Topics in Cognitive Science 5 (2):251-269 (2013)

Abstract
Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size
Keywords Assertion level  Machine learning  Proof presentation  Automated reasoning  Proof tutoring  Proof granularity
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DOI 10.1111/tops.12012
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Mathematics and Plausible Reasoning.George Polya - 1954 - Princeton University Press.
The AProS Project: Strategic Thinking & Computational Logic.Wilfried Sieg - 2007 - Logic Journal of the IGPL 15 (4):359-368.

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