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Education and Information Technologies

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31-07-2021

Disclosure of students’ mathematical reasoning through collaborative technology-enhanced learning environment

Authors: Nazlı Aksu, Yılmaz Zengin

Published in: Education and Information Technologies | Issue 2/2022

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Abstract

We focus on students’ mathematical reasoning in a technology-enhanced collaborative learning environment. We adopt a dialogical approach to analyze students' mathematical reasoning. The participants of this study include six middle school students. The data consist of participants’ written productions, dynamic materials, and the transcriptions of the participants’ discourse. The analysis shows that the integration of dynamic mathematics software into the ACODESA method contributes to their collective mathematical reasoning productively. The use of dynamic mathematics software as mediational artefacts and productive discussion as semiotic mediation are also required to enhance the participants’ both structural and process aspects of mathematical reasoning. The mediational role of dynamic mathematics software also helps them to make dynamic connection between mathematical reasoning and proving. In addition, participants’ representations evolve in the technology-enhanced learning environment and this evolution contributes to the development of mathematical reasoning.

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Albaladejo, I. R. M., García, M. D. M., & Codina, A. (2015). Developing mathematical competencies in secondary students by introducing dynamic geometry systems in the classroom. Education and Science, 40(177), 43–58.

Arzarello, F., Bartolini Bussi, M. G., Leung, A., Mariotti, M. A., & Stevenson, I. (2012). Experimental approach to theoretical thinking: Artefacts and proofs. In G. Hanna & M. De Villers (Eds.), Proof and proving in mathematics education: The 19th ICMI study (New ICMI Study Series) (pp. 97–137). Springer.CrossRef

Bassey, M. (1999). Case study research in educational settings. Open University Press.

Bernabeu, M., Moreno, M., & Llinares, S. (2018). Primary school children’s (9 years-old) understanding of quadrilaterals. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd conference of the international group for the psychology of mathematics education (vol. 2, pp. 155–162). Umeå: PME.

Bernabeu, M., Moreno, M., & Llinares, S. (2021). Primary school students’ understanding of polygons and the relationships between polygons. Educational Studies in Mathematics, 106(2), 251–270.CrossRef

Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer.CrossRef

Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the Van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31–48.CrossRef

Carlsen, M. (2018). Upper secondary students’ mathematical reasoning on a sinusoidal function. Educational Studies in Mathematics, 99(3), 277–291. https://doi.org/10.1007/s10649-018-9844-1MathSciNetCrossRef

Clements, D. H., & Battista, M. T. (1990). The effects of Logo on children’s conceptualizations of angles and polygons. Journal for Research in Mathematics Education, 21(5), 356–371.CrossRef

Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29(3), 573–604.CrossRef

Duval, R. (1995). Sémiosis et pensée humaine: Registres sémiotiques et apprentissages intellectuels [Semiosis and human thinking: Semiotic registers and intellectual learning]. Lang.

Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 37–52). Kluwer.

Eriksson, H., & Sumpter, L. (2021). Algebraic and fractional thinking in collective mathematical reasoning. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-021-10044-1CrossRef

Falcade, R., Laborde, C., & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317–333.CrossRef

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60–72.CrossRef

Hershkowitz, R. (1989). Visualization in geometry: Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1 & 2), 61–75.

Hitt, F. (2011). Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom. International Journal of Mathematical Education in Science and Technology, 42(6), 723–735.CrossRef

Hitt, F., & Dufour, S. (2021). Introduction to calculus through an open-ended task in the context of speed: representations and actions by students in action. ZDM Mathematics Education, 53(3), 635–647.CrossRef

Hitt, F., & González-Martín, A. (2015). Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflexion) method. Educational Studies in Mathematics, 88(2), 201–219.CrossRef

Hitt, F., Saboya, M., & Cortés C. (2017). Task design in a paper and pencil and technological environment to promote inclusive learning: An example with polygonal numbers. In G. Aldon, F. Hitt, L. Bazzini & Gellert U. (Eds.), Mathematics and technology. A C.I.E.A.E.M. Sourcebook (pp. 57–74). Springer.

Hohenwarter, J., Hohenwarter, M., & Lavicza, Z. (2008). Introducing dynamic mathematics software to secondary school teachers: The case of GeoGebra. JI of Computers in Mathematics and Science Teaching, 28(2), 135–146.

Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16.CrossRef

Kaur, H. (2015). Two aspects of young children’s thinking about different types of dynamic triangles: Prototypicality and inclusion. ZDM-Mathematics Education, 47(3), 407–420.CrossRef

Kollosche, D. (2021). Styles of reasoning for mathematics education. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-021-10046-zCrossRef

Kontorovich, I., & Zazkis, R. (2016). Turn vs. shape: teachers cope with incompatible perspectives on angle. Educational Studies in Mathematics, 93(2), 223–243.CrossRef

Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning (pp. 229–269). Lawrence Erlbaum.

Linell, P. (1998). Approaching dialogue: Talk, interaction and contexts in dialogical perspectives. John Benjamins.CrossRef

Lithner, J. (2000). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41(2), 165–190.CrossRef

Mason, M. M. (1989). Geometric understanding and misconceptions among gifted fourth-eighth graders. In Paper presented at the Annual Meeting of the American Educational Research Association. San Francisco, CA.

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.CrossRef

McCrone, S. S. (2005). The development of mathematical discussions: An investigation in a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.CrossRef

McMillan, J. H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7th ed.). Pearson.

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Sage.

Moore, K. C. (2014). Quantitative reasoning and the sine function. Journal for Research in Mathematics Education, 45(1), 102–138.CrossRef

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston: NCTM.

Olsson, J., & Granberg, C. (2019). Dynamic Software, task solving with or without guidelines, and learning outcomes. Technology, Knowledge and Learning, 24(3), 419–436.CrossRef

Peirce, C. S. (1956). Sixth paper: Deduction, induction, and hypothesis. In M. R. Cohen (Ed.), Chance, love, and logic: Philosophical essays (pp. 131–153). G. Braziller.

Radford, L. (1998). On culture and mind, a post-Vygotskian semiotic perspective, with an example from Greek mathematical thought. In Paper presented at the 23rd Annual Meeting of the Semiotic Society of America, Victoria College, University of Toronto, Canada. Retrieved Jan 25, 2019, from http://www.luisradford.ca/pub/102_On_culture_mind2.pdf.

Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70.CrossRef

Radford, L. (2008). Theories in mathematics education: A brief inquiry into their conceptual differences. ICMI 11 Survey team 7: The notion and role of theory in mathematics education research. Retrieved Dec 20, 2018, from http://www.luisradford.ca/pub/31_radfordicmist7_EN.pdf.

Reid, D. A. (2003). Forms and uses of abduction. In M. A. Mariotti (Ed.), Proceedings of 3rd Conference of European Society for Research in Mathematics Education (pp. 1–10). CERME.

Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1–3), 13–57.CrossRef

Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.CrossRef

Sfard, A. (2012). Introduction: Developing mathematical discourse-some insights from communicational research. International Journal of Educational Research, 51–52, 1–9.CrossRef

Tsamir, P., Tirosh, D., & Stavy, R. (1998). Do equilateral polygons have equal angels? In A. Olivier, & K. Newstead (Eds.), Proceeding of the 22nd conference of the international group for the psychology of mathematics education (Vol. 4, pp. 137–144). Stellenbosch.

Usiskin, Z. (2008). The classification of quadrilaterals: A study of definition. Information Age Publishing.

Zengin, Y. (2017). Investigating the use of the Khan Academy and mathematics software with a flipped classroom approach in mathematics teaching. Educational Technology & Society, 20(2), 89–100.

Zengin, Y. (2018). Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. Educational Studies in Mathematics, 99(3), 311–333.CrossRef

Zengin, Y. (2019). Development of mathematical connection skills in a dynamic learning environment. Education and Information Technologies, 24(3), 2175–2194.CrossRef

Zengin, Y. (2021). Construction of proof of the Fundamental Theorem of Calculus using dynamic mathematics software in the calculus classroom. Education and Information Technologies. Advance online publication.

Title: Disclosure of students’ mathematical reasoning through collaborative technology-enhanced learning environment
Authors: Nazlı Aksu
Yılmaz Zengin
Publication date: 31-07-2021
Publisher: Springer US
Published in: Education and Information Technologies / Issue 2/2022
Print ISSN: 1360-2357
Electronic ISSN: 1573-7608
DOI: https://doi.org/10.1007/s10639-021-10686-x

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