# Mathematics anxiety in preservice teachers: Its relationship to their conceptual and procedural knowledge of fractions

- 481 Downloads
- 8 Citations

## Abstract

The objective of the present study was to examine the relationship between mathematics anxiety and the procedural and conceptual knowledge of fractions in prospective teachers. Thirty-two preservice teachers enrolled in an elementary mathematics methods course were administered the Revised Mathematics Anxiety Rating Scale (RMARS, Baloğlu, 2002). Procedural and conceptual knowledge of fractions was assessed with a validated paper and pencil test (Saxe, Gearhart, & Nasir, 2001) and with four additional problems created by the researchers. Results indicated that as mathematics anxiety scores increased, scores on the validated measure of procedural knowledge of fractions decreased. The same relationship was found between the RMARS and the validated measure of conceptual knowledge. The findings provide some insight on the cognitive and pedagogical factors associated with mathematics anxiety in the preservice teacher population, underscoring the importance of facilitating their proficiency in both mathematical procedures and concepts.

## Keywords

Preservice Teacher Prospective Teacher Mathematical Knowledge Conceptual Knowledge Procedural Knowledge## Preview

Unable to display preview. Download preview PDF.

## References

- Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences.
*Current Directions in Psychological Science, 11*(5), 181–185.CrossRefGoogle Scholar - Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance.
*Journal of Experimental Psychology: General, 130*(2), 224–237.CrossRefGoogle Scholar - Ashcraft, M. H., Kirk, E. P., & Hopko, D. (1998). On the cognitive consequences of mathematics anxiety. In C. Donlan (Ed.),
*The development of mathematical skills*(pp. 175–196). Hove, England: Psychology Press.Google Scholar - Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division.
*Journal for Research in Mathematics Education, 21*(2), 132–144.CrossRefGoogle Scholar - Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.),
*Multiple perspectives on mathematics teaching and learning*(pp. 83–104). Westport, CT: Ablex.Google Scholar - Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide?
*American Educator, 29*(3), 14–46.Google Scholar - Ball, D. L., & Rowan, B. (2004). Introduction: Measuring instruction.
*The Elementary School Journal, 105*(1), 3–10.CrossRefGoogle Scholar - Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?”
*Journal of Teacher Education, 59*(5), 389–407.CrossRefGoogle Scholar - Baloğlu, M. (2002). Construct and concurrent validity and internal consistency, split-half, and parallel-model reliability of the revised mathematics rating scale.
*Dissertation Abstracts International, 63*, 6-B. (UMI No. 3058162)Google Scholar - Baloğlu, M., & Koçak, R. (2006). A multivariate investigation of the differences in mathematics anxiety.
*Personality and Individual Differences, 40*, 1325–1335.CrossRefGoogle Scholar - Battista, M. T. (1986). The relationship of mathematics anxiety and mathematical knowledge to the learning of mathematical pedagogy by preservice elementary teachers.
*School Science and Mathematics, 86*(1), 10–19.CrossRefGoogle Scholar - Behr, M. J., Lesh, R., Post, T. R., & Silver, E. (1983). Rational-number concepts. In R. Lesh & M. Landau (Eds.),
*Acquisitions of mathematics concepts and processes*(pp. 91–126). New York: Academic Press.Google Scholar - Bessant, K. C. (1995). Factors associated with types of mathematics anxiety in college students.
*Journal for Research in Mathematics Education, 26*(4), 327–345.CrossRefGoogle Scholar - Bowd, A. D., & Brady, P. H. (2003). Gender differences in mathematics anxiety among preservice teachers and perceptions of their elementary and secondary school experience with mathematics.
*Alberta Journal of Educational Research, 49*(1), 24–36.Google Scholar - Brady, P., & Bowd, A. (2005). Mathematics anxiety, prior experience and confidence to teach mathematics among pre-service education students.
*Teachers and Teaching: Theory and Practice, 11*(1), 37–46.CrossRefGoogle Scholar - Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000).
*How people learn: Brain, mind, experience, and school: Expanded edition*. Washington, DC: National Academy Press.Google Scholar - Cohen, J. (1960). A coefficient of agreement for nominal scales.
*Educational and Psychological Measurement, 20*, 37–46.CrossRefGoogle Scholar - Cohen, J. (1988).
*Statistical power analysis*(2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar - Conrad, K. S., & Tracy, D. M. (1992).
*Lowering preservice teachers’ math anxiety through an experience-based mathematics methods course*. (ERIC Document Reproductions Service No. ED355099)Google Scholar - Cooper, S. E., & Robinson, D. A. G. (1991). The relationship of mathematics selfefficacy beliefs to mathematics anxiety and performance.
*Measurement and Evaluation in Counseling and Development, 24*(1), 4–13.Google Scholar - D’Ambrosio, B. S., & Mewborn, D. S. (1994). Children’s construction of fractions and their implications for classroom instruction.
*Journal of Research in Childhood Education, 8*(2), 150–161.CrossRefGoogle Scholar - Eysenck, M. W., & Calvo, M. G. (1992). Anxiety and performance: The processing efficiency theory.
*Cognition and Emotion, 6*, 409–434.CrossRefGoogle Scholar - Faust, M. W., Ashcraft, M. H., & Fleck, D. E. (1996). Mathematics anxiety effects in simple and complex addition.
*Mathematical Cognition, 2*(1), 25–62.CrossRefGoogle 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 - Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety.
*Journal for Research in Mathematics Education, 21*(1), 33–46.CrossRefGoogle Scholar - Hiebert, J., Carpenter, T. R., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., et al. (1997).
*Making sense: Teaching and learning mathematics with understanding*. Portsmouth, NH: Heinemann.Google Scholar - Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.),
*Conceptual and procedural knowledge: The case of mathematics*(pp. 1–27). Hillsdale, NJ: Erlbaum.Google Scholar - Hiebert, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction.
*Cognition and Instruction, 14*(3), 251–283.CrossRefGoogle Scholar - 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 - Hopko, D. R., Ashcraft, M. H., Gute, J., Ruggiero, K. J., & Lewis, C. (1998). Mathematics anxiety and working memory: Support for the existence of a deficient inhibition mechanism.
*Journal of Anxiety Disorders, 12*(4), 343–355.CrossRefGoogle Scholar - Kazelskis, R. (1998). Some dimensions of mathematics anxiety: A factor analysis across instruments.
*Educational and Psychological Measurement, 58*(4), 623–633.CrossRefGoogle Scholar - 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 - Kilpatrick, J., Swafford, J., & Findell, B. (2001).
*Adding it up: Helping children learn mathematics*. Washington: National Academy Press.Google Scholar - Lefevre, J., Kulak, A. G., & Heymans, S. L. (1992). Factors influencing the selection of university majors varying in mathematical content.
*Canadian Journal of Behavioural Science, 23*(4), 276–289.Google Scholar - Ma, L. (1999).
*Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States*. Mahwah, NJ: Erlbaum.Google Scholar - Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics.
*Journal for Research in Mathematics Education, 30*, 520–540.CrossRefGoogle Scholar - Ma, X., & Xu, J. (2004). The causal ordering of mathematics anxiety and mathematics achievement: A longitudinal panel analysis.
*Journal of Adolescence, 27*, 165–179.CrossRefGoogle Scholar - McLeod, D. B. (1989). The role of affect in mathematical problem solving. In D. B. McLeod and V. M. Adams (Eds.),
*Affect and mathematical problem solving: A new perspective*(pp. 20–36). NY: Springer-Verlag.Google Scholar - McLeod, D. B. (1994). Research on affect and mathematics learning in the JRME: 1970 to the present.
*Journal for Research in Mathematics Education, 25th Anniversary Special Issue, 25*(6), 637–647.Google Scholar - Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrolment intentions and performance in mathematics.
*Journal of Educational Psychology, 82*(1), 60–70.CrossRefGoogle Scholar - Miller, H., & Bichsel, J. (2004). Anxiety, working memory, gender, and math performance.
*Personality and Individual Differences, 37*, 591–606.CrossRefGoogle Scholar - National Commission on Teaching and America’s Future. (1997).
*Doing what matters most: Investing in quality teaching*. New York: Author.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - Osana, H. P., Lacroix, G. L., Rayner, V., Pitsolantis, N., & Ing, W. (2008).
*The role of teachers’ knowledge and classroom practices in the mathematical development of first-grade students*. Poster presented at the Banff International Conference on Behavioural Science, Banff, Alberta, Canada.Google Scholar - Osana, H. P., Lacroix, G. L., Tucker, B. J., & Desrosiers, C. (2006). The role of content knowledge and problem features on preservice teachers’ appraisal of elementary mathematical tasks.
*Journal of Mathematics Teacher Education, 9*(4), 347–380.CrossRefGoogle Scholar - Pellegrino, J. W., Chudowsky, N., & Glaser, R. (2001).
*Knowing what students know: The science and design of educational assessment*. Washington, DC: National Academy Press.Google Scholar - Perkins, D. N. (1999). The many faces of constructivism.
*Educational Leadership, 57*(3), 6–11.Google Scholar - Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data.
*Journal of Counseling Psychology, 19*(6), 551–554.CrossRefGoogle Scholar - Saxe, G. B., Gearhart, M., & Nasir, N. S. (2001). Enhancing students’ understanding of mathematics: A study of three contrasting approaches to professional support.
*Journal of Mathematics Teacher Education, 4*, 55–79.CrossRefGoogle Scholar - Sloan, T., Daane, C. J., & Giesen, J. (2002). Mathematics anxiety and learning styles: What is the relationship in elementary preservice teachers?
*School Science and Mathematics, 102*(2), 84–87.CrossRefGoogle Scholar - Sloan, T. R., Vinson, B., Haynes, J., & Gresham, R. (1997, November).
*A comparison of pre-and post-levels of mathematics anxiety among preservice teacher candidates enrolled in a mathematics methods course*. Paper presented at the annual meeting of the MidSouth Educational Research Association, Memphis, TN.Google Scholar - Star, J. R. (2005). Reconceptualizing procedural knowledge.
*Journal for Research in Mathematics Education, 36*(5), 404–411.Google Scholar - Tabachnick, B. G., & Fidell, L. S. (2001).
*Using multivariate statistics*(4th ed.). Needham Heights, MA: Allyn & Bacon.Google Scholar - Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions.
*Journal for Research in Mathematics Education, 31*(1), 5–25.CrossRefGoogle Scholar - Tirosh, D., Fischbein, E., Graeber, A. O., & Wilson, J. W. (1998). Prospective elementary teachers’ conceptions of rational number. Retrieved October 6, 2006, from http://jwilson.coe.uga.edu/Texts.Folder/Tirosh/Pros.El.Tchrs.htmlGoogle Scholar
- Trice, A. D., & Ogden, E. D. (1986). Correlates of mathematics anxiety in first-year elementary school teachers.
*Educational Research Quarterly, 11*(3), 2–4.Google Scholar - Trujillo, K. M., & Hadfield, O. D. (1999). Tracing the roots of mathematics anxiety through in-depth interviews with preservice teachers.
*College Student Journal, 33*(2), 219–232.Google Scholar - Turner, J. C., Midgley, C., Meyer, D. K., Gheen, M., Anderman, E. M., Kang, Y., et al. (2002). The classroom environment and students’ reports of avoidance strategies in mathematics: A multimethod study.
*Journal of Educational Psychology, 94*(1), 88–106.CrossRefGoogle Scholar - Uusimaki, L., & Nason, R. (2004). Causes underlying pre-service teachers’ negative beliefs and anxieties about mathematics. In M. J. Høines & A. B. Fuglestad (Eds.),
*Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education*(Vol. 4, pp. 369–376). Bergen, Norway: Bergen University.Google Scholar - Vinson, B. (2001). A comparison of preservice teachers’ mathematics anxiety before and after a methods class emphasizing manipulatives.
*Early Childhood Education Journal, 29*(2), 89–94.CrossRefGoogle Scholar - Widmer, C. C., & Chavez, A. (1982). Math anxiety and elementary school teachers.
*Education, 102*(3), 272–276.Google Scholar - Wigfield, A., & Meece, J. L. (1988). Math anxiety in elementary and secondary school students.
*Journal of Educational Psychology, 80*(2), 210–216.CrossRefGoogle Scholar - Wilson, S., & Thornton, S. (2005).
*’I am really not alone in this anxiety’: Bibliotherapy and pre-service primary teachers’ self-image as mathematicians*. Paper presented at the 28th Annual Conference of the Mathematics Education Research Group of Australasia, Melbourne, Australia.Google Scholar - Wood, E. F. (1988). Math anxiety and elementary teachers: What does research tell us?
*For the Learning of Mathematics, 8*(1), 8–13.Google Scholar - Wu, H. (1997).
*On the education of mathematics teachers*. Retrieved from University of California, Berkeley Web site:*http://www.math.berkeley.edu/~wu/*Google Scholar - Wu, H. (2001, Summer). How to prepare students for algebra.
*American Educator*, 1–7.Google Scholar - Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction.
*Educational Studies in Mathematics, 63*(2), 113–121.CrossRefGoogle Scholar