#### Prospective elementary and secondary school mathematics teachers’ statistical reasoning

Rabia KARATOPRAK , Gülseren KARAGÖZ AKAR, Bengü BÖRKAN

The gap between theory and practice has become a critical issue in the effort of improving the learning of mathematics. Beliefs may have been one of the contributing factors to the widening of the gap between theory and practice. Therefore, examining the relationship between beliefs and practices in mathematics is crucial to gain an overview of the preparation of potential teacher candidates and the development of teacher education in the future. This study aims to examine the relationship between beliefs held by pre-service elementary school teachers and the instructional practices in mathematics class. This study employs the case study that focuses on one of the pre-service elementary school teachers who is undertaking practical field experience in the 2015/2016 academic year. The findings of this study indicate that the instructional practices do not necessarily reflect the beliefs that are held. On the other hand, beliefs about the nature of mathematics influence more dominant than the other beliefs against instructional practices.

Teacher beliefs, pre-service elementary school teachers, instructional practices, mathematics class

Paper Details | |
---|---|

Topic | Mathematics Education |

Pages | 629 - 642 |

Issue | IEJEE, Volume 8, Issue 4 |

Date of acceptance | 30 May 2016 |

Read (times) | 591 |

Downloaded (times) | 380 |

Applefield, J. M., Huber, R., & Moallem, M. (2000). Constructivism in theory and practice: Toward a better understanding. *The High School Journal, 84*(2), 35-53.

Arı, E., Tunçer, B. K., & Demir, M. K. (2016). Primary School Teachers' Views on Constructive Classroom Management. *International Electronic Journal of Elementary Education, 8*(3), 363-378.

Barkatsas, A. T., & Malone, J. (2005). A typology of mathematics teachers’ beliefs about teaching and learning mathematics and instructional practices. *Mathematics Education Research Journal, 17*(2), 69-90.

Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. *Educational Studies in Mathematics, 79*(1), 127-147. doi: 10.1007/s10649-011-9333-2

Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2003). *Assessment for learning: Putting it into practice*. Maidenhead, U.K.: Open university Press.

Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2004). Working inside the black box: Assessment for learning in the classroom. *Phi Delta Kappan, 86*(1), 9-21.

Chan, K.-w. (2004). Preservice Teachers' Epistemological Beliefs and Conceptions about Teaching and Learning: Cultural Implications for Research in Teacher Education. *Australian Journal of Teacher Education, 29*(1), 1.

Chassapis, D. (2007). Integrating the philosophy of mathematics in teacher training courses: A Greek case as an example. In F. Karen & J. P. V. Bendegem (Eds.), *Philosophical Dimensions in Mathematics Education* (Vol. 42, pp. 61-79). New York: Springer.

De Corte, E. (2003). Intervention research: A tool for bridging the theory-practice gap in mathematics education. Paper presented at the Proceedings of the International Conference, The Mathematics Education into the 21st Century Project, Brno Czech Republic.

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), *Mathematics teaching: The state of the art* (pp. 249–253). New York: Falmer.

Ernest, P. (1991). *The philosophy of mathematics education*. London: Routledge Falmer.

Fennema, E., Carpenter, T. P., & Franke, M. L. (1992). *Cognitively Guided Instruction. NCRMSE research review: The teaching and learning of mathematics,* (ERIC Document Reproduction Service No. ED 372929, 1, 2). National Center for Research in Mathematical Sciences Education Madison, WI.

Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), *Beliefs: A hidden variable in mathematics education?* (Vol. 31, pp. 39-57). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Geiger, V., & Goos, M. (2006). Living in the gap: A tale of two different types of researchers. In P. Grootenboer, R. Zevenbergen & M. Chinappan (Eds.), *Identities, cultures and learning spaces, Proceedings at the 29th annual conference of the Mathematics Education Research Group of Australasia* (pp. 254-261). Sydney: MERGA.

Goldin, G. A., Epstein, Y. M., Schorr, R. Y., & Warner, L. B. (2011). Beliefs and engagement structures: behind the affective dimension of mathematical learning. *ZDM, 43*(4), 547-560. doi: 10.1007/s11858-011-0348-z

Hersh, R. (1997). *What is mathematics, really?* Oxford, New York: Oxford University Press.

Kundi, G. M., & Nawaz, A. (2010). From objectivism to social constructivism: The impacts of information and communication technologies (ICTs) on higher education. *Journal of Science and Technology Education Research, 1*(2), 30-36.

Leder, G. C., & Forgasz, H. J. (2002). Measuring mathematical beliefs and their impact on the learning of mathematics. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), *Beliefs: A hidden variable in mathematics education* (Vol. 31, pp. 95-114). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Lee, C. (2006). *Language for learning mathematics: Assessment for learning in practice*. Berkshire, England: Open University Press.

Malone, J. (2000). Bridging the gap: A challenge for the dual community. In J. Bana & A. Chapman (Eds.), *Mathematics education beyond 2000, Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia* (pp. 27-36). Perth, WA: MERGA.

McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grows (Ed.), *Handbook of research on mathematics teaching and learning* (pp. 575-596). New York: Macmillan.

Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. *Review of educational research, 62*(3), 307-332.

Perkkilä, P. (2003). Primary school teachers’ mathematics beliefs and teaching practices. In M. A. Mariotti (Ed.), *Proceedings of the Third Conference of the European Society for Research in Mathematics Education* (pp. 1-8). Bellaria, Italy.

Ponte, J. P. D. (1994). Knowledge, beliefs, and conceptions in mathematics teaching and learning. Paper presented at the Proceedings of the fifth international conference on systematic cooperation between theory and practice in mathematics education.

Ponte, J. P. D., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. In A. Gutiérrez & P. Boero (Eds.), *Handbook of research on the psychology of mathematics education: Past,Present, and Future* (pp. 461-494). Rotterdam: Sense Publisher.

Purnomo, Y. W. (2014). *Serial Matematika untuk PGSD: Bilangan Cacah dan Bulat.* Bandung: Alfabeta.

Purnomo, Y. W. (2015). Pengembangan desain pembelajaran berbasis penilaian dalam pembelajaran matematika. *Cakrawala Pendidikan, 34*(2), 182-191.

Purnomo, Y. W., Kowiyah, Alyani, F., & Assiti, S. S. (2014). Assessing Number Sense Performance of Indonesian Elementary School Students. *International Education Studies, 7*(8), 74-84. doi: 10.5539/ies.v7n8p74

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.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), *Handbook of research on mathematics teaching and learning* (pp. 334-370). New York: Macmillan.

Shield, M. (1999). The conflict between teachers’ beliefs and classroom practices. In J. M. Truran & K. M. Truran (Eds.), *Making the difference: Proceedings of the 22nd annual conference of the Mathematics Education Research Group of Australasia* (pp. 439-445). Adelaide: MERGA.

Smith, T. (2000). Bridging the research-practice gap: Developing a pedagogical framework that promotes mathematical thinking and understanding. *Mathematics Teacher Education and Development, 2*(1), 4-16.

Sriraman, B. (2004). The influence of Platonism on mathematics research and theological beliefs. *Theology and Science, 2*(1), 131-147.

Sumantri, M. S., & Satriani, R. (2016). The Effect of Formative Testing and Self-Directed Learning on Mathematics Learning Outcomes. *International Electronic Journal of Elementary Education, 8*(3), 507-524.

Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). *Teacher education study in mathematics (TEDS-M), conceptual framework.* Teacher Education and Development International Study Center, College of Education, Michigan State University, East Lansing, MI.

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 Co, Inc.

Törner, G. (2002). Mathematical beliefs—A search for a common ground: Some theoretical considerations 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?* (Vol. 31, pp. 73-94). Dordrecht, The Netherlands: Kluwer Academic Publishers.

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*(1), 89-110.

White-Fredette, K. (2010). Why not philosophy? Problematizing the philosophy of mathematics in a time of curriculum reform. *The Mathematics Educator, 19*(2).

Yang, D.-C., & Wu, W.-R. (2010). The study of number sense: Realistic activities integrated into third-grade math classes in Taiwan. *The*

Rabia KARATOPRAK , Gülseren KARAGÖZ AKAR, Bengü BÖRKAN

Read (times)1335
Read

Read (times)646
Read

Read (times)328
Read

Mary REID , Steven REID

Read (times)273
Read

Feride ÖZYILDIRIM-GÜMÜŞ , Yeter ŞAHİNER

Read (times)242
Read

Deniz KAYA

Read (times)239
Read

Jennifer EDELMAN

Read (times)103
Read