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

Dor Abrahamson; Uri Wilensky

doi:10.1007/s10758-007-9110-6

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

Dor Abrahamson^*, Uri Wilensky

^*Corresponding author for this work

School of Education and Social Policy

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

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 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.

Original language	English (US)
Pages (from-to)	23-55
Number of pages	33
Journal	International Journal of Computers for Mathematical Learning
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s10758-007-9110-6
State	Published - Apr 2007

Funding

Acknowledgements We wish to express our gratitude to members of the design-research team at The Center for Connected Learning and Computer-Based Modeling, who supported us in facilitating classroom implementations and in collecting data: Sharona T. Levy, Matthew W. Berland, and Joshua W. Unterman. Thank you to Walter Stroup for his valuable comments on the design and classroom implementation of participatory simulation activities. Thank you Eric Betzold, our Research Program Coordinator, for coordinating the many implementation details of this project. Thank you also to Ms. Ruth Janusz, the 6th-grade science-and-mathematics teacher who hosted our implementation and helped with classroom management and in facilitating the design. Thanks to Mr. Paul Brinson, the district’s Chief Information Officer, for evaluating our project and approving the implementation. Thank you Ms. Barb Hiller, the district’s Assistant Superintendent for Curriculum and Instruction, for matching us with the school. Thanks to Mr. Gordon Hood, the school principal, for providing a research site and coordinating with teachers. Also, thank you to all the students who voluntarily participated in this study. Finally, we are grateful to the two anonymous IJCML reviewers who helped us improve and shape this draft. This work was supported by National Science Foundation grant REC 0126227. Completing this paper was facilitated by the first author’s National Academy of Education/Spencer Postdoctoral Fellowship 2005–2006. 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.

ASJC Scopus subject areas

Theoretical Computer Science
General Engineering
Computer Science Applications
Computational Theory and Mathematics

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10.1007/s10758-007-9110-6

Cite this

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title = "Learning axes and bridging tools in a technology-based design for statistics",

abstract = "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 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.",

author = "Dor Abrahamson and Uri Wilensky",

note = "Funding Information: Acknowledgements We wish to express our gratitude to members of the design-research team at The Center for Connected Learning and Computer-Based Modeling, who supported us in facilitating classroom implementations and in collecting data: Sharona T. Levy, Matthew W. Berland, and Joshua W. Unterman. Thank you to Walter Stroup for his valuable comments on the design and classroom implementation of participatory simulation activities. Thank you Eric Betzold, our Research Program Coordinator, for coordinating the many implementation details of this project. Thank you also to Ms. Ruth Janusz, the 6th-grade science-and-mathematics teacher who hosted our implementation and helped with classroom management and in facilitating the design. Thanks to Mr. Paul Brinson, the district{\textquoteright}s Chief Information Officer, for evaluating our project and approving the implementation. Thank you Ms. Barb Hiller, the district{\textquoteright}s Assistant Superintendent for Curriculum and Instruction, for matching us with the school. Thanks to Mr. Gordon Hood, the school principal, for providing a research site and coordinating with teachers. Also, thank you to all the students who voluntarily participated in this study. Finally, we are grateful to the two anonymous IJCML reviewers who helped us improve and shape this draft. This work was supported by National Science Foundation grant REC 0126227. Completing this paper was facilitated by the first author{\textquoteright}s National Academy of Education/Spencer Postdoctoral Fellowship 2005–2006. Funding Information: 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{\textquoteright} AERA 2004 paper titled S.A.M.P.L.E.R.: Statistics As Multi-Participant Learning-Environment Resource.",

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month = apr,

doi = "10.1007/s10758-007-9110-6",

language = "English (US)",

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

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