Modeling Chilean Mathematics Teachers’ Instructional Beliefs on Problem Solving Practices


This study was designed to examine predictors of instructional beliefs related to problem solving that influence mathematics in-service teachers’ practices in the Chilean context. A total of 713 in-service mathematics teachers from various elementary schools participated in the survey study during 2015 and 2016. Results showed that teachers’ traditional beliefs are directly associated with their teacher-centered practices, while there was an indirect relation among reformed beliefs and student-centered practices through teachers’ self-efficacy beliefs and their beliefs about the value of problem solving. This association among beliefs and practices suggests that educators and policy makers should be aware of, when designing a teacher professional development, the need to emphasize other variables such as teachers’ self-efficacy and value of the task.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1


  1. Ávalos, B., & De Los Rios, D. (2013). Reform environment and teacher identity in Chile. In D. B. Napier & S. Majhanovich (Eds.), Education, dominance and identity (pp. 153–175). Rotterdam: Sense.

  2. Ávalos, B., & Matus, C. (2010). La formación inicial docente en Chile desde una óptica internacional. Informe nacional del Estudio Internacional IEA TEDS-M [Initial training in Chile from an international perspective. National Report of International Study of IEA TEDS-M]. Santiago: Ministerio de Educación.

  3. Ávalos, B., & Valenzuela, J. P. (2016). Education for all and attrition/retention of new teachers: A trajectory study in Chile. International Journal of Educational Development, 49, 279–290.

  4. Ayarza, R. O., Soto, D. S., & Crocci, H. S. (2007). Renovación de la enseñanza del álgebra elemental: Un aporte desde la didáctica [Renewing the teaching of elementary algebra: A contribution of didactics]. Estudios Pedagógicos (Valdivia), 33(2), 81–100.

  5. Bandalos, D. L. (2002). The effects of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling. Structural Equation Modeling, 9(1), 78–102.

  6. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W H. Freeman.

  7. Bellei, C., & Morawietz, L. (2016). Strong content, weak tools twenty-first-century competencies in the Chilean educational reform. In F. M. Reimers & C. Chung (Eds.), Teaching and learning for the twenty-first century: Educational goals, policies, and curricula from six nations (pp. 93–125). Cambridge: Harvard Education Press.

  8. Bellei, C., & Vanni, X. (2015). Chile: The evolution of educational policy, 1980–2014. In S. Shwartzman (Ed.), Education in South America: Education around the world (pp. 179–200). London: Bloomsbury.

  9. Bent, G. J., Bakx, A., & Den Brok, P. (2017). Primary education teachers’ self-efficacy beliefs for teaching geography lessons. International Research in Geographical and Environmental Education, 26(2), 150–165.

  10. Blömeke, S., & Kaiser, G. (2014). Theoretical framework, study design and main results of TEDS-M. In S. Blömeke, F. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 19–48). Dordrecht, The Netherlands: Springer.

  11. Bong, M. (2001). Role of self-efficacy and task-value in predicting college students’ course performance and future enrollment intentions. Contemporary Educational Psychology, 26(4), 553–570.

  12. Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. ZDM, 38(2), 178–195.

  13. Byrne, B. (2010). Structural equation modeling using AMOS: Basic concepts, applications, and programming (2nd ed.). New York: Taylor and Francis Group.

  14. Cárcamo, R. A., & Castro, P. J. (2015). Concepciones sobre el Aprendizaje de Estudiantes de Pedagogía de la Universidad de Magallanes y Docentes en Ejercicio en la Educación Básica de la ciudad de Punta Arenas, Chile [Conceptions about learning among pre-service students in University of Magallanes and in-service elementary teachers in Punta Arenas, Chile]. Formación Universitaria, 8(5), 13–24.

  15. Carrillo, J. (1998). Exploring relationships between teachers’ conceptions and problem solving modes in mathematics. In E. Pehkonen & G. Törner (Eds.), The state of art in mathematics-related beliefs research. Helsinki, Finland: University of Helsinki.

  16. Chen, I. (2009). Behaviorism and developments in instructional design and technology. In P. Rogers, G. Berg, J. Boettcher, C. Howard, L. Justice, & K. Shenck (Eds.), Encyclopedia of distance learning (pp. 153–173). Hershey: Idea Group Incorporated.

  17. Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947–967.

  18. Contreras, S. A. (2009). Creencias curriculares y creencias de actuación curricular de los profesores de ciencias chilenos [Chilean sciences teachers’ beliefs about curriculum and its performance]. Revista Electrónica de Enseñanza de las Ciencias, 8(2), 505–526.

  19. Cooney, T. J. (1994). Research and teacher education: In search of common ground. Journal for Research in Mathematics Education, 25(6), 608–636.

  20. Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of competence and motivation (pp. 105–121). New York: Guilford Press.

  21. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J., & Midgley, C. (1983). Expectancies, values and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motives (pp. 75–146). San Francisco: Freeman.

  22. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132.

  23. Eccles, J. S., Wigfield, A., & Schiefele, U. (1998). Motivation to succeed. In W. Damon & N. Eisenberg (Eds.), Handbook of child psychology: Social, emotional, and personality development (vol. 3, 5th ed., pp. 1017–1095). Hoboken: Wiley.

  24. Evers, W. J., Brouwers, A., & Tomic, W. (2002). Burnout and self-efficacy: A study on teachers’ beliefs when implementing an innovative educational system in the Netherlands. British Journal of Educational Psychology, 72(2), 227–243.

  25. Farmer, J. A., Buckmaster, A., & LeGrand, B. (1992). Cognitive apprenticeship: Implications for continuing professional education. New Directions for Adult and Continuing Education, 1992(55), 41–49.

  26. Feather, N. T. (1992). Values, valences, expectations, and actions. Journal of Social Issues, 48(2), 109–124.

  27. Felbrich, A., Kaiser, G., & Schmotz, C. (2014). The cultural dimension of beliefs: An investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries. In S. Blömeke, F. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 209–230). Dordrecht: Springer.

  28. Felmer, P., Lewin, R., Martínez, S., Reyes, C., Varas, L., Chandía, E., . . . Ortíz, A. (2014). Primary mathematics standards for pre-service teachers in Chile: A resource book for teachers and educators (Series on Mathematics Education, Vol. 9). Hackensack: World Scientific Printers.

  29. Felmer, P., & Perdomo-Díaz, J. (2016). Novice Chilean secondary mathematics teachers as problem solvers. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds), Posing and solving mathematical problems (pp. 287–308). Cham: Springer International Publishing.

  30. Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. Contemporary Educational Psychology, 41, 232–244.

  31. Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50.

  32. Grootenboer, P., & Marshman, M. (2016). The affective domain, mathematics, and mathematics education. In P. Grootenboer & M. Marshman (Eds.), Mathematics, affect and learning (pp. 13–33). Singapore: Springer.

  33. Guskey, T. R. (2002). Professional development and teacher change. Teachers and Teaching, 8(3), 381–391.

  34. Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47–57.

  35. Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation modelling: Guidelines for determining model fit. Electronic Journal of Business Research Methods, 6(1), 53–60.

  36. Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65–94.

  37. Kang, M., & Byun, H. P. (2001). A conceptual framework for a web-based knowledge construction support system. Educational Technology, 41(4), 48–53.

  38. Keys, C. W., & Bryan, L. A. (2001). Co-constructing inquiry-based science with teachers: Essential research for lasting reform. Journal of Research in Science Teaching, 38(6), 631–645.

  39. Kline, R. B. (2010). Principles and practice of structural equation modeling (3rd ed.). New York: Guilford Press.

  40. Leroy, N., Bressoux, P., Sarrazin, P., & Trouilloud, D. (2007). Impact of teachers’ implicit theories and perceived pressures on the establishment of an autonomy supportive climate. European Journal of Psychology of Education, 22(4), 529–545.

  41. Ministry of Education Republic of Chile. (2012). Bases Curriculares Matemática; Ficha Bases Curriculares 2012. Santiago, Chile: Ministerio de Educación. Retrieved from

  42. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Retrieved from

  43. Organisation for Economic Co-operation and Developmen. (2012). Development co-operation report 2012. Paris, France: OECD Publishing.

  44. Peters, E. E. (2010). Shifting to a student-centered science classroom: An exploration of teacher and student changes in perceptions and practices. Journal of Science Teacher Education, 21(3), 329–349.

  45. Polya, G. (1945). How to solve it (2nd ed., 1957). Princeton: Princeton University Press.

  46. Polya, G. (Ed.). (1981). Mathematical discovery: On understanding, learning, and teaching problem solving (Combined ed.). New York: Wiley.

  47. Powell-Moman, A. D., & Brown-Schild, V. B. (2011). The influence of a two-year professional development institute on teacher self-efficacy and use of inquiry-based instruction. Science Educator, 20(2), 47–53.

  48. Prawat, R. S. (1992). Teachers’ beliefs about teaching and learning: A constructivist perspective. American Journal of Education, 100(3), 354–395.

  49. Preiss, D., Larraín, A., & Valenzuela, S. (2011). Discurso y pensamiento en el aula matemática Chilena [Discourse and thought in Chilean math classroom]. Psykhe, 20(2), 131–146.

  50. Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550–576.

  51. Ruffinelli, A. (2016). Ley de desarrollo profesional docente en Chile: de la precarización sistemática a los logros, avances y desafíos pendientes para la profesionalización [Law on teacher professional development: From systematic precariousness to the achievements, the advances, and the remaining challenges for professionalization]. Estudios Pedagógicos, 42(4), 261–279.

  52. Sass, D. A., & Smith, P. L. (2006). The effects of parceling unidimensional scales on structural parameter estimates in structural equation modeling. Structural Equation Modeling, 13(4), 566–586.

  53. Schiefele, U., & Schaffner, E. (2015). Teacher interests, mastery goals, and self-efficacy as predictors of instructional practices and student motivation. Contemporary Educational Psychology, 42, 159–171.

  54. Schmeisser, C., Krauss, S., Bruckmaier, G., Ufer, S., & Blum, W. (2013). Transmissive and constructivist beliefs of in-service mathematics teachers and of beginning university students. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics (pp. 51–67). Rotterdam: Sense.

  55. Schoenfeld, A. H. (1999). Models of the teaching process. The Journal of Mathematical Behavior, 18(3), 243–261.

  56. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226.

  57. Swan, M. (2006). Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), 58–70.

  58. Tang, S. J., & Hsieh, F. J. (2014). The cultural notion of teacher education: Future lower secondary teachers’ beliefs on the nature of mathematics, the learning of mathematics and mathematics achievement. In S. Blömeke, F. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 231–253). Dordrecht: Springer.

  59. Tatto, M. T., Rodríguez, M., Ingvarson, L., Rowley, G., Maeda, Y., & Byun, S. Y. (2013). Development of the TEDS-M survey questionnaires. In M. T. Tatto (Ed.), Technical report of The Teacher Education and Development Study in Mathematics (TEDS-M) policy, practice, and readiness to teach primary and secondary mathematics in 17 countries (pp. 47–70). Amsterdam: International Association for the Evaluation of Educational Achievement (IEA).

  60. Thompson, A. G. (1985). Teachers’ conceptions of mathematics and the teaching of problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 281–294). Hillsdale: Erlbaum.

  61. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.

  62. Törner, G., Schoenfeld, A. H., & Reiss, K. M. (2007). Problem solving around the world: Summing up the state of the art. ZDM, 39(5–6), 353–353.

  63. Tschannen-Moran, M., & Hoy, A. W. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17(7), 783–805.

  64. Wigfield, A., Tonks, S., & Klauda, S. L. (2009). Expectancy-value theory. In K. R. Wentzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 55–75). New York: Routledge Taylor & Francis Group.

Download references


The authors are thankful to the ARPA team—mentors, teachers, and researchers, specially Dr Lisa Darragh—for their support and interest in this work.

Funding Information

Funding from FONDEF ID14I20338 and PIA-CONICYT Basal Funds for Centers of Excellence Project FB0003 is gratefully acknowledged. VG thanks the CONICYT-PCHA/Doctorado Nacional/2013 21130684. FS is also grateful to the support of CONICYT/Fondecyt Postdoctoral Project 3170673.

Author information

Correspondence to Farzaneh Saadati.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Saadati, F., Cerda, G., Giaconi, V. et al. Modeling Chilean Mathematics Teachers’ Instructional Beliefs on Problem Solving Practices. Int J of Sci and Math Educ 17, 1009–1029 (2019).

Download citation


  • Classroom practices
  • Instructional beliefs
  • Mathematics problem solving
  • Self-efficacy
  • Structural equation modeling
  • Value of problem solving