Learning Across Sites: New tools, infrastructures and practices - Earli

For EARLI members only.
Not for onward distribution.
372 O. Lindwall and J. Ivarsson
relation to the task of making a graph similar to the predefined one. Thus, the
students’ inquiries are oriented towards the tool’s responses – to what it is doing
in relation to what they are doing.
In contrast to other situations, where the students’ concerns with the technology
became the topic of the activity for quite some time, the students in this
episode soon resolve this issue. While Emily’s initial reaction to the graph expressed
surprise or frustration, her subsequent utterance – with a clearly marked change
in her voice – relates the graph to her actions “it is ‘cause you stand still here.”
This utterance is interesting not only because it identifies the dilemma they had
confronted, and implicitly resolves it, but also because Emily refers to the action
of “standing still” while simultaneously indexing a place in the graph, “here.”
Nemirovsky et al. use the notion of fusion to characterize episodes where students
are “talking, gesturing, and envisioning in ways that do not distinguish between
symbols and referents” (1998, p. 141). As they point out, fusion is both “ordinary
and pervasive” (ibid., p. 144). It is not relevant that fusion takes place. What
matters is how fusion takes place. In this episode, the students do not relate to the
graph by referring to visual or mathematical characteristics, but in terms of what
they did when producing the graph. A particular place in the graph is linked to
a certain movement and, consequently, the graph very concretely indexes places
and movements in the room. After noting that they “stand still” at a certain point,
Emily clarifies her observation by saying the graph “goes down” because of that.
Excitedly, Felicia responds to Emily’s utterances by proposing that they should not
stand still, and that “it is the velocity that should be constant.” Thus, by referring
to the movements and to how these movements result in certain visual properties
of the graphical representation, the two students establish a distinction between
position vs. time and velocity vs. time graphs.
In the words of Marton, learning to perceive something in disciplinary relevant
ways “amounts to learning to find the differences that are most critical in relation
to our goal” (2006, p. 521). In the episode illustrated here, the difference between
velocity vs. time graphs and position vs. time graphs is made salient through the
practical task of reproducing graphs by moving back and forth. The critical part of
the task, then, is to understand to what movements the graph corresponds. Since
the students initially make interpretations of the velocity vs. time graph in a way
that correspond to a position vs. time graph, arriving at an understanding of the
differences between the two types of graphs becomes critical. The students’ prior
understanding of the graph – as a position vs. time graph – becomes a background
for subsequent utterances such as “it is the velocity that should be constant.”
By looking at what the students have said and done prior to this episode, one
can note that this is the first time they talk about constant velocity. When using
undifferentiated concepts of speed and motion – which do not handle change in
speed or change in direction – the students initially had problems in interpreting
the increasingly complex graphs: central differences that made a difference were
not brought up in the students’ interaction. Gradually, however, the concepts were
replaced with ones that were more distinctive, and distinctions between constant