Learning axes and bridging tools in a technology-based design for statistics

We introduce a design-based research framework, learning axes and bridging tools, and demonstrate its application in the preparation and study of an implementation of a middle-school experimental computer-based unit on probability and statistics, ProbLab (Probability Laboratory, Abrahamson and Wilensky 2002 [Abrahamson, D., & Wilensky, U. (2002). ProbLab. Northwestern University, Evanston, IL: The Center for Connected Learning and Computer-Based Modeling, Northwestern University. http://www.ccl.northwestern.edu/curriculum/ProbLab/]). ProbLab is a mixed-media unit, which utilizes traditional tools as well as the NetLogo agent-based modeling-and-simulation environment (Wilensky 1999) [Wilensky, U. (1999). NetLogo. Northwestern University, Evanston, IL: The Center for Connected Learning and Computer-Based Modeling. http://www.ccl.northwestern.edu/netlogo/] and HubNet, its technological extension for facilitating participatory simulation activities in networked classrooms (Wilensky and Stroup 1999a) [Wilensky, U., & Stroup, W. (1999a). HubNet. Evanston, IL: The Center for Connected Learning and Computer-Based Modeling, Northwestern University]. We will focus on the statistics module of the unit, Statistics As Multi-Participant Learning-Environment Resource (S.A.M.P.L.E.R.). The framework shapes the design rationale toward creating and developing learning tools, activities, and facilitation guidelines. The framework then constitutes a data-analysis lens on The research reported on this paper was funded by NSF ROLE Grant No. REC-0126227. The opinions expressed here are those of the authors and do not necessarily reflect those of NSF. This paper is based on the authors’ AERA 2004 paper titled S.A.M.P.L.E.R.: Statistics As Multi-Participant Learning-Environment Resource. D. Abrahamson (&) Graduate School of Education, University of California, 4649 Tolman Hall, Berkeley, CA 94720-1670, USA e-mail: [email protected] U. Wilensky The Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL, USA e-mail: [email protected] 123 Int J Comput Math Learning (2007) 12:23–55 DOI 10.1007/s10758-007-9110-6 Learning axes and bridging tools in a technology-based design for statistics Dor Abrahamson Æ Uri Wilensky Published online: 21 March 2007 Springer Science+Business Media B.V. 2007 implementation cases of student insight into the mathematical content. Working with this methodology, a designer begins by focusing on mathematical representations associated with a target concept—the designer problematizes and deconstructs each representation into a pair of historical/cognitive antecedents (idea elements), each lying at the poles of a learning axis. Next, the designer creates bridging tools, ambiguous artifacts bearing interaction properties of each of the idea elements, and develops activities with these learning tools that evoke cognitive conflict along the axis. Students reconcile the conflict by means of articulating strategies that embrace both idea elements, thus integrating them into the target concept. ‘‘Such problems [—especially problems like that of composing a poem, inventing a machine, or making a scientific discovery—] are intimations of the potential coherence of hitherto unrelated things, and their solution establishes a new comprehensive entity, be it a new power, a new kind of machine, or a new knowledge of nature’’ (Polanyi 1967, p. 44). ‘‘Not that I mean as sufficing for invention the bringing together of objects as disparate as possible; most combinations so formed would be entirely sterile. But certain among them, very rare, are the most fruitful of all’’ (Poincaré 1897/2003, p. 51).