id: 06367056
dt: a
an: 2014f.00472
au: Dreyfus, Tommy; Kidron, Ivy
ti: From proof image to formal proof ‒ a transformation.
so: Rezat, Sebastian (ed.) et al., Transformation ‒ a fundamental idea of
mathematics education. New York, NY: Springer (ISBN
978-1-4614-3488-7/hbk; 978-1-4614-3489-4/ebook). 269-289 (2014).
py: 2014
pu: New York, NY: Springer
la: EN
cc: E50
ut: proof; justification; proof image; inevitability; formal proof; transition
to formal proof; Davydov’s view of abstraction; abstraction in
context; constructs; previous constructs and links between them;
concept image; concept definition
ci:
li: doi:10.1007/978-1-4614-3489-4_13
ab: Summary: We propose the notion of proof image as an intermediate stage in a
learner’s production of a proof. A proof image consists of the
cognitive structure in the learner’s mind that is associated with the
given proof. It consists of previous constructs that the learner has
selected for potential use in the proof to be constructed and of the
links between these previous constructs, links that the learner expects
to play a role in the proof. In this chapter, we focus on the
transition of a proof from proof image to formal proof. We do this
within the theoretical framework of Abstraction in Context, leaning on
Davydov’s notion of abstracting, according to which abstraction
proceeds from an unrefined and vague form to a final coherent
construct. We exemplify this transition by means of the story of K, who
constructs a proof for a theorem in analysis from his proof image. We
discuss in more detail the notion of proof image by means of the story
of L, another learner, this one being related to bifurcations in
dynamical systems.
rv: