How Teachers Encourage Students’ Mathematical Reasoning during the Covid-19 Pandemic?

Authors

  • Rohati Universitas Jambi, Jambi, Indonesia
  • Yaya S. Kusumah Universitas Pendidikan Indonesia, Bandung, Indonesia
  • Kusnandi Universitas Pendidikan Indonesia, Bandung, Indonesia
  • Marlina Universitas Jambi, Jambi, Indonesia

DOI:

https://doi.org/10.23887/jpiundiksha.v11i4.52756

Keywords:

Teacher interventions, Mathematical reasoning, Covid-19 pandemic

Abstract

Students' mathematical reasoning abilities can develop depending on the teacher's involvement in the classroom. The problem that often occurs in the class is that the teacher's actions have not been neatly arranged to encourage students' mathematical reasoning in learning mathematics. This article aims to observe the actions taken by a group of mathematics teachers in encouraging students' mathematical reasoning abilities. This type of research is qualitative research with data collected from learning recordings in the classroom. The research subjects were three junior high school, mathematics teachers. The teacher observed how students reasoned during 12 sessions as they studied and completed homework. The results of observing students' mathematical reasoning activities, such as building reasonable arguments and drawing correct conclusions, were concluded to enable teachers to test their students' mathematical reasoning. The findings of this study indicate that teachers can foster students' mathematical reasoning by applying the following strategies: (a) providing appropriate learning interventions; (b) assigning open tasks without solution methods, and (c) fostering a learning community that values ​​reasoning and the construction of shared ideas.

Author Biographies

Rohati, Universitas Jambi, Jambi, Indonesia

Department of Mathematics Education

Yaya S. Kusumah, Universitas Pendidikan Indonesia, Bandung, Indonesia

Department of Mathematics Education

Kusnandi, Universitas Pendidikan Indonesia, Bandung, Indonesia

Department of Mathematics Education

Marlina, Universitas Jambi, Jambi, Indonesia

Department of Mathematics Education

References

Aaron, W. R., & Herbst, P. G. (2015). Teachers’ perceptions of students’ mathematical work while making conjectures: an examination of teacher discussions of an animated geometry classroom scenario. International Journal of STEM Education, 2(1). https://doi.org/10.1186/s40594-015-0021-0.

Ayalon, M., & Even, R. (2016). Factors shaping students ’ opportunities to engage in argumentative activity. September 2014, 575–601.

Bleiler, S. K., Thompson, D. R., & Krajčevski, M. (2014). Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17(2), 105–127. https://doi.org/10.1007/s10857-013-9248-1.

Bragg, L. A., & Herbert, S. (2017). A" True" Story about Mathematical Reasoning Made Easy. Australian Primary Mathematics Classroom.

Branch, R. M. (2010). Instructional design: The ADDIE approach. In Instructional Design: The ADDIE Approach. https://doi.org/10.1007/978-0-387-09506-6.

Brodie, K. (2010). Teaching Mathematical Reasoning in Secondary School Classrooms. Springer New York Dordrecht Heidelberg London. https://doi.org/DOI 10.1007/978-0-387-09742-8.

Buforn, À., Fernández, C., Llinares, S., & Sánchez-matamoros, G. (2014). Characteristics of pre-service primary teachers ’ noticing of students ’ thinking related to fraction concept sub-constructs. Proceedings of CERME10, 1, 2812–3031. https://hal.science/hal-01949061/.

Corneli, J., Martin, U., Murray-Rust, D., Rino Nesin, G., & Pease, A. (2019). Argumentation Theory for Mathematical Argument. In Argumentation (Vol. 33, Issue 2). Springer Netherlands. https://doi.org/10.1007/s10503-018-9474-x.

Csanadi, A., Kollar, I., & Fischer, F. (2021). Pre-service teachers’ evidence-based reasoning during pedagogical problem-solving: better together? European Journal of Psychology of Education, 36(1), 147–168. https://doi.org/10.1007/s10212-020-00467-4.

da Ponte, J. P., & Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. Educational Studies in Mathematics, 93(1), 51–66. https://doi.org/10.1007/s10649-016-9681-z.

Dawkins, P. C., & Roh, K. H. (2016). Promoting Metalinguistic and Metamathematical Reasoning in Proof-Oriented Mathematics Courses: a Method and a Framework. International Journal of Research in Undergraduate Mathematics Education, 2(2), 197–222. https://doi.org/10.1007/s40753-016-0027-0.

Erduran, S. (2018). Toulmin’s argument pattern as a “horizon of possibilities” in the study of argumentation in science education. Cultural Studies of Science Education, 13(4), 1091–1099. https://doi.org/10.1007/s11422-017-9847-8.

Garfield, J. B., Ben-Zvi, D., Chance, B., Medina, E., Roseth, C., & Zieffler, A. (2008). Creating a Statistical Reasoning Learning Environment. In Developing Students’ Statistical Reasoning (pp. 45–63). Springer Science+Business Media B.V. https://doi.org/10.1007/978-1-4020-8383-9_3.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting Students Struggling with Mathematics:Response to Intervention (RtI) for elementary and middle schools. What Works Clearinghouse, 1–98.

Göhner, M., & Krell, M. (2020). Preservice Science Teachers’ Strategies in Scientific Reasoning: the Case of Modeling. Research in Science Education, Osborne 2013. https://doi.org/10.1007/s11165-020-09945-7.

Hallström, J., & Schönborn, K. J. (2019). Models and modelling for authentic STEM education: reinforcing the argument. International Journal of STEM Education, 6(1). https://doi.org/10.1186/s40594-019-0178-z.

Hidayat, W., & Prabawanto, S. (2018). Improving students’ creative mathematical reasoning ability students through adversity quotient and argument driven inquiry learning. IOP Conf. Series: Journal of Physics: Conf. Series, 1–6. https://doi.org/doi :10.1088/1742-6596/948/1/012005.

Hilton, A., Hilton, G., Dole, S., & Hilton, A. (2016). Promoting middle school students ’ proportional reasoning skills through an ongoing professional development programme for teachers. https://doi.org/10.1007/s10649-016-9694-7.

Kilhamn, C., Bråting, K., & Rolandsson, L. (2019). Teachers’ arguments for including programming in mathematics education. Preceedings of NORMA 20, 169–176. https://www.diva-portal.org/smash/record.jsf?pid=diva2:1541426.

Komatsu, K., & Jones, K. (2020). Correction to: Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving. Digital Experiences in Mathematics Education, 6(2), 144–144. https://doi.org/10.1007/s40751-020-00072-6.

Kooloos, C., Oolbekkink-Marchand, H., van Boven, S., Kaenders, R., & Heckman, G. (2021). Building on student mathematical thinking in whole-class discourse: exploring teachers’ in-the-moment decision-making, interpretation, and underlying conceptions. Journal of Mathematics Teacher Education, 0123456789. https://doi.org/10.1007/s10857-021-09499-z.

Kramarski, B. (2008). Promoting teachers’ algebraic reasoning and self-regulation with metacognitive guidance. Metacognition and Learning, 3(2), 83–99. https://doi.org/10.1007/s11409-008-9020-6.

Lambert, R., & Schuck, R. (2021). “The Wall Now Between Us”: Teaching Math to Students with Disabilities During the COVID Spring of 2020. Asia-Pacific Education Researcher, 30(3), 289–298. https://doi.org/10.1007/s40299-021-00568-8.

Lin, Y. W., Tseng, C. L., & Chiang, P. J. (2017). The Effect of Blended Learning in Mathematics Course. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 741–770. https://doi.org/10.12973/eurasia.2017.00641a.

Loong, E. Y., Vale, C., & Bragg, L. A. (2017). Tracking change in primary teachers ’ understanding of mathematical reasoning through demonstration lessons. Mathematics Teacher Education and Development, 19(1), 5–29. https://eric.ed.gov/?id=EJ1152733.

Magiera, M. T., & Zambak, V. S. (2021). Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records. International Journal of STEM Education, 8(1). https://doi.org/10.1186/s40594-020-00263-y.

Mata-Pereira, J., & da 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.

Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers Promoting Student Mathematical Reasoning. Investigations in Mathematics Learning, 7(2), 1–20. https://doi.org/10.1080/24727466.2014.11790339.

Mumcu, H. Y., & Aktürk, T. (2017). An analysis of the reasoning skills of pre-service teachers in the context of mathematical thinking. European Journal of Education Studies, 3(5). https://doi.org/10.46827/ejes.v0i0.652.

Oslington, G., Mulligan, J., & Van Bergen, P. (2020). Third-graders’ predictive reasoning strategies. Educational Studies in Mathematics, 104(1), 5–24. https://doi.org/10.1007/s10649-020-09949-0.

Rohati, Marlina, & Khidayatul, I. (2021). The Views of High School Students During The Covid-19 Period on Learning Mathematics. IJECA (International Journal of Education & Curriculum Application), 4(2), 64–74. https://doi.org/10.31764/ijeca.v4i2.5139.

Rohati, R., Kusumah, Y. S., & Kusnandi, K. (2022). The development of analytical rubrics : An avenue to assess students ’ mathematical reasoning behavior. Cypriot Journal of Educational Sciences, 17(8), 2553–2566. https://doi.org/https://doi.org/10.18844/cjes.v17i8.7043.

Rohati, R., Turmudi, T., & Kusnandi, K. (2021). Students’ proportional reasoning in mathematics through Covid-19 pandemic context. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(3), 1670. https://doi.org/10.24127/ajpm.v10i3.3873.

Rumsey, C., & Langrall, C. W. (2016). Promoting mathematical argumentation. Teaching Children Mathematics, 22(7), 412–419. https://doi.org/10.5951/teacchilmath.22.7.0412.

Russo, J., Bobis, J., Sullivan, P., Downton, A., Livy, S., McCormick, M., & Hughes, S. (2020). Exploring the relationship between teacher enjoyment of mathematics, their attitudes towards student struggle and instructional time amongst early years primary teachers. Teaching and Teacher Education, 88, 102983. https://doi.org/10.1016/j.tate.2019.102983.

Sawatzki, C., Downton, A., & Cheeseman, J. (2019). Stimulating Proportional Reasoning through Questions of Finance and Fairness. Mathematics Education Research Journa, 31, 465–484. https://doi.org/10.1007/s13394-019-00262-5.

Segerby, C., & Chronaki, A. (2018). Primary students’ participation in mathematical reasoning: Coordinating reciprocal teaching and systemic functional lin-guistics to support reasoning in the Swedish context. Educational Design Research: An International Journal for Design-Based Research in Education, 2(1). https://doi.org/10.15460/eder.2.1.1150.

Sgaravatti, D. (2018). Experience and reasoning : challenging the a priori / a posteriori distinction. Synthese. https://doi.org/10.1007/s11229-018-1718-7.

Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91–134. https://doi.org/10.1007/s40753-015-0003-0.

Sullivan, P., & Davidson, A. (2014). The Role of Challenging Mathematical Tasks in Creating Opportunities for Student Reasoning. 605–612.

Sumpter, L. (2018). Grade 9 Students’ Reasoning About Division of Fractions: What Are their Arguments Anchored in? Students’ and Teachers’ Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms, 135–143. https://doi.org/10.1007/978-3-319-70244-5_13.

Tatton-Brown, O. (2019). Rigour and Intuition. Erkenntnis, 86(6), 1757–1781. https://doi.org/10.1007/s10670-019-00180-9.

Timmermana, B. E. C., Strickland, D. C., Johnson, R. L., & Paynec, J. R. (2011). Development of a “universal” rubric for assessing undergraduates’ scientific reasoning skills using scientific writing. Assessment and Evaluation in Higher Education, 36(5), 509–547. https://doi.org/10.1080/02602930903540991.

Vale, C., Widjaja, W., Doig, B., & Groves, S. (2019). Anticipating students’ reasoning and planning prompts in structured problem-solving lessons. Mathematics Education Research Journal, 31(1). https://doi.org/10.1007/s13394-018-0239-5.

van der Sandt, S. (2007). Research framework on mathematics teacher behaviour: Koehler and Grouws’ framework revisited. Eurasia Journal of Mathematics, Science and Technology Education, 3(4), 343–350. https://doi.org/10.12973/ejmste/75413.

Veldhuis, M., & van den Heuvel-Panhuizen, M. (2020). Supporting primary school teachers’ classroom assessment in mathematics education: effects on student achievement. Mathematics Education Research Journal, 32(3), 449–471. https://doi.org/10.1007/s13394-019-00270-5.

Wilkinson, L. C., Bailey, A. L., & Maher. (2018). Students’ Mathematical Reasoning, Communication, and Language Representations_ A Video-Narrative Analysis _ Enhanced Reader.pdf. Ecnu Review of Education, 1(3), 1–22. https://doi.org/10.30926/ecnuroe 2018010301.

Yao, X., & Manouchehri, A. (2020). Teacher interventions for advancing students’ mathematical understanding. Education Sciences, 10(6), 1–21. https://doi.org/10.3390/educsci10060164.

Yeh, C. Y. C., Cheng, H. N. H., Chen, Z. H., Liao, C. C. Y., & Chan, T. W. (2019). Enhancing achievement and interest in mathematics learning through Math-Island. Research and Practice in Technology Enhanced Learning, 14(1). https://doi.org/10.1186/s41039-019-0100-9.

Yilmaz, Z., & Topal, Z. O. (2014). Connecting Mathematical Reasoning and Language Arts Skills: The Case of Common Core State Standards. Procedia - Social and Behavioral Sciences, 116, 3716–3721. https://doi.org/10.1016/j.sbspro.2014.01.829.

Zazkis, D., & Villanueva, M. (2016). Student Conceptions of What it Means to Base a Proof on an Informal Argument. International Journal of Research in Undergraduate Mathematics Education, 2(3), 318–337. https://doi.org/10.1007/s40753-016-0032-3.

Zhen, B., Weber, K., & Mejia-Ramos, J. P. (2016). Mathematics Majors’ Perceptions of the Admissibility of Graphical Inferences in Proofs. International Journal of Research in Undergraduate Mathematics Education, 2(1), 1–29. https://doi.org/10.1007/s40753-015-0010-1.

Downloads

Published

2022-12-24

Issue

Section

Articles