Reasoning in the Teaching of Mathematics
Keywords:
mathematics, reasoning, critical thinking, National Assessment of KnowledgeAbstract
As a critical thinking skill in elementary education, reasoning or substantiation has been verified with a task in the National Assessment of Knowledge at least since 2006. In reasoning tasks, both the aspects of mathematical and of reading literacy are intertwined. Solving such tasks in the National Assessment of the Knowledge of Mathematics is a good indicator for identifying possible differences in the achievements of sixth and ninth grade pupils. In the paper we focused on the same tasks that appeared in the National Assessment of Knowledge in 2016 and 2019, as we wanted to find out, among other things, whether pupils from sixth to ninth grade had made any progress. The success in solving the tasks was analysed according to whether the tasks were solved correctly or not and whether the pupils had attempted solving them at all. Typical errors that pupils had made while solving the tasks and various examples of correctly solved tasks were reviewed. We have found that it would be necessary to incorporate such didactic approaches and strategies into the teaching of mathematics, as that would improve the success rate of solving reasoning tasks in mathematics.
References
ACARA (Australian Curriculum, Assessment and Reporting Authority) (2013). Critical and Creative Thinking Learning Continuum. Pridobljeno dne 24.09.2020 s svetovnega spleta: http://www.acara.edu.au/verve/_resources/General_capabilities_-CCT_-_learning_continuum.pdf.
Cankar, G., Semen, E., Knežević, M. in Urank, M. (2020). Priročnik za uporabo orodja za ugotavljanje kakovosti izkazanega znanja: Nacionalno preverjanje znanja (OrKa Ric, verzija 3.1.1). Ljubljana: Državni izpitni center.
Chua, B.L. (2017). A framework for classifying mathematical justification tasks. Dublin: CERME.
Cobb, P., Wood, T., Yackel, E. in McNeal, B. (1992). Characteristics of classroom mathematics tradition: An interactional analysis. American Educational Research Journal, 29(3), 573–604.
Critical Thinking Consortium (2013). Critical thinking in elementary mathematics: What? Why? When? And How?. Pridobljeno dne 24.09.2020 s svetovnega spleta: https://tc2.ca/uploads/PDFs/TIpsForTeachers/CT_elementary_math.pdf.
Depolli Steiner, K. (2018). Typology of teacher education students’ pedagogical beliefs. Didactica Slovenica – Pedagoška obzorja, 33(1), 104–115.
Hanna, G. (2000). Proof, Explanation and Exploration: an Overview. Educational Studies in Mathematics, 44(1–2), 5–23.
Jacob, S.M. (2012). Mathematical achievement and critical thinking skills in asynchronous discussion forums. Procedia – Social and Behavioral Sciences, 31, 800–804.
Kazemi, E. in Hintz, A. (2014). Intentional Talk: How to Structure and Lead Productive Mathematical Discussions. Portsmouth: Stenhouse Publishers.
Kosi Ulbl, I. (2014). Matematično znanje bodočih inženirjev. Didactica Slovenica – Pedagoška obzorja, 29(3–4), 79–97.
Lesseig, K. (2016). Fostering Teacher Learning of Conjecturing, Generalising and Justifying through Mathematics Studio. Mathematics Teacher Education and Development, 18(1), 100–118.
Magajna, Z. (2012). Med utemeljevanjem in dokazovanjem. V: KUPM, Zbornik prispevkov, str. 26–34. Pridobljeno dne 15.11.2019 s svetovnega spleta: https://www.zrss.si/pdf/zbornikprispevkovkupm2012.pdf.
Magajna, Z. in Žakelj, A. (2012). NPZ kot instrument za longitudinalno sledenje matematičnega znanja. V: Žakelj, A., Borstner, M. (ur.). Razvijanje in vrednotenje znanja: zbornik prispevkov s posveta. Ljubljana: Zavod RS za šolstvo, 33–36.
Mešinović, S., Cotič, M. in Žakelj A. (2017) Učenje in poučevanje osnovnih geometrijskih pojmov. Didactica Slovenica – Pedagoška obzorja, 32(2), 49–66.
Peter, E.E. (2012). Critical thinking: Essence for teaching mathematics and mathematics problem solving skills. African Journal of Mathematics and Computer Science Research, 5(3), 39–43.
RIC (2016). Nacionalno preverjanje znanja. Letno poročilo o izvedbi v šolskem letu 2015/2016. Ljubljana: Državni izpitni center. Pridobljeno dne 15.11.2019 s svetovnega spleta: https://www.ric.si/mma/Letno %20poro %20 %20ilo %20NPZ %202016/2016122114351304/.
RIC (2019). Nacionalno preverjanje znanja. Letno poročilo o izvedbi v šolskem letu 2018/2019. Ljubljana: Državni izpitni center. Pridobljeno dne 15.11.2020 s svetovnega spleta: https://www.ric.si/mma/Letno %20poro %20 %20ilo %20NPZ %202019/2019120913232271/.
Sharma, S. (2015). Promoting risk taking in mathematics classrooms: The importance of creating a safe learning environment. Mathematics Enthusiast, 12(2), 290–306.
Siriwat, R. in Katwibun, D. (2017). Exploring critical thinking in a mathematics problem-based learning classroom. V: Downton, A., Livy, S., Hall, J. (ur.). 40 years on: We are still learning! Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia. Melbourne: MERGA, 474–481.
Sun, J. in Van Es, E.A. (2015). An exploratory study of the influence that analysing teaching has on preservice teachers’ classroom practice. Journal of Teacher Education, 66(3), 201–214.
Špijunović, K. in Maričić, S. (2011). Development of pupils’ critical thinking in the initial teaching of mathematics. Didactica Slovenica – Pedagoška obzorja, 26(4), 66–76.
Thompson, C. (2011). Critical thinking across the curriculum: Process over output. International Journal of Humanities and Social Science, 1(9), 1–7.
Tunca, N. (2015). The regression level of constructivist learning environment characteristics on classroom environment characteristics supporting critical thinking. Eurasian Journal of Educational Research, 60, 181–200.
Učni načrt. Program osnovna šola. Matematika (2011). Ljubljana: Ministrstvo za šolstvo in šport.
Yuliani, K. in Saragih, S. (2015). The development of learning devices based guided discovery model to improve understanding concept and critical thinking mathematically ability of students at Islamic junior high school of Medan. Journal of Education and Practice, 6(24), 116–129.
Života Radović, V. (2014). Dejavnosti učencev med poukom. Didactica Slovenica – Pedagoška obzorja, 29(1), 33–45.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Jerneja Bone, Mara Cotič, Darjo Felda

This work is licensed under a Creative Commons Attribution 4.0 International License.


