Representational Variant of the Force Concept Inventory (R-FCI)

Developed by Pasi Nieminen, Antti Savinainen, and Jouni Viiri

Purpose To comprehensively evaluate students’ skills in using multiple representations, specifically their ability to use different representations consistently between isomorphic questions.
Format Pre/post, Multiple-choice
Duration 30 min
Focus Mechanics Content knowledge (kinematics, forces, graphing, multiple representations)
Level High school
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Sample questions from the R-FCI:

R-FCI Implementation and Troubleshooting Guide

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P. Nieminen, A. Savinainen, and J. Viiri, Force Concept Inventory-based multiple-choice test for investigating students' representational consistency, Phys. Rev. ST Phys. Educ. Res. 6 (2), 020109 (2010).
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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 multiple-choice questions on the R-FCI are based on 9 questions from the 1995 version of the FCI. This sub-set of questions was chosen because they were the most appropriate for being transformed into different representations. For each question, three isomorphic variations were created, each having a different representation. The developers sought to keep contexts and answer choices as similar as possible to the original FCI question. The R-FCI was given to over 100 students, who also gave a written explanation for each answer, and 92% of correct answers also had correct reasoning. Appropriate statistical analyses of reliability, difficulty and discrimination were conducted and reasonable values found. The R-FCI has been given to over 400 students at one Finnish high school and results are published in 4 peer-reviewed publications.


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Typical Results

There are three ways to calculate scores on the RFCI. Below are typical results for pre-, post-test and normalized gain from (Nieminen, Savinainen and Viiri 2010). This paper includes typical results for the other two ways of calculating RFCI scores. 

An earlier version of the assessment (previously called the Representation Test) was developed in 2006, consisting of 21 items concerning gravitation and Newton’s third law. The assessment was then improved and expanded until in 2007 the final version consisted of 27 items concerning gravitation and Newton’s first, second and third laws.

The R-FCI is based on nine items taken from the 1995 version of the FCI: items number 1, 4, 13, 17, 22, 24, 26, 28, and 30. For each of the nine FCI items, the R-FCI contains three items that are all isomorphic variants of the same question.