Developing a Learning Progression of Buoyancy to Model Conceptual Change: A Latent Class and Rule Space Model Analysis

  • Yizhu Gao
  • Xiaoming Zhai
  • Björn Andersson
  • Pingfei Zeng
  • Tao XinEmail author


We applied latent class analysis and the rule space model to verify the cumulative characteristic of conceptual change by developing a learning progression for buoyancy. For this study, we first abstracted seven attributes of buoyancy and then developed a hypothesized learning progression for buoyancy. A 14-item buoyancy instrument was administered to 1089 8th grade students to verify and refine the learning progression. The results suggest four levels of progression during conceptual change when 8th grade students understand buoyancy. Students at level 0 can only master Density. When students progress to level 1, they can grasp Direction, Identification, Submerged volume, and Relative density on the basis of the prior level. Then, students gradually master Archimedes’ theory as they reach level 2. The most advanced students can further grasp Relation with motion and arrive at level 3. In addition, this four-level learning progression can be accounted for by the Qualitative–Quantitative–Integrative explanatory model.


Buoyancy Learning progression Latent class analysis Rule space model Conceptual change 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Yizhu Gao
    • 1
  • Xiaoming Zhai
    • 2
  • Björn Andersson
    • 3
  • Pingfei Zeng
    • 4
  • Tao Xin
    • 1
    Email author
  1. 1.Collaborative Innovation Center of Assessment toward Basic Education QualityBeijing Normal UniversityBeijingChina
  2. 2.Graduate School of EducationStanford UniversityStanfordUSA
  3. 3.Centre for Educational MeasurementUniversity of OsloOsloNorway
  4. 4.College of Teacher EducationZhejiang Normal UniversityJinghua CityChina

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