A Validity Framework for the Design of Comparative International Research in Mathematics Education



In this chapter, we introduce the reader to the importance of measurement validity and the challenges involved in developing the FIRSTMATH knowledge assessments and questionnaires for beginning primary and secondary teachers and their pupils. There are three main challenges: collecting validity evidence and documenting the entire validation process; providing evidence of measurement invariance which is of particular importance given the international comparative nature of the intended inferences; and the development of scales that are appropriate, meaningful, and useful. Evidence is presented regarding how the FIRSTMATH researchers responded to each challenge, the psychometric properties of the FIRSTMATH assessments, and the procedures used to improve these instruments to measure well across countries.


  1. AERA, APA, & NCME. (2014). Standards for educational and psychological testing. Washington, DC: AERA.Google Scholar
  2. Albano, A. D., & Rodriguez, M. C. (2013). Examining differential math performance by gender and opportunity to learn. Educational and Psychological Measurement, 73(5), 836–856.Google Scholar
  3. Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York, NY: Guilford.Google Scholar
  4. Kane, M. (2013). The argument-based approach to validation. School Psychology Review, 42(4), 448–457.Google Scholar
  5. Linacre, J. M. (2012). Winsteps (Version 3.7) [Computer software]. Beaverton, OR:
  6. Muthén, L. K., & Muthén, B. O. (2012). Mplus. (Version 7). [Software program]. Scholar
  7. Reckase, M. D. (2010). NCME 2009 presidential address: “What I think I know”. Educational Measurement: Issues and Practice, 29, 3–7.CrossRefGoogle Scholar
  8. Tatto, M. T. (Ed.). (2013). The Teacher Education and Development Study in Mathematics (TEDS-M). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries: Technical report. Amsterdam, the Netherlands: International Association for the Evaluation of Educational Achievement.Google Scholar
  9. Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, NJ: Lawrence Erlbaum.Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Mary Lou Fulton Teachers CollegeArizona State UniversityTempeUSA
  2. 2.Educational PsychologyUniversity of MinnesotaMinneapolisUSA
  3. 3.College of EducationMichigan State UniversityEast LansingUSA
  4. 4.Center for Science, Mathematics & Computer EducationUniversity of Nebraska-LincolnLincolnUSA
  5. 5.Faculty of Mathematics and Informatics, the University of SofiaInstitute of Mathematics and Informatics, Bulgarian Academy of SciencesSofiaBulgaria
  6. 6.Oakland Community CollegeEast LansingUSA

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