Assessments »Inventory of Galilean Transformation of uniform linear motion in position-time graphs
Inventory of Galilean Transformation of uniform linear motion in position-time graphs (IGT)

Developed by Eliane Merki, Andreas Lichtenberger, Sarah Hofer, Andreas Vaterlaus

Purpose To assess students’ ability to interpret position–time graphs of uniform linear motion when transforming between different frames of reference according to Galilean transformations.
Format Pre/post, Multiple-choice
Duration 20 min
Focus Mechanics Content knowledge (kinematics)
Level Intro college, High school
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Example questions from the IGT:

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IGT: Developer's website
E. Merki, S. Hofer, A. Vaterlaus, and A. Lichtenberger, Inventory of Galilean Transformation of uniform linear motion in position-time graphs, Phys. Rev. Phys. Educ. Res. 21 (2), 020118 (2025).
RESEARCH VALIDATION
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Bronze Validation
This is the third highest level of research validation, corresponding to at least 3 of the validation categories below.

Research Validation Summary

Based on Research Into:

  • Student thinking

Studied Using:

  • Student interviews
  • Expert review
  • Appropriate statistical analysis

Research Conducted:

  • At multiple institutions
  • By multiple research groups
  • Peer-reviewed publication

The IGT demonstrated satisfactory psychometric properties in a sample of 326 Swiss upper-secondary students. The mean item difficulty (0.55), discrimination index (0.42), and point-biserial coefficient (0.43) were within the desired ranges, and Ferguson’s delta (0.96) indicated strong overall discriminatory power. Confirmatory factor analysis supported the intended three-factor structure corresponding to the three types of Galilean transformations, while Rasch analysis confirmed the expected progression in item difficulty from identity transformations (T1) to transformations between stationary frames (T2) and transformations to a moving frame (T3). The analysis of distractors revealed several alternative conceptions, including difficulties distinguishing overtaking from crossing, translating coordinate systems in the correct direction, and interpreting changes in position–time graphs when transforming to a moving frame of reference. Item 15 showed inadequate discrimination and point-biserial correlation and was therefore recommended for removal, resulting in the 14-item IGT14 version.

References

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Language Translator(s)  
German

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Typical Results

In the validation study, 326 Swiss upper-secondary students completed the 15-item IGT, achieving a mean score of 8.24 out of 15 (SD = 2.86). These scores were obtained from students in the advanced track of upper secondary school, primarily after a brief introduction to frames of reference and a 15-minute predict–observe–explain sequence on Galilean transformations.

The original IGT consists of 15 multiple-choice items. The recommended version, IGT14, was released in 2025 and contains 14 items, omitting the final item of the original IGT. The IGT14 is the version recommended for use because its psychometric properties were within the desired ranges for item difficulty, discrimination, and point-biserial correlation.