id: 06083897
dt: a
an: 2012e.00492
au: Tall, David; Yevdokimov, Oleksiy; Koichu, Boris; Whiteley, Walter;
Kondratieva, Margo; Cheng, Ying-Hao
ti: Cognitive development of proof.
so: Hanna, Gila (ed.) et al., Proof and proving in mathematics education. The
19th ICMI study. Berlin: Springer (ISBN 978-94-007-2128-9/hbk;
978-94-007-2129-6/ebook). New ICMI Study Series 15, 13-49 (2012).
py: 2012
pu: Berlin: Springer
la: EN
cc: E50 C30 D30
ut: mathematical proof; cognitive development; perception and action; geometric
proof; operational proof; formal set-theoretic definition; formal
deduction
ci:
li: doi:10.1007/978-94-007-2129-6_2
ab: Summary: This article traces the long-term cognitive development of
mathematical proof from the young child to the frontiers of research.
It uses a framework building from perception and action, through proof
by embodied actions and classifications, geometric proof and
operational proof in arithmetic and algebra, to the formal
set-theoretic definition and formal deduction. In each context, proof
develops over the long-term from the recognition and description of
observed properties and the links between them, the selection of
specific properties that can be used as definitions from which other
properties may be deduced, to the construction of â€˜crystalline
conceptsâ€™ whose properties are a consequence of the context. These
include Platonic objects in geometry, symbols having relationships in
arithmetic and algebra and formal axiomatic systems whose properties
are determined by their definitions.
rv: