Test of Understanding of Vectors (TUV)

Developed by Pablo Barniol and Genaro Zavala

Purpose To assess students’ understanding of vector concepts in problems without a physical context.
Format Pre/post, Multiple-choice
Duration 35 min
Focus Mathematics Content knowledge (magnitude, direction, components, unit vector, addition, subtraction, multiplication, dot and cross product)
Level Intro college
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Sample questions from the TUV:

TUV sample question


TUV sample question

TUV Implementation and Troubleshooting Guide

Everything you need to know about implementing the TUV in your class.

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P. Barniol and G. Zavala, Test of understanding of vectors: A reliable multiple-choice vector concept test, Phys. Rev. ST Phys. Educ. Res. 10 (1), 010121 (2014).
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Silver Validation
This is the second highest level of research validation, corresponding to at least 5 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 TUV were developed based on student thinking about vectors collected using open-ended questions. Students’ responses to these questions were used to create the answer choices. This initial set of questions was reviewed by experts, tested with students and revised. Statistical analyses of reliability, difficulty and discrimination were conducted and reasonable values found. The TUV has been given to about 3000 students at four institutions and results published in 3 peer-reviewed papers. There are several other peer-reviewed papers by the developers where they studied vector concepts. 


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Language Translator(s)  
Arabic Hisham Bani-Salameh
Spanish Pablo Barniol and Genaro Zavala

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Typical Results

Typical Results from Barniol and Zavala 2013:

The average score among a sample of 423 students who took the test in English in a calculus-based introductory electricity and magnetism course at a large private Mexican university was 13.52 of 20 points, or 68%.

The latest version of the TUV, released in 2014, is version 1.