- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Physics Education Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Organizing energy instruction around the work and energy relation to support knowledge integration in secondary physics

Zihao Yang and Lei Bao*

  • School of Biological Science and Medical Engineering, Research Center for Learning Science, Key Laboratory of Child Development and Learning Science, Ministry of Education, Southeast University, Nanjing 211189, China

  • *Contact author: lei.bao@outlook.com
PDF

Phys. Rev. Phys. Educ. Res. 22, 020119 – Published 24 August, 2026

DOI: https://doi.org/10.1103/wjyg-1hmx

Abstract

Energy is a central idea in physics, but students often learn energy as a set of loosely connected terms, equations, and conservation statements rather than as an integrated explanatory framework. Prior physics education research (PER) has shown that students have persistent difficulty identifying appropriate systems, tracing energy changes across systems and forms, and applying energy conservation in unfamiliar contexts. Drawing on the knowledge integration perspective and on research on systems-based energy reasoning, this study developed a conceptual framework for a ninth-grade energy unit in which the work and energy relation served as the central organizing relation linking energy change, energy conservation, and contextualized problem solving. We implemented a conceptual-framework-based instructional intervention and compared it with regular textbook-sequence instruction in a quasi-experimental study involving two intact ninth-grade classes in China. Both groups studied the same curriculum content for the same amount of instructional time and were taught by the same teacher. Analysis of covariance showed that, after controlling for pretest performance, the intervention group significantly outperformed the control group on the overall post-test score and on the three conceptual categories of energy change, energy conservation, and the work and energy relation. Statistical mediation analyses further showed that the intervention group’s post-test advantage was associated with students’ performance on the work and energy relation. In the post-test mediation model, this indirect association was larger for atypical context performance than for typical context performance. These findings provide classroom-based evidence that reorganizing energy instruction around a core conceptual relation can support students’ integrated understanding and application of energy ideas. The study contributes to PER by extending conceptual-framework-based instruction to a broader secondary energy unit and by clarifying how a work-centered organization may support reasoning beyond familiar surface features.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. National Research Council, A Framework for K–12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (The National Academies Press, Washington, DC, 2012).
  2. L. Bao and K. Koenig, Physics education research for 21st century learning, Discip. Interdiscip. Sci. Educ. Res. 1, 2 (2019).
  3. J. Nordine, D. Fortus, Y. Lehavi, K. Neumann, and J. Krajcik, Modelling energy transfers between systems to support energy knowledge in use, Stud. Sci. Educ. 54, 177 (2018).
  4. K. Neumann, T. Viering, W. J. Boone, and H. E. Fischer, Towards a learning progression of energy, J. Res. Sci. Teach. 50, 162 (2013).
  5. C. F. Herrmann Abell and G. E. DeBoer, Investigating a learning progression for energy ideas from upper elementary through high school, J. Res. Sci. Teach. 55, 68 (2018).
  6. H.-S. Lee and O. L. Liu, Assessing learning progression of energy concepts across middle school grades: The knowledge integration perspective, Sci. Educ. 94, 665 (2010).
  7. M. Kubsch, What affects the continued learning about energy? Evidence from a 4-year longitudinal study, J. Res. Sci. Teach. 61, 975 (2024).
  8. J. W. Jewett Jr., Energy and the confused student I: Work, Phys. Teach. 46, 38 (2008).
  9. J. W. Jewett Jr., Energy and the confused student II: Systems, Phys. Teach. 46, 81 (2008).
  10. R. A. Lawson and L. C. McDermott, Student understanding of the work-energy and impulse-momentum theorems, Am. J. Phys. 55, 811 (1987).
  11. B. A. Lindsey, P. R. L. Heron, and P. S. Shaffer, Student ability to apply the concepts of work and energy to extended systems, Am. J. Phys. 77, 999 (2009).
  12. B. A. Lindsey, P. R. L. Heron, and P. S. Shaffer, Student understanding of energy: Difficulties related to systems, Am. J. Phys. 80, 154 (2012).
  13. A. R. Daane, S. B. McKagan, S. Vokos, and R. E. Scherr, Energy conservation in dissipative processes: Teacher expectations and strategies associated with imperceptible thermal energy, Phys. Rev. ST Phys. Educ. Res. 11, 010109 (2015).
  14. R. G. Tobin, S. J. Lacy, S. Crissman, N. Haddad, O. Wentink, and L. Seeley, Where does energy go when it is “gone”? Promoting understanding of energy dissipation, Am. J. Phys. 87, 569 (2019).
  15. J. Nordine, J. Krajcik, and D. Fortus, Transforming energy instruction in middle school to support integrated understanding and future learning, Sci. Educ. 95, 670 (2011).
  16. A. R. Daane, S. Vokos, and R. E. Scherr, Goals for teacher learning about energy degradation and usefulness, Phys. Rev. ST Phys. Educ. Res. 10, 020111 (2014).
  17. E. Kim and S.-J. Pak, Students do not overcome conceptual difficulties after solving 1000 traditional problems, Am. J. Phys. 70, 759 (2002).
  18. M. Alonso, Problem solving vs. conceptual understanding, Am. J. Phys. 60, 777 (1992).
  19. M. T. H. Chi, P. J. Feltovich, and R. Glaser, Categorization and representation of physics problems by experts and novices, Cogn. Sci. 5, 121 (1981).
  20. P. T. Hardiman, R. Dufresne, and J. P. Mestre, The relation between problem categorization and problem solving among experts and novices, Mem. Cognit. 17, 627 (1989).
  21. A. Mason and C. Singh, Assessing expertise in introductory physics using categorization task, Phys. Rev. ST Phys. Educ. Res. 7, 020110 (2011).
  22. M. C. Linn, The knowledge integration perspective on learning and instruction, in The Cambridge Handbook of the Learning Sciences, edited by R. K. Sawyer (Cambridge University Press, Cambridge, 2005), pp. 243—264.
  23. O. L. Liu, K. Ryoo, M. C. Linn, E. Sato, and V. Svihla, Measuring knowledge integration learning of energy topics: A two-year longitudinal study, Int. J. Sci. Educ. 37, 1044 (2015).
  24. W. Xu, Q. Liu, K. Koenig, J. Fritchman, J. Han, S. Pan, and L. Bao, Assessment of knowledge integration in student learning of momentum, Phys. Rev. Phys. Educ. Res. 16, 010130 (2020).
  25. Z. Liu, S. Pan, X. Zhang, and L. Bao, Assessment of knowledge integration in student learning of simple electric circuits, Phys. Rev. Phys. Educ. Res. 18, 020102 (2022).
  26. D. Tong, J. Liu, Y. Sun, Q. Liu, X. Zhang, S. Pan, and L. Bao, Assessment of student knowledge integration in learning work and mechanical energy, Phys. Rev. Phys. Educ. Res. 19, 010127 (2023).
  27. L. Bao and J. C. Fritchman, Knowledge integration in student learning of Newton’s third law: Addressing the action-reaction language and the implied causality, Phys. Rev. Phys. Educ. Res. 17, 020116 (2021).
  28. L. Xie, Q. Liu, H. Lu, Q. Wang, J. Han, X. M. Feng, and L. Bao, Student knowledge integration in learning mechanical wave propagation, Phys. Rev. Phys. Educ. Res. 17, 020122 (2021).
  29. C. Lu, Y. Liu, S. Xu, S. Zhou, H. Mei, X. Zhang, L. Yang, and L. Bao, Conceptual framework assessment of knowledge integration in student learning of measurement uncertainty, Phys. Rev. Phys. Educ. Res. 19, 020145 (2023).
  30. D. Ye, J. Qian, W. Xu, Y. Lu, S. Wang, L. Xiao, and L. Bao, Assessment of knowledge integration in student learning of galvanic cell: An interdisciplinary approach connecting physics and chemistry, Phys. Rev. Phys. Educ. Res. 20, 020129 (2024).
  31. Z. Liu, S. Pan, and L. Bao, Effectiveness of conceptual-framework-based instruction on promoting knowledge integration in learning simple electric circuit, Phys. Rev. Phys. Educ. Res. 20, 020113 (2024).
  32. D. Tong, H. Wu, H. Ren, Z. Wang, S. Pan, and L. Bao, Promoting knowledge integration in work and mechanical energy through conceptual framework and cooperative learning instruction, Phys. Rev. Phys. Educ. Res. 21, 010163 (2025).
  33. W. Xu, Y. Jiang, L. Yang, and L. Bao, Conceptual framework based instruction for promoting knowledge integration in learning momentum, Phys. Rev. Phys. Educ. Res. 19, 020124 (2023).
  34. L. Xie, Y. Li, Q. Fu, Y. Xiao, L. Yang, and L. Bao, Assessing and enhancing university students’ knowledge integration in learning electromagnetic induction, Int. J. Sci. Educ. 47, 1659 (2025).
  35. J.-X. Yao, Y.-Y. Guo, and K. Neumann, Refining a learning progression of energy, Int. J. Sci. Educ. 39, 2361 (2017).
  36. J.-X. Yao, Y.-X. Liu, and Y.-Y. Guo, Learning progression-based design: Advancing the synergetic development of energy understanding and scientific explanation, Instr. Sci. 51, 397 (2023).
  37. T. Wyrwich, M. Kubsch, H. Drachsler, and K. Neumann, Tracking students’ progression in developing understanding of energy using AI technologies, Phys. Rev. Phys. Educ. Res. 21, 010152 (2025).
  38. D. Fortus, M. Kubsch, T. Bielik, J. Krajcik, Y. Lehavi, K. Neumann, J. Nordine, S. Opitz, and I. Touitou, Systems, transfer, and fields: Evaluating a new approach to energy instruction, J. Res. Sci. Teach. 56, 1341 (2019).
  39. M. Kubsch, S. Opitz, J. Nordine, K. Neumann, D. Fortus, and J. Krajcik, Exploring a pathway towards energy conservation through emphasizing the connections between energy, systems, and fields, Discip. Interdiscip. Sci. Educ. Res. 3, 2 (2021).
  40. K. Fiedler, M. Kubsch, K. Neumann, and J. Nordine, Supporting learning about energy with fields: Evidence from a mixed-methods study, J. Res. Sci. Teach. 62, 1859 (2025).
  41. J. W. Warren, Energy and its carriers: A critical analysis, Phys. Educ. 18, 209 (1983).
  42. A. Van Heuvelen and X. Zou, Multiple representations of work-energy processes, Am. J. Phys. 69, 184 (2001).
  43. G. Swackhamer, Cognitive resources for understanding energy (2005).
  44. Ministry of Education of the People’s Republic of China, Physics Curriculum Standards for Compulsory Education, 2022 Edition [in Chinese] (Beijing Normal University Press, Beijing, 2022).
  45. People’s Education Press Curriculum and Teaching Materials Research Institute, Physics, Grade 9, Complete Volume, Compulsory Education Textbook [in Chinese] (People’s Education Press, Beijing, 2013).
  46. L. Ding, Designing an Energy Assessment to Evaluate Student Understanding of Energy Topics, Ph.D. thesis, North Carolina State University, Raleigh, NC, 2007.
  47. C. Singh and D. Rosengrant, Multiple-choice test of energy and momentum concepts, Am. J. Phys. 71, 607 (2003).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/wjyg-1hmx for item sources and modifications, classification criteria, field test results, and additional evidence supporting the interpretation of the assessment scores.
  49. National Research Council, How People Learn: Brain, Mind, Experience, and School: Expanded Edition (The National Academies Press, Washington, DC, 2000).
  50. M. T. H. Chi and K. A. VanLehn, Seeing deep structure from the interactions of surface features, Educ. Psychol. 47, 177 (2012).
  51. M. T. H. Chi, J. D. Slotta, and N. De Leeuw, From things to processes: A theory of conceptual change for learning science concepts, Learn. Instr. 4, 27 (1994).

Outline

Information

Phys. Rev. Phys. Educ. Res. 22, 020119– Published 24 August, 2026
  • Received 13 May 2026
  • Accepted 28 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation