Journal of Mathematics Teacher Education

, Volume 11, Issue 2, pp 127–138 | Cite as

Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills



The purpose of this paper is to share a performance assessment task and rubric designed to assess secondary school mathematics preservice teachers’ pedagogical content knowledge and skills. The assessment task and rubric were developed in collaboration with five education faculty, four arts and sciences faculty, and four high school teachers over a period of one year. Over this period, the group met more than 15 times and designed an assessment task and rubric to measure secondary school preservice teachers’ pedagogical content knowledge and skills. The assessment task and rubric were piloted at the end of the year and extensively revised using the pilot data. The redesigned task and rubric were successfully carried out in the second and subsequent years. Other teacher education programs can benefit from this assessment of teacher candidates’ pedagogical content knowledge and skills.


Secondary school preservice teachers Mathematics education NCATE/NCTM Program Standards Teachers’ knowledge Pedagogical content knowledge and skills Performance assessment Rubric 



The research reported in this manuscript was supported by a grant from Title II federal funding through the Connecticut State Department of Education (CSDE) to Eastern Connecticut State University. The opinions expressed in this manuscript do not necessarily reflect the opinion and policy of the federal government or CSDE. We gratefully acknowledge the help of Jeanelle Day, Laura Dawley, Ken Dobush, Ann Higginbotham, Ross Koning, Kathy Lake, Karen Legg, Steve Merlino, Georgette Nemr, Elaine Reynolds, Irv Richardson, Leslie Ricklin, Dan Rothermel, Elena Tapia, and Janice Vuolo who diligently worked for a year in the development of the performance task and rubric presented in this manuscript. This work would not have been possible without their generous time and support. We would also like to thank the anonymous reviewers for their valuable comments and suggestions in earlier versions of this article.


  1. Berliner, D. C. (2005). The near impossibility of testing for teacher quality. Journal of Teacher Education, 56, 205–213.CrossRefGoogle Scholar
  2. Connecticut State Board of Education (2001). Connecticut academic performance test: Second generation mathematics handbook. Hartford, CT: Author.Google Scholar
  3. Danielson, C., & Marquez, E. (1998). A collection of performance tasks and rubrics: High school mathematics. Larchmont, NY: Eye on Education.Google Scholar
  4. Darling-Hammond, L., & Snyder, J. (2000). Authentic assessment of teaching in context. Teaching and Teacher Education, 16, 523–545.CrossRefGoogle Scholar
  5. Delandshere, G., & Arens, S. A. (2003). Examining the quality of evidence in preservice teacher portfolios. Journal of Teacher Education, 54, 57–73.CrossRefGoogle Scholar
  6. Haertel, E. H. (1991). New forms of teacher assessment. Review of Research in Education, 17, 3–29.Google Scholar
  7. Hamilton, L. (2003). Assessment as a policy tool. Review of Research in Education, 27, 25–68.CrossRefGoogle Scholar
  8. Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35, 330–351.CrossRefGoogle Scholar
  9. Holt-Reynolds, D. (2000). What does the teacher do? Constructivist pedagogies and prospective teachers’ beliefs about the role of a teacher. Teaching and Teacher Education, 16(1), 21–32.CrossRefGoogle Scholar
  10. Linn, R. L. (2000). Assessments and accountability. Educational Researcher, 29(2), 4–16.Google Scholar
  11. National Council for Accreditation of Teacher Education (2006). Professional standards for the accreditation of schools, colleges, and departments of education. Washington, DC: Author.Google Scholar
  12. National Council for Teachers of Mathematics (1995). Assessment standards for school mathematics. Reston, VA: Author.Google Scholar
  13. National Council for Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  14. NCATE/NCTM Program Standards (2003). Standards for secondary mathematics teachers. Retrieved June 10, 2006 from
  15. Reynolds, A. (1992). What is competent beginning teaching? A review of the literature. Review of Educational Research, 62, 1–35.Google Scholar
  16. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  17. Timmerman, M. A. (2002). Learning to teach: Prospective teachers’ evaluation of students’ written responses on a 1992 NAEP graphing task. School Science and Mathematics, 102, 346–358.Google Scholar
  18. Valli, L., & Rennert-Ariev, P. (2002). New standards and assessments? Curriculum transformation in teacher education. Journal of Curriculum Studies, 34(2), 201–225.CrossRefGoogle Scholar
  19. Vogler, K. E. (2002). The impact of high-stakes, state-mandated student performance assessment on teachers’ instructional practices. Education, 123(1), 39–55.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Mathematics EducationEastern Connecticut State UniversityWillimanticUSA
  2. 2.Mathematics DepartmentEastern Connecticut State UniversityWillimanticUSA

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