
06367056
a
2014f.00472
Dreyfus, Tommy
Kidron, Ivy
From proof image to formal proof  a transformation.
Rezat, Sebastian (ed.) et al., Transformation  a fundamental idea of mathematics education. New York, NY: Springer (ISBN 9781461434887/hbk; 9781461434894/ebook). 269289 (2014).
2014
New York, NY: Springer
EN
E50
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
doi:10.1007/9781461434894_13
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.