# A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs

## Abstract

The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.

### Keywords

Mathematics Teacher education Teacher beliefs Teacher change Teacher knowledge### References

- Anderson, R., Green, M., & Loewen, P. (1988). Relationships among teachers’ and students’ thinking skills, sense of efficacy, and student achievement.
*The Alberta Journal of Educational Research,**34*(2), 148–165.Google Scholar - Ball, D. L. (1988).
*Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education*. Unpublished doctoral dissertation, Michigan State University, East Lansing.Google Scholar - Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education.
*The Elementary School Journal,**90*(4), 449–466. doi:10.1086/461626.CrossRefGoogle Scholar - Ball, D. L. (1991). Research on teaching mathematics: Making subject matter part of the equation. In J. Brophy (Ed.),
*Advances in research on teaching*(Vol. 2, pp. 1–48). Greenwich, CT: JAI Press.Google Scholar - 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 - Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change.
*Psychological Review,**84*(2), 191–215. doi:10.1037/0033-295X.84.2.191.CrossRefGoogle Scholar - Battista, M. T. (1994). Teacher beliefs and the reform movement in mathematics.
*Phi Delta Kappan,**75*(6), 462–470.Google Scholar - Carpenter, T. P., & Fennema, E. (1991).
*Integrating research on teaching and learning mathematics*. Albany: State University of New York Press.Google Scholar - Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999).
*Children’s mathematics: Cognitively guided instruction*. Portsmouth, NH: Heinemann.Google Scholar - Carpenter, T. P., Franke, M. L., & Levi, L. (2003).
*Thinking mathematically: Integrating arithmetic & algebra in elementary school*. Portsmouth, NH: Heinemann.Google Scholar - Clark, C. M., & Peterson, P. L. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.),
*Handbook of research on teaching*(3rd ed., pp. 255–296). New York: Macmillan.Google Scholar - Coladarci, T. (1992). Teachers’ sense of efficacy and commitment to teaching.
*Journal of Experimental Education,**60*, 323–337.Google Scholar - Dean, C. (undated).
*Content validity: Mapping the items from the A04 and B04 forms to the NCTM standards*. Unpublished manuscript, University of Michigan, Ann Arbor.Google Scholar - Dewey, J. (1933).
*How we think: A restatement of the relation of reflective thinking to the educative process*. Boston: Heath.Google Scholar - Enochs, L. G., Smith, P. L., & Huinker, D. (2000). Establishing factorial validity of the mathematics teaching efficacy beliefs instrument.
*School Science and Mathematics,**100*, 194–203.Google Scholar - Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction.
*Journal for Research in Mathematics Education,**27*, 404–434. doi:10.2307/749875.CrossRefGoogle Scholar - 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.Google Scholar - Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (1993). Using children’s knowledge in instruction.
*American Educational Research Journal,**30*(3), 403–434.Google Scholar - Grossman, P. (1990).
*The making of a teacher: Teacher knowledge and teacher education*. New York: Teachers College Press.Google Scholar - Guskey, T. R. (1986). Staff development and the process of teacher change.
*Educational Researcher,**15*(5), 5–12.Google Scholar - Harper, N. W., & Daane, C. J. (1998). Causes and reduction of math anxiety in preservice elementary teachers.
*Action in Teacher Education,**19*(4), 29–38.Google Scholar - Hart, L. (2002). Preservice teachers’ beliefs and practice after participating in an integrated content/methods course.
*School Science and Mathematics,**102*, 4–14.Google Scholar - Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety.
*Journal for Research in Mathematics Education,**21*, 33–46. doi:10.2307/749455.CrossRefGoogle Scholar - Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, G. W. Martin, & D. Schifter (Eds.),
*A research companion to principles and standards for school mathematics*(pp. 5–23). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching.
*The Elementary School Journal,**105*(1), 11–30. doi:10.1086/428763.CrossRefGoogle Scholar - Hoy, A. W. (2004). The educational psychology of teacher efficacy.
*Educational Psychology Review,**16*, 153–176. doi:10.1023/B:EDPR.0000026711.15152.1f.CrossRefGoogle Scholar - Hoy, A. W., & Woolfolk, A. E. (1990). Socialization of student teachers.
*American Educational Research Journal,**27*, 279–300.Google Scholar - Huinker, D., & Madison, S. K. (1997). Preparing efficacious elementary teachers in science and mathematics: The influence of methods courses.
*Journal of Science Teacher Education,**8*(2), 107–126. doi:10.1023/A:1009466323843.CrossRefGoogle Scholar - Karp, K. S. (1991). Elementary school teachers’ attitudes towards mathematics: The impact on students’ autonomous learning skills.
*School Science and Mathematics,**91*, 265–270.Google Scholar - Lortie, D. (1975).
*Schoolteacher: A sociological study*. Chicago: University of Chicago Press.Google Scholar - Ma, L. (1999a).
*Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States*. Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Ma, X. (1999b). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics.
*Journal for Research in Mathematics Education,**30*, 520–541. doi:10.2307/749772.CrossRefGoogle Scholar - 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.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct.
*Review of Educational Research,**62*(1), 307–332.Google Scholar - Peterson, P. L., Fennema, E., Carpenter, T., & Loef, M. (1989). Teachers’ pedagogical content beliefs in mathematics.
*Cognition and Instruction,**6*, 1–40. doi:10.1207/s1532690xci0601_1.CrossRefGoogle Scholar - Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.),
*Second handbook of research on mathematics teaching and learning*(pp. 257–315). United States: Information Age Publishing.Google Scholar - Plourde, L. A. (2002). The influence of student teaching on preservice elementary teacher’s science self-efficacy and outcome expectancy beliefs.
*Journal of Instructional Psychology,**29*, 245–253.Google Scholar - Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data.
*Journal of Counseling Psychology,**19*, 551–554. doi:10.1037/h0033456.CrossRefGoogle Scholar - Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula, T. J. Buttery, & E. Guyton (Eds.),
*Handbook of research on teacher education*(2nd ed., pp. 102–119). New York: Simon & Schuster Macmillan.Google Scholar - Riggs, I. M., & Enochs, L. G. (1990). Toward the development of an elementary teachers’ science teaching efficacy belief instrument.
*Science Education,**74*, 625–637. doi:10.1002/sce.3730740605.CrossRefGoogle Scholar - Romberg, T., & Carpenter, T. (1986). Research on teaching and learning mathematics: Two disciplines of scientific inquiry. In M. C. Wittrock (Ed.),
*Handbook of research on teaching*(3rd ed., pp. 850–873). New York: Macmillan.Google Scholar - Schifter, D., Bastable, V., & Russell, S. J. (with Cohen, S, Lester, J. B., & Yaffee, L.). (1999a).
*Building a system of tens: Casebook*(Developing mathematical ideas: Number and operations, part 1. A collaborative project by the staff and participants of Teaching to the Big Ideas). Parsippany, NJ: Dale Seymour.Google Scholar - Schifter, D., Bastable, V., & Russell, S. J. (with Yaffee, L., Lester, J. B., & Cohen, S). (1999b).
*Making meaning for operations: Casebook*(Developing mathematical ideas: Number and operations, part 2. A collaborative project by the staff and participants of Teaching to the Big Ideas). Parsippany, NJ: Dale Seymour.Google Scholar - Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching.
*Educational Researcher,**15*(2), 4–14.Google Scholar - Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform.
*Harvard Educational Review,**57*(1), 1–22.Google Scholar - Siedel, H., & Hill, H. (2003).
*Content validity: Mapping SII/LMT mathematics items onto NCTM and California standards*. Ann Arbor: Unpublished manuscript, University of Michigan.Google Scholar - Smith, J. P. (1996). Efficacy and teaching mathematics by telling: A challenge for reform.
*Journal for Research in Mathematics Education,**27*, 387–402. doi:10.2307/749874.CrossRefGoogle Scholar - Smith, S. Z., Smith, M. E., & Williams, S. R. (2005). Elaborating a change process model for elementary mathematics teachers’ beliefs and practices.
*Current Issues in Education, 8*(19). Retrieved February 27, 2006 from http://cie.asu.edu/volume8/index.html . - Spradley, J. P. (1979).
*The ethnographic interview*. Orlando, FL: Harcourt Brace Jovanovich.Google Scholar - Suinn, R. M., Edie, C. A., Nicoletti, J., & Spinelli, P. R. (1972). The MARS, a measure of mathematics anxiety: Psychometric data.
*Journal of Clinical Psychology,**28*, 373–375. doi:10.1002/1097-4679(197207)28:3+<373::AID-JCLP2270280320>3.0.CO;2-C.CrossRefGoogle Scholar - Swetman, D. (1994). Fourth-grade math: The beginning of the end?
*Reading Improvement,**31*, 173–176.Google Scholar - TERC. (1998).
*Investigations in number, data, and space*. White Plains, NY: Dale Seymour Publications.Google Scholar - Thompson, A. (1992). Teacher’s 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.Google Scholar - Tobias, S. (1978).
*Overcoming math anxiety*. New York: W. W. Norton and Company.Google Scholar - Tooke, D. J., & Lindstrom, L. C. (1998). Effectiveness of a mathematics methods course in reducing math anxiety of preservice elementary teachers.
*School Science and Mathematics,**98*, 136–139.CrossRefGoogle Scholar - Utley, J., Moseley, C., & Bryant, R. (2005). The relationship between science and mathematics teaching efficacy of preservice elementary teachers.
*School Science and Mathematics,**105*(2), 82–88.Google Scholar - Vacc, N. N., & Bright, G. W. (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking.
*Journal for Research in Mathematics Education,**30*, 89–110. doi:10.2307/749631.CrossRefGoogle Scholar - Vinson, B. M. (2001). A comparison of preservice teachers’ mathematics anxiety before and after a methods class emphasizing manipulatives.
*Early Childhood Education Journal,**29*, 89–94. doi:10.1023/A:1012568711257.CrossRefGoogle Scholar - Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development: The role of beliefs. In G. Leder, E. Pehkonen, & G. Toerner (Eds.),
*Beliefs: A hidden variable in mathematics education?*(pp. 127–148). Dordrecht, The Netherlands: Kluwer Academic Press.Google Scholar - Wilson, S. M., Shulman, L. S., & Richert, A. (1987). “150 different ways of knowing”: Representations of knowledge in teaching. In J. Calderhead (Ed.),
*Exploring teacher thinking*(pp. 104–124). Sussex, UK: Holt, Rinehart and Winston.Google Scholar - Wood, E. F. (1988). Math anxiety and elementary teachers: What does the research tell us?
*For the Learning of Mathematics,**8*, 8–13.Google Scholar