Research Article

Relationship between pre-service teachers’ mathematical knowledge for teaching fractions and their teaching practices: What is the role of teacher anxiety?

Charles Kwabena Sie 1 * , Douglas Darko Agyei 1
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1 Department of Mathematics and ICT Education, University of Cape Coast, Cape Coast, GHANA* Corresponding Author
Contemporary Mathematics and Science Education, 4(2), 2023, ep23017, https://doi.org/10.30935/conmaths/13252
Published Online: 08 May 2023, Published: 01 July 2023
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ABSTRACT

This study examined the role of mathematics anxiety in the relationship between pre-service teachers’ (PSTs’) mathematical knowledge for teaching fractions (MKTF) and their teaching practices. The study was based on the mathematics teaching proficiency model that identifies teacher knowledge and productive dispositions as variables that influence teachers’ practice. Data was collected from 171 PSTs using three instruments: mathematical knowledge for teaching fractions test, teaching practices test and mathematics anxiety questionnaire. Based on bi-variate correlation analyses, the results showed significant correlations: between PSTs’ MKTF and their teaching practices, and PSTs’ MKTF and their mathematics anxiety. Multiple regression analyses further showed that PSTs’ MKTF significantly predicted their teaching practices, and that anxiety increased magnitude of regression coefficient associated with MKTF in predicting performance in teaching practices. However, since the increase was insignificant, the study concluded that anxiety does not perform any significant role in the relationship between PSTs’ MKTF and their teaching practices. Thus, the study asserts that to train mathematics teachers in Ghana to proficiently teach mathematics depend on training them to acquire mathematical knowledge for teaching and independent of their anxiety levels. This study has implications for mathematics teacher education and professional development in Ghana.
Keywords: mathematical knowledge for teaching fractions, mathematics anxiety, mathematical task framework, teaching practices, suppressor variable, mathematics teaching proficiency

CITATION (APA)

Sie, C. K., & Agyei, D. D. (2023). Relationship between pre-service teachers’ mathematical knowledge for teaching fractions and their teaching practices: What is the role of teacher anxiety?. Contemporary Mathematics and Science Education, 4(2), ep23017. https://doi.org/10.30935/conmaths/13252

REFERENCES

  1. Abreh, M. K., Owusu, K. A., & Amedahe, F. K. (2018). Trends in performance of WASSCE candidates in the science and mathematics in Ghana: Perceived contributing factors and the way forward. Journal of Education, 198(1), 113-123. https://doi.org/10.1177/0022057418800950
  2. Addae, B. D., & Agyei, D. D. (2018). High school students’ attitudes towards the study of mathematics and their perceived teachers’ teaching practices. European Journal of Educational and Development Psychology, 6(2), 1-14.
  3. 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. https://doi.org/10.1007/s10649-005-5072-6
  4. Anamuah-Mensah, J., & Mereku, D. K. (2005). Ghanaian JSS2 students’ abysmal mathematics achievement in TIMSS 2003: A consequence of the basic school mathematics curriculum. Mathematics Connection, 5(1), 1-13. https://doi.org/10.4314/mc.v5i1.21489
  5. Anamuah-Mensah, J., Mereku, D. K., & Asabere-Ameyaw, A. (2004). Ghanaian junior secondary school students’ achievement in mathematics and science: Results from Ghana’s participation in the 2003 trends in international mathematics and science study. Ministry of Education Youth and Sports.
  6. Arbaugh, F., Lannin, J., Jones, D. L., & Park-Rogers, M. (2006). Examining instructional practices in core-plus lessons: Implications for professional development. Journal of Mathematics Teacher Education, 9(6), 517-550. https://doi.org/10.1007/s10857-006-9019-3
  7. Artzt, A. F., & Armour-Thomas, E. (1999). A cognitive model for examining teachers’ instructional practice in mathematics: A guide for facilitating teacher refection. Educational Studies in Mathematics, 40(3), 211-235. https://doi.org/10.1023/A:1003871918392
  8. Austin, S., Wadlington, E., & Bitner, J. (1992). Effect of beliefs about mathematics on math anxiety and math self-concept in elementary teachers. Education, 112(3), 390-396.
  9. Avcu, R. (2019). Turkish pre-service middle level mathematics teachers’ knowledge for teaching fractions. RMLE Online, 42(9), 1-20. https://doi.org/10.1080/19404476.2019.1681624
  10. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407. https://doi.org/10.1177/0022487108324554
  11. Banilower, E. R., Boyd, S. E., Pasley, J. D., & Weiss, I. R. (2006). Lessons from a decade of mathematics and science reform: A capstone report for the local systemic change through teacher enhancement initiative. Horizon Research, Inc. https://www.horizon-research.com/the-lsc-capstone-report-lessons-from-a-decade-of-mathematics-and-science-reform
  12. 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. https://doi.org/10.1111/j.1949-8594.1986.tb11580.x
  13. Bessant, K. C. (1995). Factors associated with types of mathematics anxiety in college students. Journal for Research in Mathematics Education, 26(4), 327-345. https://doi.org/10.5951/jresematheduc.26.4.0327
  14. Borich, G. D. (2014). Effective teaching methods: research-based practice, 8/E. Pearson.
  15. 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. https://doi.org/10.1080/1354060042000337084
  16. Bryant, M. M. G. (2009). A study of pre-service teachers: Is it really mathematics anxiety? [PhD thesis, University of Massachusetts Amherst].
  17. Charalambous, C. Y. (2008). Preservice teachers’ mathematical knowledge for teaching and their performance in selected teaching practices: Exploring a complex relationship [PhD thesis, University of Michigan].
  18. Charalambous, C. Y. (2015). Working at the intersection of teacher knowledge, teacher beliefs, and teaching practice: A multiple case study. Journal of Mathematics Teacher Education, 18(5), 427-445. https://doi.org/10.1007/s10857-015-9318-7
  19. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. Lawrence Erlbaum.
  20. Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. Routledge. https://doi.org/10.4324/9781315456539
  21. Cole, Y. (2012). Assessing elemental validity: The transfer and use of mathematical knowledge for teaching measures in Ghana. ZDM, 44(3), 415-426. https://doi.org/10.1007/s11858-012-0380-7
  22. Conger, A. J. (1974). A revised definition for suppressor variables: A guide to their identification and interpretation. Educational and Psychological Measurement, 34(1), 35-46. https://doi.org/10.1177/001316447403400105
  23. Courville, T., & Thompson, B. (2001). Use of structure coefficients in published multiple regression articles: b is not enough. Educational & Psychological Measurement, 61, 229-248. https://doi.org/10.1177/0013164401612006
  24. de Groot, A. (1965). Thought and choice in chess. Mouton.
  25. Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13-33. https://doi.org/10.1080/0260747890150102
  26. 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). Macmillan.
  27. Fumador, S. E., & Agyei, D. D. (2018). Students’ errors and misconceptions in algebra: Exploring the impact of remedy using diagnostic conflict and conventional teaching approaches, International Journal of Education, Learning and Development, 6(10), 1-15.
  28. Gresham, G. (2008). Mathematics anxiety and mathematics teacher efficacy in elementary pre-service teachers. Teaching Education, 19(3), 171-184. https://doi.org/10.1080/10476210802250133
  29. Hashimoto-Gotoh, T., Iwabe, N., Tsujimura, A., Takao, K., & Miyakawa, T. (2009). KF-1 ubiquitin ligase: An anxiety suppressor. Frontiers in Neuroscience, 3, 4. https://doi.org/10.3389/neuro.01.004.2009
  30. Haylock, D. (2003) Mathematics explained for primary teachers. Paul Chapman.
  31. Herbst, P. G. (2006). Teaching geometry with problems: Negotiating instructional situations and mathematical tasks. Journal for Research in Mathematics Education, 37(4), 313-347.
  32. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404).
  33. Hill, H. C., Blunk, M., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26, 430-511. https://doi.org/10.1080/07370000802177235
  34. 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. https://doi.org/10.1086/428763
  35. Hinton, P., McMurray, I., & Brownlow, C. (2014). SPSS explained. Routledge. https://doi.org/10.4324/9781315797298
  36. Hoover, M., Mosvold, R., Ball, D. L., & Lai, Y. (2016). Making progress on mathematical knowledge for teaching. The Mathematics Enthusiast, 13(1), 3-34. https://doi.org/10.54870/1551-3440.1363
  37. Horst, P. (1941). The prediction of personnel adjustment. Social Science Research and Council Bulletin, 48, 431-436.
  38. Kelly, W. P., & Tomhave, W. K. (1985). A study of math anxiety/math avoidance in preservice elementary teachers. Arithmetic Teacher, 32(5), 51-53. https://doi.org/10.5951/AT.32.5.0051
  39. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. National Academy Press.
  40. Kogelman, S., & Warren, J. (1978) Mind over math. McGraw Hill.
  41. Kulm, G., & Li, Y. (2009). Curriculum research to improve teaching and learning: National and cross-national studies. ZDM, 41(6), 709. https://doi.org/10.1007/s11858-009-0217-1
  42. Levine, G. (1996). Variability in anxiety for teaching mathematics among pre-service elementary school teachers enrolled in a mathematics course. https://eric.ed.gov/?id=ED398067
  43. Lindner, J. R., Murphy, T. H., & Briers, G. E. (2001). Handling nonresponse in social science research. Journal of Agricultural Education, 42(4), 43-53. https://doi.org/10.5032/jae.2001.04043
  44. Loukas, A., Paulos, S. K., & Robinson, S. (2005). Early adolescent social and overt aggression: Examining the roles of social anxiety and maternal psychological control. Journal of Youth and Adolescence, 34(4), 335-345. https://doi.org/10.1007/s10964-005-5757-2
  45. Lui, A. M., & Bonner, S. M. (2016). Preservice and inservice teachers’ knowledge, beliefs, and instructional planning in primary school mathematics. Teaching and Teacher Education, 56, 1-13. https://doi.org/10.1016/j.tate.2016.01.015
  46. May, D. K. (2009). Mathematics self-efficacy and anxiety questionnaire [PhD thesis, University of Georgia].
  47. McFatter, R. M. (1979). The use of structural equation models in interpreting regression equations including suppressor and enhancer variables. Applied Psychological Measurement, 3, 123-135. https://doi.org/10.1177/014662167900300113
  48. Mereku, D. K. (2012). Quality education, challenges of less endowed schools: The role of the students [Paper presentation]. The 2nd Speech and Prize Given Day Celebration of the Apeguso SHS.
  49. Mischel, W., & Shoda, Y. (1995). A cognitive-affective system theory of personality: reconceptualizing situations, dispositions, dynamics, and invariance in personality structure. Psychological Review, 102(2), 246. https://doi.org/10.1037/0033-295X.102.2.246
  50. MoE. (2017). The national teacher education curriculum framework: The essential elements of initial teacher education. Ministry of Education, Ghana.
  51. Pandey, S., & Elliott, W. (2010). Suppressor variables in social work research: Ways to identify in multiple regression models. Journal of the Society for Social Work and Research, 1(1), 28-40. https://doi.org/10.5243/jsswr.2010.2
  52. Peker, M. (2009). Pre-service teachers’ teaching anxiety about mathematics and their learning styles. EURASIA Journal of Mathematics, Science and Technology Education, 5(4), 335-345. https://doi.org/10.12973/ejmste/75284
  53. Perry, A. B. (2004). Decreasing math anxiety in college students. College Student Journal, 38(2), 321.
  54. Raudenbush, S. W. (2008). Advancing educational policy by advancing research on instruction. American Educational Research Journal, 45(1), 206-230. https://doi.org/10.3102/0002831207312905
  55. Rayner, V., Pitsolantis, N., & Osana, H. (2009). Mathematics anxiety in preservice teachers: Its relationship to their conceptual and procedural knowledge of fractions. Mathematics Education Research Journal, 21(3), 60-85. https://doi.org/10.1007/BF03217553
  56. Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246. https://doi.org/10.3102/00346543075002211
  57. Sabers, D. S., Cushing, K.S., & Berliner, D.C. (1991). Differences among teachers in a task characterized by simultaneity, multidimensionality, and immediacy. American Educational Research Journal, 28, 63-88. https://doi.org/10.3102/00028312028001063
  58. Shechtman, N., Roschelle, J., Haertel, G., & Knudsen, J. (2010). Investigating links from teacher knowledge to classroom practice, to student learning in the instructional system of the middle-school mathematics classroom. Cognition and Instruction, 28(3), 317-359. https://doi.org/10.1080/07370008.2010.487961
  59. Shieh, G. (2006). Suppression situations in multiple linear regression. Educational and Psychological Measurement, 66, 435-447. https://doi.org/10.1177/0013164405278584
  60. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  61. Stein, K. M., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268275. https://doi.org/10.5951/MTMS.3.4.0268
  62. Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Information Age.
  63. Sugilar, S. (2016). Factors of students participating in online examination. Journal of Education and Learning, 10(2), 119-126. https://doi.org/10.11591/edulearn.v10i2.3256
  64. Swars, S. L., Daane, C. J., & Giesen, J. (2006). Mathematics anxiety and mathematics teacher efficacy: What is the relationship in elementary preservice teachers? School Science and Mathematics, 106(7), 306-315. https://doi.org/10.1111/j.1949-8594.2006.tb17921.x
  65. Tabachnick, B. G., & Fidell, L. A. (2007). Using multivariate statistics. Pearson Education.
  66. Tarr, J. E., Chàvez, O., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students’ opportunity to learn. School Science and Mathematics, 106(4), 191-201. https://doi.org/10.1111/j.1949-8594.2006.tb18075.x
  67. Tobias, S. (1978). Overcoming math anxiety. W. W. Norton & Company.
  68. Trice, A. D., & Ogden, E. D. (1986). Correlates of mathematics anxiety in first-year elementary school teachers. Educational Research Quarterly, 11(3), 2-4.
  69. Van de Walle, J. A. (2010). Elementary and middle school mathematics: Teaching developmentally (7th edn.). Allyn & Bacon.
  70. Vinson, B. M. (2001). A comparison of preservice teachers’ mathematics anxiety before and after a methods class emphasizing manipulatives. Early Childhood Education Journal, 29(2), 89-94. https://doi.org/10.1023/A:1012568711257
  71. WAEC Report. (2019). Chief examiners’ report in basic education certificate examination. West African Examination Council.
  72. Weiss, I. R., & Pasley, J. D. (2004). What is high-quality instruction? Educational Leadership, 61(5), 24.
  73. Wilkins, J. L. M. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11, 139-164. https://doi.org/10.1007/s10857-007-9068-2