DESIGN PRINCIPLES OF PRE-SERVICE TEACHER EDUCATION TO DEVELOP PROSPECTIVE TEACHERS’ KNOWLEDGE OF MATHEMATICAL REASONING

Volume 8, Issue 4, August 2023     |     PP. 158-173      |     PDF (197 K)    |     Pub. Date: August 1, 2023
DOI: 10.54647/education880455    111 Downloads     160758 Views  

Author(s)

Ana Henriques, Instituto de Educação, Universidade de Lisboa. Alameda da Universidade, 1649-013 Lisboa, Portuga
Hélia Oliveira, Instituto de Educação, Universidade de Lisboa. Alameda da Universidade, 1649-013 Lisboa, Portuga
Leonor Santos, Instituto de Educação, Universidade de Lisboa. Alameda da Universidade, 1649-013 Lisboa, Portuga

Abstract
Mathematical reasoning (MR), highlighted in curricular orientations, is a necessary students’ skill in mathematical learning. As the knowledge to promote this skill is limited and challenging for teachers practices, is required to use adequate design principles in pre-service teacher education to develop PTs mathematical and didactical knowledge to promote students’ MR in teaching practices. This study aims to establish and understand positive contributes of adopted design principles and their operationalization in pre-service teacher education experiments, and the results revealed the potential of adopted design principles to promote the development of PTs’ knowledge of MR and ability to promote students’ MR in teaching practices.

Keywords
Design principles, Pre-service teacher education, Mathematical reasoning Prospective teachers´ knowledge

Cite this paper
Ana Henriques, Hélia Oliveira, Leonor Santos, DESIGN PRINCIPLES OF PRE-SERVICE TEACHER EDUCATION TO DEVELOP PROSPECTIVE TEACHERS’ KNOWLEDGE OF MATHEMATICAL REASONING , SCIREA Journal of Education. Volume 8, Issue 4, August 2023 | PP. 158-173. 10.54647/education880455

References

[ 1 ] 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. https://doi.org/10.1177/0022487108324554
[ 2 ] Boston, M. D., & Smith, M. S. (2011). A ´task-centric approach´ to professional development: Enhancing and sustaining mathematics teachers´ ability to implement cognitively challenging mathematical tasks. ZDM: International Journal of Mathematics Teacher Education, 43, 965–977. https://doi.org/10.1007/s11858-011-0353-2
[ 3 ] Breen, S., & O´Shea, A. (2019). Designing mathematical thinking tasks. PRIMUS, 29(1), 9–20. https://doi.org/10.1080/10511970.2017.1396567
[ 4 ] Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer US. https://doi.org/10.1007/978-0-387-09742-8
[ 5 ] Buchbinder, O., & McCrone, S. (2020). Preservice teachers learning to teach proof through classroom implementation: Successes and challenges. Journal of Mathematical Behavior, 58, 100779. https://doi.org/10.1016/j.jmathb.2020.100779
[ 6 ] Davidson, A., Herbert, S., & Bragg, L. A, (2019). Supporting elementary teachers’ planning and assessing of mathematical reasoning. International Journal of Science and Mathematics Education, 17, 1151–1171. https://doi.org/10.1007/s10763-018-9904-0
[ 7 ] Dempsey, M., & O´Shea, A. (2020). The role of task classification and design in curriculum making for preservice teachers of mathematics. The Curriculum Journal, 31(3), 436-453. https://doi.org/10.1002/curj.18
[ 8 ] Erickson, F. (1986). Qualitative methods in research on teaching. In M. Wittrock (Ed.), Handbook of Research on Teaching (pp. 119-161). MacMillan.
[ 9 ] Fuentes, S. Q., & Ma, J. (2018). Promoting teacher learning: A framework for evaluating the educative features of mathematics curriculum materials. Journal of Mathematics Teacher Education, 21(4), 351-382. https://doi.org/10.1007/s10857-017-9366-2
[ 10 ] Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers‟ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400. https://www.jstor.org/stable/40539304
[ 11 ] Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1-16.
[ 12 ] Kilic, H., Dogan, O., Yilmaz, Z., & Donmez, P. (2017). Pre-service teachers‟ reflections on task design and implementation. CERME 10, Feb 2017, Dublin, Ireland. https://hal.archives-ouvertes.fr/hal-01950498
[ 13 ] Lannin, J., Ellis, A. B., & Elliot, R. (2011). Developing essential understanding of mathematics reasoning for teaching mathematics in prekindergarten-grade 8. National Council of Teachers of Mathematics.
[ 14 ] Leavy, A., & Hourigan, M. (2020). Posing mathematically worthwhile problems: developing the problem posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23, 341–361. https://doi.org/10.1007/s10857-018-09425-w
[ 15 ] Lee, E.-J., Lee, K.-H., & Park, M. (2019). Developing preservice teachers’ abilities to modify mathematical tasks: Using noticing-oriented activities. International Journal of Science and Mathematics Education, 17(5), 965–985. https://doi.org/10.1007/s10763-018-9891-1
[ 16 ] Lin, F-L., Lee, K-H., Tabach, M., Stylianides, G. (2011). Principles of task design for conjecturing and proving. In G. Hanna & M. de Villiers (Eds.), Proof and Proving in Mathematics Education, New ICMI Study Series (vol 15, pp. 305-325). Dordrecht: Springer.
[ 17 ] Mata-Pereira, J. & Ponte, J. P. (2016). Ações do professor para o desenvolvimento do raciocínio matemático dos alunos. Educação e Matemática, 137, 38-41.
[ 18 ] Mata-Pereira, J., & Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186. https://doi.org/10.1007/s10649-017-9773-4
[ 19 ] Ministério da Educação (2021). Aprendizagens Essenciais de. Matemática. Lisboa: DGE.
[ 20 ] Menezes, L., Canavarro, A. P., & Oliveira, H. (2012). Teacher practice in an inquiry-based mathematics classroom. Hellenic Mathematical Society-International Journal for Mathematics in Education, 14, 357-362.
[ 21 ] NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
[ 22 ] Oliveira, H., & Henriques, A., (2021). Preservice mathematics teachers’ knowledge about the potential of tasks to promote students’ mathematical reasoning. International Journal of Research in Education and Science (IJRES), 7(4), 1299-1318. https://doi.org/10.46328/ijres.2472
[ 23 ] Park, Hyejin, & Magiera, Marta T. (2020). Prospective Teachers' Interpretations of Mathematical Reasoning. Mathematical and Statistical Science Faculty Research and Publications. 107. https://epublications.marquette.edu/math_fac/107
[ 24 ] Ponte, J. P., & Chapman, O. (2015). Prospective mathematics teachers’ learning and knowledge for teaching. In L. English & D. Kirshner (Eds.), Handbook of International Research in Mathematics Education: Third Edition (pp. 275–296). New York, NY: Routledge/Taylor & Francis.
[ 25 ] Ponte, J. P. & Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. Educational Studies in Mathematics, 93(1), 51-66.
[ 26 ] Ponte, J. P., Quaresma, M., & Mata-Pereira, J. (2020). Como desenvolver o raciocínio matemático na sala de aula?. Educação e Matemática, 156, 7-11. APM.
[ 27 ] Ponte, J. P., Carvalho, R., Mata-Pereira, J., & Quaresma, M. (2016). Investigação baseada em design para compreender e melhorar as práticas educativas. Quadrante, 25(2), 77-98. https://doi.org/10.48489/quadrante.22934
[ 28 ] REASON (2020). Princípios para elaboração de tarefas para promover o raciocínio matemático dos alunos. http://reason.ie.ulisboa. pt/produtos/
[ 29 ] Ribeiro, A. J., & Ponte, J. P. (2020). A theoretical model for organizing and understanding teacher learning opportunities to teach mathematics. Zetetiké, Campinas, SP, 28, 1-20. https://doi.org/10.20396/zet.v28i0.8659072.
[ 30 ] Rivera, F. D., & Becker, J. R. (2009). Algebraic Reasoning through Patterns. Mathematics Teaching in the Middle School, 15(4), 212–221. https://doi.org/10.5951/MTMS.15.4.0212
[ 31 ] Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: NCTM.
[ 32 ] Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488. https://doi.org/10.2307/1163292
[ 33 ] Stein, M. K., Engle, R., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematical discussions: Five practices for help teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340.
[ 34 ] Thompson, D. R. (2012). Modifying textbook exercises to incorporate reasoning and communication into the primary mathematics classroom. In B. Kaur & T. Lam (Eds.), Reasoning, Communication and Connections in Mathematics (pp. 57–74). World Scientific Publishing Company.
[ 35 ] Watson, A. & Ohtani, M. (2015). Task design in mathematics education: The 22nd ICMI study (New ICMI study series). Springer.
[ 36 ] Zazkis, R., Liljedahl, P., & Sinclair, N. (2009). Lesson plays: Planning teaching versus teaching planning. For the Learning of Mathematics, 29(1), pp. 40-47.