id: 06639325
dt: j
an: 2016f.00667
au: Santos-Trigo, Manuel; Moreno-Armella, Luis; Camacho-Machín, Matías
ti: Problem solving and the use of digital technologies within the mathematical
working space framework.
so: ZDM, Math. Educ. 48, No. 6, 827-842 (2016).
py: 2016
pu: Springer, Berlin/Heidelberg
la: EN
cc: D50 U70 C70 D40
ut: problem solving; empirical and formal reasoning; mathematical working
space; digital technologies
ci:
li: doi:10.1007/s11858-016-0757-0
ab: Summary: The aim of this study is to analyze and document the extent to
which high school teachers rely on a set of technology affordances to
articulate epistemological and cognitive actions in problem solving
approaches. Participants were encouraged to construct dynamic
representations of tasks and always to look for different ways to
identify and support mathematical relations. To this end, three
interrelated geneses (instrumental, semiotic, discursive) proposed in
the Mathematical Working Space frame are used to document ways in which
the participants constructed dynamic configuration of mathematical
tasks as a means initially to explore invariants and eventually
formulate conjectures based on empirical arguments. Technology
affordances that involve dragging objects, quantifying parameters,
graphing loci and using sliders were important for the participants to
articulate semiotic and discursive geneses. Thus, the participants’
approaches that appeared individual, small group and plenary
discussions contributed to identifying initial conjectures that later
were analyzed via empirical, geometric or algebraic arguments. In
addition, the participants recognized that a working space to
understand mathematical ideas and to solve problems should foster
mathematical discussions beyond formal settings. The use of digital
technologies plays an important role in both representing and exploring
mathematical tasks and in following the discussion outside the formal
class. As a result, the participants outlined a possible route to
implement a route for learners to integrate activities to account for
instrumental, semiotic, and discursive genesis.
rv: