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

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For EARLI members only. Not for onward distribution. Differences that make a difference 371 In the sequence, the discrepancy is not only represented by the computer but also responded to by the students. While Felicia’s “oops” indicates that something went wrong, Emily, with laughter in her voice, exclaims, “what’s it doing.” Their previous encounters with probeware were limited to the production and interpretation of position vs. time graphs, and with this lack of familiarity with the technology, they were still not sure what they had to do in order to produce velocity vs. time graphs. By using a concept from Nemirovsky et al. (1998), the students gradually adopt a tool perspective by investigating what kind of actions make a difference in Figure 22.2 Two students interacting with the motion sensor and the interface
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
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Contents For EARLI members only. No
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Foreword For EARLI members only. No
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From episode 3.1 For EARLI members
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Sequence 5 (continued) For EARLI me
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Sequence 6 (continued) For EARLI me
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References For EARLI members only.
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Learning Across Sites: New tools, infrastructures and practices - Earli

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