000). The design of hypermedia tools for learning: Fostering conceptual change and transfer of complex scientific knowledge. The Journal of the Learning Sciences, 9(2), 145–199.

    Article  Google Scholar 

  • Jacobson, M. J., & Azevedo, R. (2008). Advances in scaffolding learning with hypertext and hypermedia: Theoretical, empirical, and design issues. Educational Technology Research and Development, 56(1), 1–3.

    Article  Google Scholar 

  • Jacobson, M. J., & Kapur, M. (2012). Learning environments as emergent phenomena: Theoretical and methodological implications of complexity. In D. Jonassen & S. Land (Eds.), Theoretical foundations of learning environments (2nd ed., pp. 303–334). New York, NY: Routledge.

    Google Scholar 

  • Jacobson, M. J., & Spiro, R. J. (1993). Hypertext learning environments, cognitive flexibility, and the transfer of complex knowledge: An empirical investigation. (No. 573) (pp. 301–333). Champaign, IL: University of Illinois, Center for the Study of Reading. http://www.eric.ed.gov/ERICWebPortal/detail?accno=ED355508.

  • Jacobson, M. J., & Spiro, R. J. (1995). Hypertext learning environments, cognitive flexibility, and the transfer of complex knowledge: An empirical investigation. Journal of Educational Computing Research, 12(4), 301–333.

    Article  Google Scholar 

  • Jacobson, M. J., & Wilensky, U. (2006). Complex systems in education: Scientific and educational importance and implications for the learning sciences. Journal of the Learning Sciences, 15(1), 11–34.

    Article  Google Scholar 

  • Jonassen, D. H. (2011a). Learning to solve problems: A handbook for designing problem-solving learning environments. New York: Routledge.

    Google Scholar 

  • Jonassen, D. H. (2011b). Supporting problem solving in PBL. Interdisciplinary Journal of Problem-Based Learning, 5(2), 95–112.

    Article  Google Scholar 

  • Jörg, T., Davis, B., & Nickmans, G. (2007). Towards a new, complexity science of learning and education. Educational Research Review, 2(2), 145–156.

    Article  Google Scholar 

  • Keiser, J. M., Klee, A., & Fitch, K. (2003). An assessment of students’ understanding of angle. Mathematics Teaching in the Middle School, 9(2), 116–119.

    Google Scholar 

  • Kisa, M. T., & Stein, M. K. (2015). Learning to see teaching in new ways: A foundation for maintaining cognitive demand. American Educational Research Journal, 52(1), 105–136.

    Article  Google Scholar 

  • Kolodner, J. L. (2006). Case-based reasoning. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 225–242). New York, NY: Cambridge University Press.

    Google Scholar 

  • Li, T., & Jonassen, D. H. (1996). The effect of lesson structures on prediction and inference. In Proceedings of Selected Research and Development Presentations at the 1996 National Convention of the Association for Educational Communications and Technology (Vol. 18, pp. 423–429). ERIC. http://files.eric.ed.gov/fulltext/ED397772.pdf#page=432.

  • Lima, M., Koehler, M. J., & Spiro, R. J. (2004). Collaborative interactivity and integrated thinking in Brazilian business schools using cognitive flexibility hypertexts: The panteon project. Journal of Educational Computing Research, 31(4), 371–406.

    Article  Google Scholar 

  • Lima, M., Koehler, M. J., & Spiro, R. (2010). Cognitive flexibility hypertexts and the development of creative and critical thinking in business education: The Panteon Project. FACEF Pesquisa, 7(3). http://legacy.unifacef.com.br/revistas/index.php/facefpesquisa/article/view/39.

  • Morrison, G. R., Ross, S. M., Kalman, H. K., & Kemp, J. E. (2011). Designing effective instruction (6th ed.). Hoboken, NJ: Wiley.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, D.C.

  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.

    Google Scholar 

  • Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2–3), 165–190.

    Article  Google Scholar 

  • Reitan, R. M. (1992). Trail making test: Manual for administration and scoring. Tucson: Reitan Neuropsychology Laboratory.

    Google Scholar 

  • Sandoval, W. (2014). Conjecture mapping: An approach to systematic educational design research. Journal of the Learning Sciences, 23(1), 18–36. doi:10.1080/10508406.2013.778204.

    Article  Google Scholar 

  • Sawyer, R. K. (2014). Introduction: The new science of learning. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (2nd ed., pp. 1–18). New York, NY: Cambridge University Press.

    Chapter  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning the think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–371). New York, NY: Macmillan.

    Google Scholar 

  • Schoenfeld, A. H. (Ed.). (1994). Reflections on doing and teaching mathematics. In Mathematical thinking and problem solving (pp. 53–70). Hillsdale, NJ: Erlbaum.

  • Shapiro, A. M. (2008). Hypermedia design as learner scaffolding. Educational Technology Research and Development, 56(1), 29–44.

    Article  Google Scholar 

  • Spiro, R. J., Collins, B. P., & Ramchandran, A. (2007a). Modes of openness and flexibility in “cognitive flexibility hypertext” learning environments. In B. Khan (Ed.), Flexible learning in an information society (pp. 18–25). Hershey, PA: Information Science Publishing.

    Chapter  Google Scholar 

  • Spiro, R. J., Collins, B. P., & Ramchandran, A. (2007b). Reflections on a post-Gutenberg epistemology for video use in ill-structured domains: Fostering complex learning and cognitive flexibility. Retrieved October 21, 2012, from http://postgutenberg.typepad.com/newgutenbergrevolution/2008/06/new-paper-on-cf.html.

  • Spiro, R. J., Collins, B. P., Thota, J. J., & Feltovich, P. J. (2003). Cognitive flexibility theory: Hypermedia for complex learning, adaptive knowledge application, and experience acceleration. Educational Technology, 43(5), 5–10.

    Google Scholar 

  • Spiro, R. J., Coulson, R. L., Feltovich, P. J., & Anderson, D. K. (1988). Cognitive flexibility theory: Advanced knowledge acquisition in ill-structured domains (Technical Report No. 441). Champaign, IL: University of Illinois, Center for the Study of Reading.

  • Spiro, R. J., Feltovich, P. J., Jacobson, M. J., & Coulson, R. L. (1992). Cognitive flexibility, constructivism, and hypertext: Random access instruction for advanced knowledge acquisition in ill-structured domains. In Constructivism and the technology of instruction: A conversation (pp. 57–75). Hillsdale, NJ: Lawrence Erlbaum.

  • Spiro, R. J., Vispoel, W., Schmitz, J., Samarapungavan, A., & Boerger, A. (1987). Knowledge acquisition for application: Cognitive flexibility and transfer in complex content domains (Technical Report No. 409). Champaign, IL: University of Illinois, Center for the Study of Reading.

  • Strobel, J., Jonassen, D. H., & Ionas, I. G. (2008). The evolution of a collaborative authoring system for non-linear hypertext: A design-based research study. Computers & Education, 51(1), 67–85.

    Article  Google Scholar 

  • Swan, K. (1994). History, hypermedia, and criss-crossed landscapes. Journal of Educational Multimedia and Hypermedia, 3(2), 120–139.

    Google Scholar 

  • Wells, A. T., & McCrory, R. (2011). Hypermedia and learning: Contrasting interfaces to hypermedia systems. Computers in Human Behavior, 27(1), 195–202.

    Article  Google Scholar 

  • Zottmann, J. M., Goeze, A., Frank, C., Zentner, U., Fischer, F., & Schrader, J. (2012). Fostering the analytical competency of pre-service teachers in a computer-supported case-based learning environment: A matter of perspective? Interactive Learning Environments, 20(6), 513–532.

    Article  Google Scholar 

  • Zydney, J., & Grincewicz, A. (2011). The use of video cases in a multimedia learning environment for facilitating high school students’ inquiry into a problem from varying perspectives. Journal of Science Education and Technology, 20(6), 715–728.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. West Virginia University, 604-J Allen Hall, PO Box 6122, Morgantown, WV, 26506, USA

    Keri D. Valentine

  2. The University of Georgia, 222 River’s Crossing, 850 College Station Road, Athens, GA, 30602, USA

    Theodore J. Kopcha

Authors
  1. Keri D. Valentine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Theodore J. Kopcha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Keri D. Valentine.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Valentine, K.D., Kopcha, T.J. The embodiment of cases as alternative perspective in a mathematics hypermedia learning environment. Education Tech Research Dev 64, 1183–1206 (2016). https://doi.org/10.1007/s11423-016-9443-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11423-016-9443-8

Keywords

Search

Navigation