Journal of Mathematics Teacher Education

, Volume 11, Issue 2, pp 139–164 | Cite as

The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices



This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.


Teacher mathematics attitudes Teacher beliefs Teacher mathematics content knowledge Instruction 


  1. Adler, J., Ball, D. L., Krainer, K., Lin, F. L., & Novatna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educational Studies in Mathematics, 60, 359–381.CrossRefGoogle Scholar
  2. American Council on Education (1990). To touch the future. Transforming the way teachers are taught. Washington, DC: American Council on Education. Retrieved December 22, 2006, from:
  3. Anderson, J. R. (2005). Cognitive psychology and its implications (6th ed.). New York, NY: Worth Publishers.CrossRefGoogle Scholar
  4. Anderson, J., White, P., & Sullivan, P. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem-solving beliefs and practices. Mathematics Education Research Journal, 17(2), 9–38.Google Scholar
  5. Arbuckle, J. L., & Worthke, W. (1995). Amos 4.0 User’s Guide. Chicago, IL: SmallWaters Corporation.Google Scholar
  6. Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy: Final report. London: King’s College, London.Google Scholar
  7. Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: A proposed system and its control processes. In K. Spence, & J. Spence (Eds.), The psychology of learning and motivation (Vol. 2, pp. 89–195). New York: Academic Press.Google Scholar
  8. Australian Education Council (1990). A national statement on mathematics for Australian schools. Canberra: Curriculum Corporation.Google Scholar
  9. Ball, D. L. (1990a). The mathematical understanding that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449–466.CrossRefGoogle Scholar
  10. Ball, D. L. (1990b). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144.CrossRefGoogle Scholar
  11. Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the equation. In J. Brophy (Ed.), Advances in research on teaching (Vol. 2, pp. 1–48). Greenwich, CT: JAI Press Inc.Google Scholar
  12. Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). Washington, DC: American Educational Research Association.Google Scholar
  13. Baroody, A. J., & Coslick, R. T. (1998). Fostering children’s mathematical power: An investigative approach to K-8 mathematics instruction. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  14. Begle, E. G. (1979). Critical variables in mathematics education: Findings from a survey of the empirical literature. Washington, DC: Mathematical Association of American and National Council of Teacher of Mathematics.Google Scholar
  15. Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238–246.CrossRefGoogle Scholar
  16. Beswick, K. (2006). Changes in preservice teachers’ attitudes and beliefs: The net impact of two mathematics education units and intervening experiences. School Science and Mathematics, 106(1), 36–47.Google Scholar
  17. Bishop, A. J. (2001). What values do you teach when you teach mathematics? Teaching Children Mathematics, 7(6), 346–349.Google Scholar
  18. Bishop, A. J. (1991). Mathematical enculturation: A cultural perspective on mathematics education. Boston, MA: Kluwer Academic Publishers.Google Scholar
  19. Borasi, R. (1992). Learning mathematics through inquiry. Portsmouth, NH: Heinemann.Google Scholar
  20. Borasi, R., Fonzi, J., Smith, C. F., & Rose, B. J. (1999). Beginning the process of rethinking mathematics instruction: A professional development program. Journal of Mathematics Teacher Education, 2(1), 49–78.CrossRefGoogle Scholar
  21. Brand, B. R., & Wilkins, J. L. M. (2007). Using self-efficacy as a construct for evaluating elementary science and mathematics methods courses. Journal of Science Teacher Education, 18(2), 297–317.CrossRefGoogle Scholar
  22. Brown, C. A., & Cooney, T. J. (1982). Research on teacher education: A philosophical orientation. Journal of Research and Development in Education, 15(4), 13–18.Google Scholar
  23. Bush, W. S. (1989). Mathematics anxiety in upper elementary school teachers. School Science and Mathematics, 89(6), 499–509.Google Scholar
  24. Byrne, B. M. (2001). Structural equation modeling with AMOS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  25. Cady, J., Meier, S. L., Lubinski, C. A. (2006). The mathematical tale of two teachers: A longitudinal study relating mathematics instructional practices to level of intellectual development. Mathematics Education Research Journal, 18(1), 3–26.Google Scholar
  26. Cobb, P., & McClain, K. (2006). Guiding inquiry-based math learning. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 171–185). New York, NY: Cambridge University Press.Google Scholar
  27. Cooney, T. J. (1985). A beginning teachers’ view of problem solving. Journal for Research in Mathematics Education, 16, 324–336.CrossRefGoogle Scholar
  28. Cooney, T. J., & Wilson, M. R. (1993). Teachers’ thinking about functions: Historical and research perspectives. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions. Hillsdale, N.J.: Lawrence Erlbaum Associates.Google Scholar
  29. Czerniak, C. M., & Schriver, M. (1994). An examination of preservice science teachers’ beliefs and behaviors as related to self-efficacy. Journal of Science Teacher Education, 5(3), 77–86.CrossRefGoogle Scholar
  30. Deng, Z. (1995). Estimating the reliability of the teacher questionnaire used in the teacher education and learning to teach (TELT) study. East Lansing, Michigan: Michigan State Univeristy, National Center for Research on Teacher Learning.Google Scholar
  31. Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33.CrossRefGoogle Scholar
  32. Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan Publishing Company.Google Scholar
  33. Gilbert, R. K., & Bush, W. S. (1988). Familiarity, availability, and use of manipulative devices in mathematics at the primary level. School Science and Mathematics, 88(6), 459–469.Google Scholar
  34. Gonzalez, E. J., & Smith, T. A. (Eds.) (1997). User’s guide for the TIMSS international database (primary and middle school years, 1995 assessment): Supplement 2. Chestnut, Hill, MA: Boston College.Google Scholar
  35. Grossman, P. L., Wilson, A. M., & Shulman, L. S. (1989). Teachers of substance: Subject matter knowledge for teaching. In M. C. Reynolds (Ed.), Knowledge base for the beginning teacher (pp. 23–36). New York: Pergamon Press.Google Scholar
  36. Guskey, T. R. (1988). Teacher efficacy, self-concept, and attitudes toward the implementation of instructional innovation. Teaching & Teacher Education, 4(1), 63–69.CrossRefGoogle Scholar
  37. Hatfield, M. (1994). Use of manipulative devices: Elementary school cooperating teachers self-report. School Science and Mathematics, 94(6), 303–309.Google Scholar
  38. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.Google Scholar
  39. Herbal-Eisenmann, B. A., Lubienski, S., & Id-Deed, L. (2006). Reconsidering the study of mathematics instruction practices: the importance of curricular context in understanding local and global teacher change. Journal of Mathematics Teacher Education, 9, 313–345.CrossRefGoogle Scholar
  40. Horizon Research (2000). Local systemic change: 1999–2000 core evaluation data collection manual. Chapel Hill, NC: Horizon Research, Inc.Google Scholar
  41. Hoyle, R. H. (1995). The structural equation modeling approach: Basic concepts and fundamental issues. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 1–15). Thousand Oaks, CA: Sage.Google Scholar
  42. International Association for the Evaluation of Educational Achievement (1998). User’s guide for the third international mathematics and science study (TIMSS) and U.S. augments data files: Appendix, U. S. Questionnaires. Chestnut Hill, MA: TIMSS Study Center.Google Scholar
  43. Jarrett, D. (1997). Inquiry strategies for science and mathematics learning: It’s just good teaching. Portland, OR: Northwest Regional Educational Laboratory.Google Scholar
  44. Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. Washington, DC: Falmer Press.Google Scholar
  45. Karp, K. S. (1991). Elementary school teachers’ attitudes toward mathematics: The impact on students’ autonomous learning skills. School Science and Mathematics, 91(6), 265–270.Google Scholar
  46. Kelly, W. P., & Tomhave, W. K. (1985). A study of math anxiety/math avoidance in preservice elementary teachers. Arithmetic Teacher, 32(5), 51–53.Google Scholar
  47. Kennedy, M. M., Ball, D. L., & McDiarmid, G. W. (1993). A study package of examining and tracking changes in teachers’ knowledge. East Lansing, Michigan: Michigan State University, The National Center for Research on Teacher Education (ERIC document Reproduction Service No. ED359170).Google Scholar
  48. Kloosterman, P., & Harty, H. (1987). Current teaching practices in science and mathematics in Indiana elementary schools. Final report. Bloomington, IN: Indiana University (ERIC document Reproduction Service No. ED285772).Google Scholar
  49. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.Google Scholar
  50. Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Journal of Mathematics Teacher Education, 9(1), 91–102.CrossRefGoogle Scholar
  51. Leder, G. C., Pehkonen, E., & Torner, G. (Eds.). (2002). Beliefs: A hidden variable in mathematics education. Netherlands: Kluwer Academic Publishers.Google Scholar
  52. Lloyd, G. M., & Wilson, M. (1998). Supporting innovation: The impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29, 248–274.CrossRefGoogle Scholar
  53. Lloyd, G. M. (2002). Mathematics teachers’ beliefs and experiences with innovative curriculum materials. The role of curriculum in teacher development. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.). Beliefs: A hidden variable in mathematics education (pp. 149–159). Netherlands: Kluwer Academic Publishers.Google Scholar
  54. Lloyd, G. M. (1999). Two teachers’ conceptions of a reform curriculum: Implications for mathematics teacher development. Journal of Mathematics Teacher Education, 2, 227–252.CrossRefGoogle Scholar
  55. Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics Education, 28(1), 26–47.CrossRefGoogle Scholar
  56. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematic in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  57. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: MacMillan Publishing Company.Google Scholar
  58. Mewborn, D. (2001). Teachers content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Teacher Education and Development, 3, 28–36.Google Scholar
  59. Miller, J. D., Kimmel, L., Hoffer, T. B., & Nelson, C. (2000). Longitudinal study of American youth: User’s manual. Chicago, IL: International Center for the Advancement of Scientific Literacy, Northwestern University.Google Scholar
  60. Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13(2), 125–145.CrossRefGoogle Scholar
  61. National Council of Teacher of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.Google Scholar
  62. National Council of Teacher of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  63. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19, 317–328.CrossRefGoogle Scholar
  64. Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(1), 307–332.Google Scholar
  65. Quinn, R. J. (1997). Effects of mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. Journal of Educational Research, 92(2), 108–113.CrossRefGoogle Scholar
  66. 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.CrossRefGoogle Scholar
  67. Rech, J., Hartzell, J., & Stephens, L. (1993). Comparisons of mathematical competencies and attitudes of elementary education majors with established norms of a general college population. School Science and Mathematics, 93(3), 141–44.Google Scholar
  68. Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (pp. 102–119). New York: Simon & Schuster.Google Scholar
  69. Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.CrossRefGoogle Scholar
  70. Second International Mathematics Study (1995). Technical report IV: Instrument book. Urbana, IL: University of Illinois.Google Scholar
  71. Steiger, J. H. & Lind, J. C. (1980, June). Statistically based tests for the number of common factors. Paper presented at the Psychometric Society Annual Meeting, Iowa City, IA.Google Scholar
  72. Szydlik, J. E., Szydlik, S. D., Benson, S. R. (2003). Exploring changes in pre-service elementary teachers’ mathematical beliefs. Journal of Mathematics Teacher Education, 6, 253–279.CrossRefGoogle Scholar
  73. Teague, P. T., & Austin-Martin, G. G. (1981). Effects of a mathematics methods course on prospective elementary school teachers’ math attitudes, math anxiety and teaching performance. Paper presented at the Annual Meeting of the Southwest Educational Research Association, Dallas, TX (ERIC Document Reproduction Service No. ED200557).Google Scholar
  74. Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–127.CrossRefGoogle Scholar
  75. 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 Publishing Company.Google Scholar
  76. TIMSS (1998a). TIMSS mathematics items for the middle school years: Released set for population 2 (seventh and eighth grades). Chestnut, Hill, MA: Boston College.Google Scholar
  77. TIMSS (1998b). TIMSS mathematics and science items for the final year of secondary school: Released item set for population 3. Chestnut Hill, MA: Boston College.Google Scholar
  78. Trice, A. D., & Ogden, E. P. (1987). Correlates of mathematics anxiety in first-year elementary school teachers. Educational Research Quarterly, 11(3), 2–4.Google Scholar
  79. Weiss, I. R. (1994). A profile of science and mathematics education in the United States, 1993. Chapel Hill, NC: Horizon Research, Inc.Google Scholar
  80. Wilkins, J. L. M., & Brand, B. R. (2004). Change in preservice teachers’ beliefs: An evaluation of a mathematics methods course. School Science and Mathematics, 104(5), 226–232.CrossRefGoogle Scholar
  81. Wilson, M., & Cooney, T. J. (2002). Mathematics teacher change and development. The role of beliefs. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 127–147). Netherlands: Kluwer Academic Publishers.Google Scholar
  82. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Teaching and LearningVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations