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

被引：25

作者：

Abrahamson D. ^{[1
]}

Wilensky U. ^{[2
]}

机构：

[1] Graduate School of Education, University of California, 4649 Tolman Hall, Berkeley

[2] Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL

来源：

International Journal of Computers for Mathematical Learning | 2007年 / 12卷 / 1期

基金：

美国国家科学基金会;

关键词：

Mathematical Concept; Idea Element; Target Concept; Design Framework; Mathematical Understanding;

D O I：

10.1007/s10758-007-9110-6

中图分类号：

学科分类号：

摘要：

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. © Springer Science+Business Media, Inc. 2007.

引用

页码：23 / 55

页数：32

共 73 条

[1]

Abrahamson D., Keeping meaning in proportion: The multiplication table as a case of pedagogical bridging tools, (2004)

[2]

Abrahamson D., The shape of things to come: The computational pictograph as a bridge from combinatorial space to outcome distribution, International Journal of Computers for Mathematical Learning, 11, 1, pp. 137-146, (2006)

[3]

Abrahamson D., Mathematical representations as conceptual composites: Implications for design, Proceedings of the Twenty Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, pp. 464-466, (2006)

[4]

Abrahamson D., Berland M.W., Shapiro R.B., Unterman J.W., Wilensky U.J., Leveraging epistemological diversity through computer-based argumentation in the domain of probability, For the Learning of Mathematics, 26, 3, pp. 39-45, (2006)

[5]

Abrahamson D., Cendak R.M., The odds of understanding the Law of Large Numbers: A design for grounding intuitive probability in combinatorial analysis, Proceedings of the Thirtieth Conference of the International Group for the Psychology of Mathematics Education, PME, 2, pp. 1-8, (2006)

[6]

Abrahamson D., Wilensky U., NetLogo 9-Blocks model, (2004)

[7]

Artigue M., Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work, International Journal of Computers for Mathematical Learning, 7, 3, pp. 245-274, (2002)

[8]

Bamberger J., Ziporyn E., Getting it wrong, The World of Music: Ethnomusicology and Music Cognition, 34, 3, pp. 22-56, (1991)

[9]

Bereiter C., Scardamalia M., Cognitive coping strategies and the problem of "inert knowledge, Thinking and learning skills: Current research and open questions, 2, pp. 65-80, (1985)

[10]

Berland M., Wilensky U., Virtual robotics in a collaborative constructionist learning environment, annual meeting of the American Educational Research Association, (2004)

← 1 2 3 4 5 6 7 8 →