id: 06169774
dt: a
an: 2013c.00897
au: Tall, David
ti: The evolution of technology and the mathematics of change and variation:
using human perceptions and emotions to make sense of powerful ideas.
so: Hegedus, Stephen J. (ed.) et al., The SimCalc vision and contributions.
Democratizing access to important mathematics. Dordrecht: Springer
(ISBN 978-94-007-5695-3/hbk; 978-94-007-5696-0/ebook). Advances in
Mathematics Education, 449-461 (2013).
py: 2013
pu: Dordrecht: Springer
la: EN
cc: U50 D20
ut: technology in mathematics education; computer aided instruction;
perceptions; emotions; change in the nature of technology
ci: ME 2013c.00051
li: doi:10.1007/978-94-007-5696-0_25
ab: Summary: This chapter reflects on the evolution of the mathematics of
change and variation as technology affords the possibility of
conceptualizing and communicating ideas for a wider range of learners
than the few who traditionally study the higher levels of calculus. It
considers the overall program of development conceived by Jim Kaput,
instantiated in the SimCalc software as part of a full range of
development using technology for “expressing, communicating,
reasoning, computing, abstracting, generalizing, and formalizing"
mathematical ideas [{\it J. J. Kaput} and {\it J. Roschelle}, ibid.,
13‒26 (2013; ME 2013c.00051)]. The development begins with
interactive representations of dynamic real-world situations and
extends the perceptual ideas of continuity and linearity through the
operational symbolism of calculus and on to the formalizing power of
mathematical analysis. It reveals that the Kaput program has the
distinction that its overall framework contains the essence for
continuing the complementary evolution of technology and the
conceptions of mathematical change and variation. Furthermore, it
envisages changes that we have, as yet, not implemented, such is the
speed of technological change. In particular, new technology enables us
not only to build more powerful ways of performing numerical and
symbolic algorithms that may be represented visually and dynamically,
it also provides new forms of input and gesture to offer an embodied,
kinesthetic, and emotionally powerful experience of engaging with
mathematics. This can be shared widely through fundamental human
perception and action, and can develop in the longer term through
symbolism and human reason to the mathematical literacy required of
today’s citizens, the theoretical applications of mathematics
essential for today’s society, and on to the boundaries of
mathematical research that takes us into the future.
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