Investigating Pre-Service Teachers’ Beliefs Towards Mathematics: A Case Study

Bhesh Mainali 1 *
More Detail
1 Rider University, Lawrenceville, NJ, USA
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 4, pp. 412-435. https://doi.org/10.30935/scimath/12103
Published: 22 May 2022
OPEN ACCESS   2463 Views   1351 Downloads
Download Full Text (PDF)

ABSTRACT

This case study investigated two pre-service elementary teachers’ changes in beliefs towards mathematics, learning mathematics, and teaching mathematics from the beginning to the end of mathematics methods courses. One of the participants had mathematics learning disability (MLD). The analysis of data gathered using concept maps and interviews at the beginning and end of the method courses revealed mixed findings between the two participants. The findings indicated that both pre-service teachers held negative beliefs before they took methods courses because they believed mathematics was boring, confusing, time-consuming, and a difficult subject. The data also suggested that learning mathematics was difficult and teaching mathematics was challenging. Their negative beliefs were associated primarily with their past school experiences as well as instructional strategies employed at school. One of the participants positively changed her beliefs at the end of the method courses since she described mathematics as a dynamic, creative, and useful subject. However, the other participant with MLD still held negative beliefs primarily about mathematics, as well as for learning and teaching mathematics at the end of the method courses. Data also revealed that utilizing appropriate instructional strategies based on individuals learning styles helped to make learning and teaching mathematics easy and interesting.
Keywords: belief, concept map, pre-service teachers, mathematics learning disability, methods course

CITATION

Mainali, B. (2022). Investigating Pre-Service Teachers’ Beliefs Towards Mathematics: A Case Study. European Journal of Science and Mathematics Education, 10(4), 412-435. https://doi.org/10.30935/scimath/12103

REFERENCES

  • Aldridge, S., & Bobis, J. (2001). Multiple learning contexts: A vehicle for changing preservice teachers’ mathematical beliefs, knowledge and practices. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and beyond: Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 43-49). Australia.
  • Andrews, P. (2000, September 23). The influence of context on teachers’ conceptions of mathematics and its teaching [Paper presentation]. The European Conference on Educational Research, Edinburgh, UK.
  • Artzt, A. F. (1999). A structure to enable preservice teachers of mathematics to reflect on their teaching. Journal of Mathematics Teachers Education, 2(2), 143-166. https://doi.org/10.1023/A:1009999004407
  • Badian, N. A. (1983). Arithmetic and nonverbal learning. In H. R. Myklebust (Ed.), Progress in learning disabilities (pp. 235-264). Grune and Stratton.
  • Barbro, G. (2008). Concept maps as research tool in mathematics education. In Proceedings of the 3rd International Conference on Concept Mapping. Finland.
  • Berk, D., & Cai, J. (2019). Mathematics teacher beliefs. In M. A. Peters (Ed.), Encyclopedia of teacher education. Springer. https://doi.org/10.1007/978-981-13-1179-6_236-1
  • Beswick, K. (2006). Change in preservice attitudes and beliefs: The net impact of two mathematics education units and intervening experiences. School Science and Mathematics, 106(1), 36-47. https://doi.org/10.1111/j.1949-8594.2006.tb18069.x
  • Beswick, K., & Dole, S. (2001). Dispelling the myths: Influencing the beliefs of pre-service primary teachers. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and beyond: Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 90-97). Australia.
  • Beswick, K., Callingham, R., & Watson, J. (2011). The nature and development of middle school mathematics teachers’ knowledge. Journal of Mathematics Teacher Education, 14(1), 1-27.
  • Bray, S. W. (2011). A collective case study of the influence of teachers’ beliefs and knowledge on error handling practices during class discussion of mathematics. Journal for Research in Mathematics Education, 42(1), 2-38. https://doi.org/10.5951/jresematheduc.42.1.0002
  • Buhmann, S. Y., & Kingsbury, M. (2015). A standardized, holistic framework for concept-map analysis combining topological attributes and global morphologies. Knowledge Management & E-Learning, 7(1), 20-35. https://doi.org/10.34105/j.kmel.2015.07.003
  • Calderhead, J., & Robson, M. (1991). Images of teaching: Students’ teachers’ early conceptions of classroom practice. Teaching and Teacher Education, 7, 1-8. https://doi.org/10.1016/0742-051X(91)90053-R
  • Chan, Y.-C., & Wong, N.-Y. (2014). Worldviews, religions, and beliefs about teaching and learning: Perception of mathematics teachers with different religious backgrounds. Educational Studies in Mathematics, 87(3), 251-277. https://doi.org/10.1007/s10649-014-9555-1
  • Chang, Y. (2015). Examining relationships among elementary mathematics teachers’ efficacy and their students’ mathematics self-efficacy and achievement. EURASIA Journal of Mathematics, Science, & Technology Education, 11, 1307-1320. https://doi.org/10.12973/eurasia.2015.1387a
  • Clark, M. L., DePiper, J. N., Frank, T. J., Nishio, M., Campbell, P. F., Smith, T. M., Griffin, M. J., Rust, A. H., Conant, D. L., & Choi, Y. (2014). Teacher characteristics associated with mathematics teachers’ beliefs and awareness of their students’ mathematical dispositions. Journal for Research in Mathematics Education, 45(2), 246-284. https://doi.org/10.5951/jresematheduc.45.2.0246
  • Collier, P. (1972). Prospective elementary teachers’ intensity and ambivalence of beliefs about mathematics and mathematics Instruction. Journal for Research in Mathematics Education, 3(3), 155-163. https://doi.org/10.5951/jresematheduc.3.3.0155
  • Ernest, P. (1989). The knowledge, beliefs, and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15, 13-33. https://doi.org/10.1080/0260747890150102
  • Ernest, P. (2016). The problem of certainty in mathematics. Educational Studies in Mathematics, 92(3), 379 -393. https://doi.org/10.1007/s10649-015-9651-x
  • Forgasz, H., & Leder, G. (2008). Beliefs about mathematics and mathematics teaching. In P. Sullivan, & T. Wood (Eds.), The international handbook of mathematics teacher education: Knowledge and beliefs in mathematics teaching and teaching development (pp. 173-192). Sense Publisher. https://doi.org/10.1163/9789087905439_010
  • Francis, D., Rapacki, L., & Eker, A. (2015). The individual, the context, and practice: A review of the research on teachers’ beliefs related to mathematics. In H. Fives, & M. G. Gill (Eds.), International handbook of research on teachers’ beliefs (pp. 336-352). Routledge.
  • Fullan, M. (1991). The new meaning of educational change. Teachers College Press.
  • Glesne, C. (2011). Becoming qualitative researchers: An introduction. Pearson.
  • Goldin, G. A. (2002). Affect, meta affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 59-72). Kluwer Academic Publisher. https://doi.org/10.1007/0-306-47958-3_4
  • Gross-Tsur, V., Manor, O., & Shalev, R. S. (1996). Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine and Child Neurology, 38, 25-33. https://doi.org/10.1111/j.1469-8749.1996.tb15029.x
  • Hart, L. (2002a). A four-year follow-up study of teachers’ beliefs after participating in teacher enhancement project. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp 161-176). Kluwer Academic Publisher. https://doi.org/10.1007/0-306-47958-3_10
  • Hart, L. (2002b). Preservice teachers’ belief and practice after participating in an integrated content/methods course. School Science and Mathematics, 102(1), 4-14. https://doi.org/10.1111/j.1949-8594.2002.tb18191.x
  • Hart, L., & Memnun, D. S. (2015). The relationship between preservice elementary mathematics teachers’ beliefs and metacognitive awareness. Journal of Education and Training Studies, 3(5), 70-77. https://doi.org/10.11114/jets.v3i5.840
  • Holt-Reynolds, D. (1992). Personal history-based beliefs as relevant prior knowledge in course work. American Educational Research Journal, 29, 325-349. https://doi.org/10.3102/00028312029002325
  • Kagan, D. M. (1992). Professional growth among preservice and beginning teachers. Review of Educational Research, 62, 129-169. https://doi.org/10.3102/00346543062002129
  • Kane, R., Sandretto, S., & Heath, C. (2002). Telling half the story: A critical review of research on the teaching beliefs of university academics. Review of Educational Research, 32(1), 177-228. https://doi.org/10.3102/00346543072002177
  • Karatas, I., Guven, B., Ozturk, Y., Arslan, S., Gursoy, K. (2017). Investigation of pre-school teachers’ beliefs about mathematics education in terms of their experience and structure of their education. EURASIA Journal of Mathematics, Science & Technology Education, 13(3), 673-689. https://doi.org/10.12973/eurasia.2017.00638a
  • Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Göbel, S. M., Grabner, R. H., Henik, A., Jordan, N. C., Karmiloff-Smith, A. D., Kucian, K., Rubinsten, O., Szucs, D., Shalev, R., & Nuerk, H.-C. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology, 4, 516. https://doi.org/10.3389/fpsyg.2013.00516
  • Kim, C., Kim, M. K., Lee, C., Spector, M., & DeMeester, K. (2013). Teacher beliefs and technology integration. Teaching and Teacher Education, 29, 76-85. https://doi.org/10.1016/j.tate.2012.08.005
  • Kinchin, I. M., Streatfield, D., & Hay, D.B. (2010). Using concept mapping to enhance the research interview. International Journal of Qualitative Methods, 9(1), 52-68. https://doi.org/10.1177/160940691000900106
  • Knafl, K. A., & Breitmayer B. J. (1991). Triangulation in qualitative research: Issues of conceptual clarity and purpose. In J. M. Morse (Ed.), Qualitative nursing research: A contemporary dialogue (pp. 226-239). SAGE. https://doi.org/10.4135/9781483349015.n26
  • Lappen, G., & Theule- Lubienski, S. (1994). Training teachers or educating professionals? What are the issues and how they are resolved? In D. Robitaille, D. Wheeler, & C. Kieran (Eds.), Selected lectures from the 7th International Congress on Mathematical Education (pp. 249-262). de L’Universite Laval.
  • Lau, W. W. F. (2021). Pre-service mathematics teachers’ professional learning in a pedagogy course: Examining changes in beliefs and confidence in teaching algebra. Mathematics Education Research Journal, 33, 223-239. https://doi.org/10.1007/s13394-019-00285-y
  • Liljedahl, P., Rosken, B., & Rolka, K. (2021). Changes to preservice elementary teachers’ beliefs about mathematics and the teaching and learning of mathematics: How and why? Journal of Adult Learning, Knowledge and Innovation, 4(21), 20-30.
  • Lloyd, G. (2002). Mathematics teachers’ beliefs and experiences with innovative curriculum materials: The role of curriculum in teacher development. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 149-159). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_9
  • Looney, L., Perry, D. R., & Steck, A. K. (2017). Turning negatives into positives: The role of an instructional math course on preservice teachers’ math beliefs. Education, 138(1), 27-40.
  • Maasepp, B., & Bobis, J. (2014). Prospective primary teachers’ belief about mathematics. Mathematics Teachers Education and Development, 16(2), 89-107.
  • Mainali, B. (2019). 9955 difficulty, and high school students’ geometry performance geometry investigating the relationships between preferences, gender, and task. International Journal of Research in Education and Science, 5(1), 224-236.
  • Mainali, B. (2021a). Making online mathematics method course interactive and effective with OER. In J. P. Howard, & J. F. Beyers (Eds.), Teaching and learning mathematics online. Chapman and Hall/CRC. https://doi.org/10.1201/9781351245586-19
  • Mainali, B. (2021b). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science, and Technology, 9(1), 1-21. https://doi.org/10.46328/ijemst.1111
  • Marita, S., & Hord, C. (2017). Review of mathematics interventions for secondary students with learning disabilities. Learning Disability Quarterly, 40(1), 29-40. https://doi.org/10.1177/0731948716657495
  • Markovits, Z. (2011). Beliefs hold by pre-school prospective teachers toward mathematics and its teaching. Procedia-Social and Behavioral Sciences, 11, 117-121. https://doi.org/10.1016/j.sbspro.2011.01.045
  • Mazzocco, M. M. M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In D. B. Berch, & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 29-47). Paul H Brookes Publishing. https://doi.org/10.1097/DBP.0b013e31817aefe8
  • Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology, 33, 318-344. https://doi.org/10.1080/87565640801982403
  • McCleary, D. F., Rowlette, E. F., Pelchar, T. K., & Bain, S. K. (2013). Interventions for learning disabilities: Does a journal-based change in focus and article type reflect or influence legal mandates? Review of Educational Research, 83(2), 196-210. https://doi.org/10.3102/0034654313476143
  • National Center for Learning Disabilities. (2007). SLD identification overview: General information and tools to get started. https://files.eric.ed.gov/fulltext/ED543737.pdf
  • NCES. (2019). Children and youth disabilities. National Center for Educational Statistics. https://nces.ed.gov/programs/coe/indicator_cgg.asp
  • Nesbit, J. C., & Adesope, O. O. (2006). Learning with concept and knowledge maps: A meta-analysis. Review of Educational Research, 76(3), 413-448. https://doi.org/10.3102/00346543076003413
  • Nisbet, S., & Warren, E. (2000). Primary teacher’s belief relating to mathematics, teaching and assessing mathematics factors that influence these beliefs. Mathematics Teachers Education and Development, 2, 34-47.
  • Penny, G. C. (2018). Rethinking the concept of learning disability. Canadian Psychology, 59(2), 197-202. https://doi.org/10.1037/cap0000128
  • Philipp, R. A., Ambrose, R., Lamb, L. C., Sowder, J. T., Schappelle, B. P., Sowder, L., Thanheiser, E., & Chauvot, J. (2007). Effects of early field experiences on the mathematical knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438-476.
  • Pullen, P. C., Lane, H. B., Ashworth, K. E., & Lovelace, S. P. (2011). Learning disabilities. In J. M. Kauffeman, & D. P. Hallahan (Eds.), Handbook of special education (pp. 187-197). Taylor & Francis.
  • 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. https://doi.org/10.2307/749691
  • Richardson, V. (2003). Constructivist pedagogy. Teachers College Record, 105(9), 1623-1640. https://doi.org/10.1046/j.1467-9620.2003.00303.x
  • Rokeach, M. (1968). Beliefs, attitudes, and values: A theory of organization and change. Jossey-Bass.
  • Rolka, K., Rosken, B., & Liljedahl, P. (2006). Challenging the mathematical belief of preservice elementary school teachers. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (pp. 441-448). PME.
  • Satsangi, R., Hammer, R., & Hogan, C. D. (2019). Video modeling and explicit instruction: A comparison of strategies for teaching mathematics to students with learning disabilities. Learning Disabilities Research & Practice, 34, 35-46. https://doi.org/10.1111/ldrp.12189
  • Schoenfeld, A. H. (1992). Mathematical problem solving. Academic Press.
  • Seawright, J., & Gerring, J. (2008). Case selection techniques in case study research: A menu of qualitative and quantitative options. Political Research Quarterly, 61, 294-308. https://doi.org/10.1177/1065912907313077
  • Shalev, R., Manor, O., & Gross-Tsur, V. (2005). Developmental dyscalculia: A prospective six-year follow-up. Developmental Medicine and Child Neurology, 47(2), 121-125. https://doi.org/10.1111/j.1469-8749.2005.tb01100.x
  • Stuart, C., & Thurlow, S. (2000). Making it their own: Preservice teachers’ experiences, beliefs, and classroom practices. Journal of Teacher Education, 51(2),13-21. https://doi.org/10.1177/002248710005100205
  • Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In A. D. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 127-146). Macmillan.
  • Torner, G. (2002). Mathematical beliefs-a search for common ground: Some theoretical consideration on structuring beliefs, some research questions, and some phenomenological observations. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 73-94). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_5
  • USDOE. (2004). IDEA, individuals with disabilities education improvement act of 2004. Public Law 108-446. United States Department of Education. https://www.govinfo.gov/app/details/PLAW-108publ446
  • Vacc, N., & Bright, G. W. (1999). Elementary preservice teachers’ belief and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89-110. https://doi.org/10.2307/749631
  • Vygotsky, L. S. (1993). Introduction: Fundamental problems of defectology. In R. W. Rieber, & A. S. Carton (Eds.), The collected works of L. S. Vygotsky: Volume 2. The fundamentals of defectology (pp. 29-51). Plenum Press. (Original work published 1929). https://doi.org/10.1007/978-1-4615-2806-7_2
  • White, A. L., Way, J., Perry, B., & Southwell, B. (2005). Mathematical attitudes, beliefs and achievement in primary pre-service mathematics teacher education. Mathematics Teacher Education and Development, 7, 33-52.
  • Wilkins, J. L., & Brand, B. (2004). Change in preservice teachers’ beliefs: An evaluation of mathematics methods course. School Science and Mathematics, 104(5), 226-232. https://doi.org/10.1111/j.1949-8594.2004.tb18245.x
  • Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development. Framing students’ mathematics-related beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 127-147). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_8
  • Xie, S., & Cai, J. (2021). Teachers’ beliefs about mathematics, learning, teaching, students, and teachers: Perspectives from Chinese high school in-service mathematics teachers. International Journal of Science and Math Education, 19(2), 747-769. https://doi.org/10.1007/s10763-020-10074-w
  • Yang, X., Kaiser, G., König, J., & Blomeke, S. (2020). Relationship between pre-service mathematics teachers’ knowledge, beliefs and instructional practices in China. ZDM-Mathematics Education, 52, 281-294. https://doi.org/10.1007/s11858-020-01145-x