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Granularity Analysis for Mathematical Proofs
Author(s) -
Schiller Marvin R. G.
Publication year - 2013
Publication title -
topics in cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.191
H-Index - 56
eISSN - 1756-8765
pISSN - 1756-8757
DOI - 10.1111/tops.12012
Subject(s) - mathematical proof , granularity , computer science , calculus (dental) , mathematics , programming language , geometry , medicine , dentistry
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.