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research questions. The VMT Project was intended to explore the phenomena of
group cognition and accordingly pursued the research question:
How does learning take place in small groups, specifically in small groups of students dis-
cussing math in a text-based online environment? What are the distinctive mechanisms or
processes that take place at the small-group level of description when the group is engaged
in problem-solving or knowledge-building tasks?
While learning phenomena at the other levels of analysis are important and inter-
act strongly with the group level, we have tried to isolate and make visible the
small-group phenomena and to generate a corpus of data for which the analysis of
the group-level interactions can be distinguished from the effects of the individual
and community levels.
The methods used to gather and analyze one's data should be appropriate to one's
research question. To support such research, one must generate and collect data that
are adequate for the selected kinds of analysis. Because we were interested in the
group processes that take place in VMT, we had to form teams that could meet
together online. In the Spring Fests, students had to be able to come back together
in the same teams on several subsequent occasions. The VMT environment had
to be instrumented to record all messages and activities that were visible to the
whole team in a way that could be played back by the analysts. The math problems
and the feedback to the teams had to be designed to encourage the kinds of math
discussions that would demonstrate processes of group cognition, such as formulat-
ing questions and proposals, coordinating drawings and textual narratives, checking
proposed symbolic solutions, reviewing the team's work and so on. A sense of these
desirable group activities and the skill of designing problems to encourage them had
to develop gradually through the design-based research iterations.
Non-laboratory Experimental Design (Validity)
Of course, to isolate the small-group phenomena we do not literally isolate our sub-
ject groups from individuals and communities. The groups consist of students, who
are individuals and who make individual contributions to the group discourse based
on their individual readings of the discourse. In addition, the groups exist and oper-
ate within community and social contexts, drawing upon the language and practices
of their math courses and of their teen and online subcultures. These are essential
features of a real-world context and we would not wish to exclude them even to the
extent possible by confining the interaction to a controlled laboratory setting. We
want the students to feel that they are in a natural setting, interacting with peers. We
do not try to restrict their use of language in any way (e.g., by providing standardized
prompts for chat postings or scripting their interactions with each other).
We are designing a service that can be used by students and others under a broad
array of scenarios: integrated with school class work, as extra-curricular activities,
as social experiences for home-schooled students, as cross-national team adventures
or simply as opportunities (in a largely math-phobic world) to discuss mathematics.
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