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Dissertation
How online small groups co-construct mathematical artifacts to do collaborative problem solving
Doctor of Philosophy (Ph.D.), Drexel University
May 2009
DOI:
https://doi.org/10.17918/etd-3115
Abstract
Developing pedagogies and instructional tools to support learning math with understanding is a major goal in math education. A common theme among various characterizations of mathematical understanding involves constructing relations among mathematical facts, procedures, and ideas encapsulated in graphical and symbolic artifacts. Discourse is key for enabling students to realize such connections among seemingly unrelated mathematical artifacts. Analysis of mathematical discourse on a moment-to-moment basis is needed to understand the potential of small-group collaboration and online communication tools to support learning math with understanding. This dissertation investigates interactional practices enacted by virtual teams of secondary students as they co-construct mathematical artifacts in an online environment with multiple interaction spaces including text-chat, whiteboard, and wiki components. The findings of the dissertation arrived at through ethnomethodologically-informed case studies of online sessions are organized along three dimensions: (a) Mathematical Affordances: Whiteboard and chat spaces allow teams to co-construct multiple realizations of relevant mathematical artifacts. Contributions remain persistentlyavailable for subsequent manipulation and reference in the shared visual field. The persistence of contributions facilitates the management of multiple threads of activities across dual media. The sequence of actions that lead to the construction and modification of shared inscriptions makes the visual reasoning process visible.(b) Coordination Methods: Team members achieve a sense of sequential organization across dual media through temporal coordination of their chat postings and drawings. Groups enact referential uses of available features to allocate their attention to specific objects in the shared visual field and to associate them with locally defined terminology. Drawings and text-messages are used together as semiotic resources in mutually elaborating ways.(c) Group Understanding: Teams develop shared mathematical understanding through joint recognition of connections among narrative, graphical and symbolic realizations of the mathematical artifacts that they have co-constructed to address their shared task. The interactional organization of the co-construction work establishes an indexical ground as support for the creation and maintenance of a shared problem space for the group. Each new contribution is made sense of in relation to this persistently available and shared indexical ground, which evolves sequentially as new contributions modify the sense of previous contributions.
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Details
- Title
- How online small groups co-construct mathematical artifacts to do collaborative problem solving
- Creators
- Murat Perit Cakır - DU
- Contributors
- Gerry Stahl (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Information Science and Technology (1995-2013); Drexel University
- Other Identifier
- 3115; 991014632261104721