Interaction of multiple tools as a kind of
system. For example, Laila interacts with the remote, including the buttons,
the layout of the buttons, the symbols on the buttons, her fingers, language of
counting, other language, her mother’s questions, the camera. Making meaning
with a tool – significance – transforms the tool into an artefact
(Vygostky/Yasmine). But in most mathematical situations, multiple tools are
used together (such as symbols, algorithms, methods, diagrams, language).
Rather than multiple artefacts emerging, they can be thought of as forming a
single artefact, or an artefact system, that assembles at a particular moment,
and continually changes, reassembles, disassembles, according to what is going
on. Meaning arises from the intertextual relations between the tools in the
artefact system. Artefactness arises from this intertextuality. I can fold a
piece of paper to help add fractions, but the task already involves the written
problem, in this case using fraction symbols, so intertextuality arises across
an artefact system comprised of the symbols, the folded paper, various
gestures, counting, etc. Conjecture: developing broader, more complex artefact
systems is a valuable aspect of mathematical thinking.
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