Educational Studies in Mathematics

, Volume 94, Issue 3, pp 329–345 | Cite as

Teachers’ pedagogical content knowledge and mathematics achievement of students in Peru

  • Santiago CuetoEmail author
  • Juan León
  • M. Alejandra Sorto
  • Alejandra Miranda


After improving enrolment rates significantly, many developing countries such as Peru are facing the challenge to increase learning levels among students. Over the past few years, many researchers have turned to teacher-related variables as a way to better understand classroom processes that may help increase learning levels among students. In this study, we analyze one of these, that falls under what Shulman (Educational Researcher, 15 (2), 4–14, 1986) called pedagogical content knowledge (PCK). Specifically, in this study, we analyze one of the areas of PCK which is knowledge of content and students. This was measured through a test where teachers were asked to explain students’ mistakes and predict responses in similar mathematics exercises. We explore if PCK is associated with the socioeconomic status of children and if it has an effect on children’s achievement. Additionally, we analyze which teacher characteristics are associated with higher scores in PCK. The analysis uses the Young Lives longitudinal survey for Peru. We found that students’ socioeconomic status at age 1 and maternal education were positively associated with their teachers’ PCK by the time students were enrolled in fourth grade, thus depicting a very unequal education system. Furthermore, teachers’ PCK was positively associated with student achievement, but only when a threshold for the PCK test was established. For our sample, male teachers, who were younger, and Spanish speakers had higher PCK scores.


Pedagogical content knowledge Mathematics achievement Peru Socioeconomic status Longitudinal study 



Preparation of this study was funded by UK aid from the Department for International Development (DFID) and co-funded by the Netherlands Ministry of Foreign Affairs from 2010 to 2014 and by Irish Aid from 2014 to 2015. The views expressed are those of the authors. They are not necessarily those of, or endorsed by, Young Lives, DFID, or other funders.


  1. An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teacher in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172. doi: 10.1023/B:JMTE.0000021943.35739.1c
  2. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A. ... Tsai, Y.-M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180. doi: 10.3102/0002831209345157
  3. Borman, G. D., & Kimball, S. M. (2005). Teacher quality and educational equality: Do teachers with higher standards‐based evaluation ratings close student achievement gaps? The Elementary School Journal, 106(1), 3–20.CrossRefGoogle Scholar
  4. Carnoy, M., & Arends, F. (2012). Explaining mathematics achievement gains in Botswana and South Africa. Prospects Quarterly Review of Comparative Education, 42(4), 453–468. doi: 10.1007/s11125-012-9246-6
  5. Chaudhury, N., Hammer, J., Kremer, M., Muralidharan, K., & Rogers, H. (2006). Missing in action: Teacher and health worker absence in developing countries. Journal of Economic Perspectives, 20(1), 91–116. doi: 10.1257/089533006776526058
  6. Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers. Providence, RI and Washington, DC: American Mathematical Society and Mathematical Association of America.CrossRefGoogle Scholar
  7. Creemers, B. P. M. (1994). The effective classroom. London: Cassell.Google Scholar
  8. Cueto, S. (2013). Evaluaciones estandarizadas del rendimiento escolar. Boletín del Consejo Nacional de Educación. Lima, CNE. Retrieved from
  9. Cueto, S., Escobal, J., Penny, M., & Ames, P. (2011). Tracking disparities: Who gets left behind? Initial Findings from Peru. Round 3 Survey Report (Young Lives). Oxford: Department of International Development, University of Oxford.Google Scholar
  10. Cueto, S., Leon, J., Guerrero, G., & Munoz, I. (2009). Psychometric characteristics of cognitive development and achievement instruments in Round 2 of Young Lives (Young Lives Technical Note No. 15). Oxford: University of Oxford.Google Scholar
  11. Cueto, S., Ramirez, C., & Leon, J. (2006). Opportunities to learn and achievement in mathematics in a sample of sixth grade students in Lima, Peru. Educational Studies in Mathematics, 62, 25–55. doi: 10.1007/s10649-006-7922-2.CrossRefGoogle Scholar
  12. Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25. doi: 10.1016/j.tate.2013.03.001
  13. Escobal, J., & Flores, E. (2008). An assessment of the young lives sampling approach in Peru (Young Lives Technical Note 3). Retrieved from
  14. Grossman, P. L., & Schoenfeld, A. (2005). Teaching subject matter. In L. Darling- Hammond, J. Bransford, P. LePage, K. Hammerness, & H. Duffy (Eds.), Preparing teachers a changing world: What teachers should learn and be able to do (pp. 201–231). San Francisco: Jossey-Bass.Google Scholar
  15. Guadalupe, C., León, J., & Cueto, S. (2013). Charting progress in learning outcomes in Peru using national assessments. Paper commissioned for the EFA Global Monitoring Report 2013/4. Paris: UNESCO.Google Scholar
  16. Guerrero, G., Leon, J., Rosales, E., Zapata, M., Freire, S., Saldarriaga, V., & Cueto, S. (2013). Young lives school survey in Peru: Design and initial findings (Young Lives Working Paper 92). Oxford: University of Oxford.Google Scholar
  17. Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (1998). Multivariate data analysis (5th ed.). Upper Saddle River: Prentice Hall.Google Scholar
  18. Harbison, R., & Hanushek, E. A. (1992). Educational performance of the poor: Lessons from Rural Northeast Brazil. New York: Oxford University Press.Google Scholar
  19. Hiebert, J., Morris, A. K., Berk, D., & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47–61.CrossRefGoogle Scholar
  20. 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(5), 330–351.CrossRefGoogle Scholar
  21. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.Google Scholar
  22. Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.CrossRefGoogle Scholar
  23. Koh, J. H. L., Chai, C. S., & Tsai, C.-C. (2014). Demographic factors, TPACK constructs, and teachers’ perceptions of constructivist-oriented TPACK. Educational Technology & Society, 17(1), 185–196.Google Scholar
  24. Koirala, H. P., Davis, M., & Johnson, P. (2008). Development of a performance assessment task and rubric to measure prospective secondary school mathematics teachers’ pedagogical content knowledge and skills. Journal of Mathematics Teacher Education, 11, 127–138.CrossRefGoogle Scholar
  25. Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 105(3), 805–820.CrossRefGoogle Scholar
  26. Lim-Teo, S. K., Chua, K. G., Cheang, W. K., & Yeo, J. K. (2007). The development of diploma in education student teachers’ mathematical pedagogical content knowledge. International Journal of Mathematics and Science and Mathematics Education, 5, 237–261. doi: 10.1007/s10763-006-9056-5
  27. Marshall, J. H., Chinna, U., Nessay, P., Hok, U. N., Savoeun, V., Tinon, S., & Veasna, M. (2009). Student achievement and education policy in a period of rapid expansion: Assessment data evidence from Cambodia. International Review of Education, 55(4), 393–413. doi: 10.1007/s11159-009-9133-4
  28. Marshall, J., & Sorto, M. A. (2012). The effects of teacher mathematics knowledge and pedagogy on student achievement in rural Guatemala. International Review of Education, 58(2), 173–197. doi: 10.1007/s11159-012-9276-6
  29. Metzler, J., & Woessmann, L. (2012). The impact of teacher subject knowledge on student achievement: Evidence from within-teacher within-student variation. Journal of Development Economics, 99(2), 486–496.CrossRefGoogle Scholar
  30. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: National Council of Teachers of Mathematics.Google Scholar
  31. Ngo, F. J. (2012). The distribution of pedagogical content knowledge in Cambodia: Gaps and thresholds in math achievement. Educational Research for Policy and Practice, 12(2), 81–100.CrossRefGoogle Scholar
  32. OECD. (2010). PISA 2009 Results: Overcoming social background. Equity in learning opportunities and outcomes (Vol. 2). Retrieved from doi: 10.1787/9789264091450-en
  33. OECD. (2013). PISA 2012 Results: What students know and can do – students performance in mathematics. Reading and science (Vol. 1). PISA, OECD Publishing. Retrieved from doi:10.1787/9789264201118-en Google Scholar
  34. Park, S., & Oliver, J. S. (2007). Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38(3), 261–184.CrossRefGoogle Scholar
  35. Passos, A., Nahara, T., Magaia, F., & Lauchande, C. (2005). The SACMEQ project II in Mozambique: A study of the conditions of schooling and the quality of education. Southern and Eastern Africa Consortium for Monitoring Educational Quality (SACMEQ) and Ministry of Education and Culture, Mozambique. Retrieved from
  36. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Newbury Park: Sage Publications.Google Scholar
  37. Rockoff, J. E., Jacob, B. A., Kane, T. J., & Staiger, D. O. (2008). Can you recognize an effective teacher when you recruit one? (NBER Working Papers 14485). Cambridge, MA: National Bureau of Economic Research.Google Scholar
  38. Rogers, W. H. (1993). Regression standard errors in clustered samples. Stata Technical Bulletin, 13, 19–23.Google Scholar
  39. Scheerens, J. (1990). School effectiveness research and the development of process indicators of school functioning. School Effectiveness and School Improvement, 1, 61–80.CrossRefGoogle Scholar
  40. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. en Matematica Educativa, 12(2), 251–290.CrossRefGoogle Scholar
  41. Sorto, M. A., Marshall, J. H., Luschei, T. F., & Carnoy, M. (2009). Teacher knowledge and teaching in Panama and Costa Rica: A comparative study. Revista Latinoamericana de Investigación.Google Scholar
  42. Turnuklu, E. B., & Yesildere, S. (2007). The pedagogical content knowledge in mathematics: Preservice primary mathematics teachers’ perspectives in Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, 1–13.Google Scholar
  43. UMC. (2004). Factores asociados al rendimiento estudiantil. Resultados de la Evaluación Nacional 2001. Documento de Trabajo n° 9. Lima: Unidad de la Medición de la Calidad Educativa del Ministerio de Educación.Google Scholar
  44. UMC. (2006). Cómo disminuir la inequidad del sistema educativo peruano y mejorar el rendimiento de sus estudiantes? Factores explicativos de la Evaluación Nacional 2004. Documento de Trabajo n° 21. Lima: Unidad de la Medición de la Calidad Educativa del Ministerio de Educación.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Santiago Cueto
    • 1
    Email author
  • Juan León
    • 1
  • M. Alejandra Sorto
    • 2
  • Alejandra Miranda
    • 1
  1. 1.GRADEBarrancoPeru
  2. 2.Texas State UniversitySan MarcosUSA

Personalised recommendations