Exploring self-efficacy beliefs within the context of teaching mathematics with concrete models

Mutlu Pişkin Tunç, Erdinç Çakıroğlu, Safure Bulut


The purpose of this study was to investigate pre-service mathematics teachers’ self-efficacy beliefs about using concrete models in teaching mathematics. Participants were 31 junior pre-service middle school mathematics teachers. Six instructional sessions based on using concrete models were carried out during a three week period. Data were collected by a survey on pre-service teachers’ efficacy beliefs about using concrete models and semi-structured interviews. Data analysis demonstrated that the instruction had positive contributions on the pre-service teachers’ self-efficacy beliefs. In addition, results revealed that pre-service teachers had confidence in themselves about using concrete models both as learners and as teachers. Moreover, they believed that using concrete models would have positive consequences in teaching process and students’ learning. However, pre-service teachers had relatively low efficacies about classroom management.


Concrete models; Pre-service mathematics teachers; Self-efficacy beliefs; Teachers’ sense of efficacy

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Aburime, F. E. (2007). How manipulatives affect the mathematics achievement of students in Nigerian schools. Educational Research Quarterly, 31(1), 3-16.

Bakkaloglu, E. (2007). Preservice elementary mathematics teachers’ efficacy beliefs about using manipulatives in teaching mathematics. Unpublished master’s thesis, Middle East Technical University, Ankara.

Bal, P. (2008). The evaluation of new mathematics curriculum in terms of teachers’ perspectives. Journal of Cukurova University Institute of Social Sciences, 17(1), 53-68.

Bandura, A. (1994). Self-efficacy. In V. S. Ramachaudran (Ed.), Encyclopedia of human behavior (Vol. 4, pp. 71-81). New York: Academic Press. (Reprinted in H. Friedman [Ed.], Encyclopedia of mental health. San Diego: Academic Press, 1998).

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W. H. Freeman. Bruner, J. S. (1961). The process of education. Cambridge: Harvard University Press.

Bayram, S. (2004). The effect of instruction with concrete models on eighth grade students’ geometry achievement and attitudes toward geometry. Unpublished master’s thesis, Middle East Technical University, Ankara.

Bruner, J. S. (1961). The process of education. Cambridge: Harvard University Press.

Cakiroglu, E. & Yildiz, B. T. (2007). Turkish preservice teachers’ views about manipulative use in mathematics education. In C. S. Sunal, & M. Kagendo (Eds.), The enterprise of education (pp. 275-289). Information Age Publishing Inc.

Clements, D. H. (1999). Concrete manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.). Thousand Oaks, CA: Sage.

Dienes, Z. (1967). A Theory of mathematics-learning. In F. J. Crosswhite, et al. (Eds.). (1973). Teaching mathematic: Psychology foundations. Worthington, Ohio, Charles A. Jones Pub. Co.

Enoch, L. G., & Riggs, I. M. (1990). Further development of an Elementary Science Teaching Efficacy Belief Instrument: A Pre-service Elementary Scale. School Science and Mathematics, 90(8), 694-706.

Enochs, L. G., Smith, P. L., & Huinker, D. (2000). Establishing factorial validity of the mathematics teaching efficacy beliefs instrument. School Science and Mathematics, 100, 194-202.

Ersoy, Y. (2005). The views of science lyceum mathematics teachers: the media of mathematics teaching and some constraints The Turkish Online Journal of Educational Technology, 4(4), 135-145.

Erşen, N.A. (2014). The effect of mathematics teaching supported with material on 6th student success, attitude, concern and permanency of learning. Unpublished master thesis, Fırat University, Elazığ, Turkey.

Fennema, E. (1972). The relative effectiveness of a symbolic and a concrete model in learning a selected mathematical principle. Journal for Research in Mathematics Education, 3(4), 233-238.

Flener, F. O. (1980). Are concrete activities the “Most Basic” elements in a mathematics program? The Elementary School Journal, 81(2), 97-107.

Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education, New York: McGraw-Hill Inc.

Fuson, K. C., & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21(3), 180-206.

Gibson, S., & Dembo, M. (1984). Teacher efficacy: A construct validation. Journal of Educational Psychology, 76, 569–582.

Gurbuz, R. (2007). Students’ and their teachers’ opinions about the instruction based on the materials on probability subject. Kastamonu Education Journal, 15(1), 259-270.

Heddens, J. W. (1997). Improving mathematics teaching by using manipulatives. Retrieved October 23, 2011, from http://www.fed.cuhk.edu.hk/~fllee/mathfor/ edumath/9706/13hedden.html.

Howard, P., Perry, B., & Tracey, D. (1997). Mathematics and manipulatives: Comparing primary and secondary mathematics teacher’s views. Paper presented at the annual conference of the Australian Association for Research in Education, Brisbane.

Johnson, K. A. (1993). Manipulatives allow everyone to learn mathematics. Contemporary Education, 65(1), 10-11.

Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2006). Do children need concrete instantiations to learn an abstract concept? Proceedings of the XXVIII Annual Conference of the Cognitive Science Society, 1167-1172. Mahwah, NJ: Erlbaum.

Karol, Y. (1991). Manipulatives: Motivating Mathematics. East Lansing, MI: National Center for Research on Teacher Learning. (ERIC Document Reproduction Service No. ED 355 097).

Kul, Ü., Çelik, S., & Aksu, Z. (2018). The Impact of Educational Material Use on Mathematics Achievement: A Meta-Analysis. International Journal of Instruction, 11(4), 303-324.

McNeil, N. M. & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulatives debate. Theory into Practice, 46(4), 309-316.

Ministry of National Education. (2004). İlköğretim matematik dersi öğretim programı 6-8. sınıflar: Öğretim programı ve klavuzu [Elementary mathematics curriculum and guide for grade levels 6 to 8]. Ankara, Turkey: MNE.

Ministry of National Education. (2013; 2017). Ortaokul matematik dersi öğretim programı 5-8. sınıflar: Öğretim programı ve klavuzu [Middle school mathematics curriculum and guide for grade levels 5 to 8]. Ankara, Turkey: MNE.

Moyer, S. P. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197.

National Council of Teachers of Mathematics (2000). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

Nevin, M. L. (1993). I do and understand. Contemporary Education, 65(1), 16-18. Pajares, F. (1996). Self-efficacy beliefs in achievement settings. Review of Educational Research, 66, 543-578.

Pajares, F. (1997). Current Directions in Self-efficacy Research. In M. Maehr & P. R. Pintrich (Eds.). Advances in Motivation and Achievement (Vol. 10, pp.1-49). Greenwich, CT: JAI Press.

Pajares, F. (2002). Overview of social cognitive theory and of self-efficacy. Retrieved September 16, 2011, from http://www.emory.edu/EDUCATION/mfp/eff.html.

Pallant, J. (2007). SPSS survival manual. U.S.A: Open University Press.

Piaget, J. (1950). The psychology of intelligence. London: Routledge & Kegan Paul.

Post, T. (1981). The Role of Manipulative Materials in the Learning of Mathematical Concepts. In Selected Issues in Mathematics Education (pp. 109-131). Berkeley, CA: National Society for the Study of Education and National Council of Teachers of Mathematics, McCutchan Publishing Corporation.

Puncher, L., Taylor, A., O’Donnell, B., & Fick, K. (2008). Teacher learning and mathematics manipulatives: A collective case study about teacher use of manipulatives in elementary and middle school mathematics lessons. School Science and Mathematics 108(7), 313-325.

Silver, E. A., Mesa, V. M., Morris, K. A., Star, J., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46(2), 501-531.

Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 499-505.

Steffe, L.P. (1990). Mathematics curriculum design: A constructivist's perspective. In L.P. Steffe & T. Wood (Eds.) Transforming children's mathematical education: International perspectives (pp. 389-398). Hillsdale, NJ: Erlbaum.

Suydam, M., & Higgins. J. (1977). Activity-based learning in elementary school mathematics. Reston, Virginia: NCTM.

Szendrei, J. (1996). Concrete materials in the classroom. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.). International handbook of mathematics education (pp. 411-434). Dordrecht: Kluwer.

Tschannen-Moran, M., Woolfolk-Hoy, A., & Hoy, W. (1998). Teacher efficacy: Its meaning and measure. Review of Education Research, 68(2), 202–248.

Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18(1), 37-54.

Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson /Allyn and Bacon.

Wheatley, K. F. (2005). The case for reconceptualizing teacher efficacy research. Teaching and Teacher Education, 21, 747-766.


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