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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Granularity analysis for mathematical proofs.

Marvin R G Schiller1

  • 1Institute of Artificial Intelligence, Ulm University, Germany. marvin.schiller@uni-ulm.de

Topics in Cognitive Science
|March 6, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a framework for analyzing mathematical proof granularity, aiding automated assessment and personalized learning in mathematics education. It explores machine learning to model expert judgments on proof step size.

Related Experiment Videos

Last Updated: May 13, 2026

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
09:00

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Published on: September 29, 2019

Area of Science:

  • Mathematics Education
  • Automated Reasoning
  • Machine Learning

Background:

  • Mathematical proofs vary in detail, requiring adaptable presentation for different audiences.
  • Automated reasoning in education needs proofs with appropriate step sizes for effective teaching.
  • Current systems may not cater to the nuanced granularity of student proof attempts.

Purpose of the Study:

  • To propose a framework for analyzing the granularity of mathematical proofs.
  • To enable automated assessment of student proofs and provide tailored feedback.
  • To support the presentation of hints and solutions at an appropriate learning pace.

Main Methods:

  • Developing classifiers to represent proof granularity models.
  • Generating classifiers manually or inferring them from expert judgments using machine learning.
  • Modeling granularity judgments from four human experts to evaluate the machine learning approach.

Main Results:

  • The proposed framework supports the analysis of proof granularity.
  • Machine learning effectively models expert judgments on proof step size.
  • A degree of subjectivity exists among experts when assessing proof granularity.

Conclusions:

  • The framework offers a viable method for assessing proof granularity in automated systems.
  • Machine learning techniques can capture expert nuances in judging proof step size.
  • Further research is needed to address the inherent subjectivity in granularity assessment.