(Page 5 of 7) - Drawing on Diverse Social and Cultural Resources in Technology-Mediated Classrooms authored by Ares, Nancy. and Stroup, Walter.

Jose: Parallel.
Lydia: They’ll be parallel [uses arms to demonstrate parallel lines].
[once the simulation was run]
Sylvia: What, what’s happening right here? [points to position graph]
Brian: Jaime.
Sylvia: What else is happening?
Jaime: No no. Everyone goes crazy again?
Sylvia: That’s true. Everyone does kind of go crazy again, or do their own thing. What’s
happening right here? [points to an intersection of two lines on the position graph].
S: Someone went up and then stopped.
Sylvia: But I mean this very point, right there.
Jaime: They’re crossing?
Sylvia: What does it mean?
Jaime and Lydia: They’re on the same floor.
Jaime: For that second.

The ways of knowing that were relevant here and across the whole activity involved shared
construction of understanding, where student’s individual elevator’s motions served as examples
for exploration and construction of, for example, an informal metric for speed, and the graphical
representations were examined for “how we did” in coordinating activity, lending a collective
sensibility to this Discourse. The shared construction and collective sense invited more
participation by students, evidenced by the finding that 57% of codes were attributed to Sylvia.
Activity building

In the IMP class, textbook-centered, step-by-step work through procedures for solving the

profit problem was the main activity, while movement between individual creation and collective
exploration of emergent mathematical objects was the main activity of the Participatory
Simulation. The sub-activities that composed the IMP main activity included responding to
known-answer questions with fill-in-the-blank answers, reporting results, and talking through the
steps of procedures (e.g., converting fractions to decimals), balanced somewhat by explanations
of procedures or why the formula “made sense” (see Table 1). The sub-activities that supported
the Participatory Simulation main activity involved interpreting graphical representations, i.e.,
predicting and visualizing position and velocity graphs based on the arrangements of elevator
floors, and observing/describing real-time development of graphs and elevators’ motion (see
Table 1). Important opportunities to draw on social and cultural resources of students were also
in evidence, as Sylvia issued open-ended invitations: “you can do whatever you want on either
side of this (required arrangement),” and, “do something interesting.” Thus, students were
invited to contribute social and academic resources (explorations, understandings) in creative,
even playful ways to the group’s efforts.
Resources

Discourses were made relevant through the use of tools or cultural artifacts, especially the

textbook in the IMP class and the networked system activities and technology in the Elevators
class. In addition, both activities drew on English and Spanish language, text (book for IMP,
worksheet for Elevators), peers and Sylvia, calculators, and mathematical symbols (profit
formula, graphs). However, the real-time public display in which students could identify their
own and others’ contributions, physical and electronic gestures (e.g., using arms to indicate
parallel lines, individual elevator motion), and multiple representations of relationships were
additional, unique resources available in the Participatory Simulation. Through the use of
gesture, multiple representations, and public display, diverse ways of knowing were involved in