General Equation-based Reasoning inventory of QuaNtity (GERQN)

Developed by Charlotte Zimmerman, Alexis Olsho, Trevor I. Smith, Philip Eaton, and Suzanne White Brahmia

Purpose To assess quantitative literacy development over the span of students’ instruction in introductory algebra-based physics.
Format Pre/post, Multiple-choice, Multiple-response
Duration 30 min
Focus Scientific reasoning (proportional reasoning, reasoning with signed quantities, co-variational reasoning)
Level Intro college, High school
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Sample questions from the GERQN:

GERQN Item 8

GERQN Item 13

C. Zimmerman, A. Olsho, T. I. Smith, P. Eaton, and S. W. Brahmia, Assessing physics quantitative literacy development in algebra-based physics, Phys. Rev. Phys. Educ. Res. 21 (2) 020108 (2025).
RESEARCH VALIDATION
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Gold Star Validation
This is the highest level of research validation, corresponding to all seven 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 GERQN items were developed based on those the original calculus-based PIQL. Items that were considered outside the scope of an algebra-based introductory physics course were removed or revised, and some items were newly developed by the research team. The questions were validated through student and expert interviews and revised iteratively. The GERQN was administered as a pre- and post-test across a year of introductory physics instruction over three years and revised as needed. Classical test theory measures were assessed including difficulty, discrimination, and reliability. Factor analysis was performed and confirmed the GERQN has the same unidimensional structure as the PIQL. The GERQN has been given to over 2,000 students at several institutions and the results are published in one peer-reviewed paper.

References

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Typical Results

Figure 8 from Zimmerman, et al., 2025. Three snapshots of GERQN results in introductory course sequence: before mechanics “PreMech”, after mechanics but before electricity & magnetism “PostMech”, and after electricity & magnetism but before thermodynamics and waves “PostEM”. The data in Fig. 8 come from a matched data set of N = 92 students from all three introductory courses. The mean and standard deviation for the scores are 10.3 ± 2.9 out of 16 items for PreMech, 10.2 ± 2.9 for PostMech, and 10.7 ± 3.0 for PostEM.

The most recent version of the GERQN, released in 2025, is version 3.0. The GERQN is algebra-based version of the PIQL. The PIQL was designed to serve undergraduate calculus-based physics courses. The GERQN is more appropriate for algebra-based courses at the college/university and high-school levels.

Variation

Physics Inventory of Quantitative Literacy

Scientific reasoning (proportional reasoning, reasoning with signed quantities, co-variational reasoning)
Intro college
Pre/post, Multiple-choice, Multiple-response