title: Granularity analysis for mathematical proofs.
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.
authors: Institute of Artificial Intelligence, Ulm University, Germany. marvin.schiller@uni-ulm.de
authors: Marvin R G
authors: MR
authors: Schiller
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D006801:Humans; D008962:Models, Theoretical; D011340:Problem Solving; D013663:Teaching / Q000379:methods*