id: 06330141
dt: j
an: 2014e.00278
au: Fan, Lianghuo; Bokhove, Christian
ti: Rethinking the role of algorithms in school mathematics: a conceptual model
with focus on cognitive development.
so: ZDM, Int. J. Math. Educ. 46, No. 3, 481-492 (2014).
py: 2014
pu: Springer, Berlin/Heidelberg
la: EN
cc: D30 D20 C30
ut: mathematics learning; learning of algorithms; teaching of algorithms;
procedures; understanding; mathematical cognition; cognitive model of
learning
ci:
li: doi:10.1007/s11858-014-0590-2
ab: Summary: Starting from the context of mathematics learning in the East and
West, this paper discusses the position and role of algorithms within
school mathematics and argues that learning of algorithms has suffered
from an alleged dichotomy between procedures and understanding, in that
algorithms have been associated with low-level cognition. The paper
first introduces a broad perspective about algorithms in school
mathematics, and then, partially drawing on Bloom’s taxonomy and
Säljö’s categorization of learning, proposes a model for the
learning of algorithms with focus on students’ cognitive development.
The model consists of three cognitive levels: (1) knowledge and skills,
(2) understanding and comprehension, and (3) evaluation and
construction. The model suggests that the learning of algorithms does
not simply imply a low level of cognition, and provides a new
perspective and framework to analyse the learning of algorithms.
Following the model, we present examples to demonstrate the three
levels and discuss related teaching strategies. We propose that the
model can be used as an analysis tool to reconceptualize the role of
algorithms in school mathematics and pose some questions for further
research and scholarly discourse in this direction.
rv: