research-article

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

Authors:

Yılmaz ZenginAuthors Info & Claims

Education and Information Technologies, Volume 27, Issue 2

Pages 1609 - 1634

https://doi.org/10.1007/s10639-021-10686-x

Published: 01 March 2022 Publication History

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.

References

[1]

Albaladejo IRM, García MDM, and Codina A Developing mathematical competencies in secondary students by introducing dynamic geometry systems in the classroom Education and Science 2015 40 177 43-58

[2]

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

[3]

Bassey M Case study research in educational settings 1999 Open University Press

[4]

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.

[5]

Bernabeu M, Moreno M, and Llinares S Primary school students’ understanding of polygons and the relationships between polygons Educational Studies in Mathematics 2021 106 2 251-270

[6]

Brodie K Teaching mathematical reasoning in secondary school classrooms 2010 Springer

[7]

Burger WF and Shaughnessy JM Characterizing the Van Hiele levels of development in geometry Journal for Research in Mathematics Education 1986 17 31-48

[8]

Carlsen M Upper secondary students’ mathematical reasoning on a sinusoidal function Educational Studies in Mathematics 2018 99 3 277-291

[9]

Clements DH and Battista MT The effects of Logo on children’s conceptualizations of angles and polygons Journal for Research in Mathematics Education 1990 21 5 356-371

[10]

Cobb P, Wood T, Yackel E, and McNeal B Characteristics of classroom mathematics traditions: An interactional analysis American Educational Research Journal 1992 29 3 573-604

[11]

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

[12]

Duval R Mammana C and Villani V Geometry from a cognitive point of view Perspectives on the teaching of geometry for the 21st century 1998 Kluwer 37-52

[13]

Eriksson H and Sumpter L Algebraic and fractional thinking in collective mathematical reasoning Educational Studies in Mathematics. 2021

[14]

Falcade R, Laborde C, and Mariotti MA Approaching functions: Cabri tools as instruments of semiotic mediation Educational Studies in Mathematics 2007 66 3 317-333

[15]

Fujita T Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon The Journal of Mathematical Behavior 2012 31 1 60-72

[16]

Hershkowitz R Visualization in geometry: Two sides of the coin Focus on Learning Problems in Mathematics 1989 11 1&2 61-75

[17]

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

[18]

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

[19]

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

[20]

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.

[21]

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

[22]

Jeannotte D and Kieran C A conceptual model of mathematical reasoning for school mathematics Educational Studies in Mathematics 2017 96 1 1-16

[23]

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

[24]

Kollosche D Styles of reasoning for mathematics education Educational Studies in Mathematics. 2021

[25]

Kontorovich I and Zazkis R Turn vs. shape: teachers cope with incompatible perspectives on angle Educational Studies in Mathematics 2016 93 2 223-243

[26]

Krummheuer G Cobb P and Bauersfeld H The ethnography of argumentation Emergence of mathematical meaning 1995 Lawrence Erlbaum 229-269

[27]

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

[28]

Lithner J Mathematical reasoning in task solving Educational Studies in Mathematics 2000 41 2 165-190

[29]

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.

[30]

Mata-Pereira J and Ponte JP Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification Educational Studies in Mathematics 2017 96 2 169-186

[31]

McCrone SS The development of mathematical discussions: An investigation in a fifth-grade classroom Mathematical Thinking and Learning 2005 7 2 111-133

[32]

McMillan JH and Schumacher S Research in education: Evidence-based inquiry 2010 7 Pearson

[33]

Miles MB, Huberman AM, and Saldana J Qualitative data analysis: A methods sourcebook 2014 3 Sage

[34]

Moore KC Quantitative reasoning and the sine function Journal for Research in Mathematics Education 2014 45 1 102-138

[35]

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

[36]

Olsson J and Granberg C Dynamic Software, task solving with or without guidelines, and learning outcomes Technology, Knowledge and Learning 2019 24 3 419-436

[37]

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.

[38]

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.

[39]

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

[40]

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.

[41]

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.

[42]

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

[43]

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

[44]

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

[45]

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.

[46]

Usiskin Z The classification of quadrilaterals: A study of definition 2008 Information Age Publishing

[47]

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

[48]

Zengin Y 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 2018 99 3 311-333

[49]

Zengin Y Development of mathematical connection skills in a dynamic learning environment Education and Information Technologies 2019 24 3 2175-2194

[50]

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.

Cited By

Zengin Y(2023)Effectiveness of a professional development course based on information and communication technologies on mathematics teachers' skills in designing technology-enhanced taskEducation and Information Technologies10.1007/s10639-023-11728-228:12(16201-16231)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10639-023-11728-2
Demir MZengin Y(2023)The effect of a technology-enhanced collaborative learning environment on secondary school students’ mathematical reasoning: A mixed method designEducation and Information Technologies10.1007/s10639-023-11587-x28:8(9855-9883)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1007/s10639-023-11587-x

Recommendations

The effect of a technology-enhanced collaborative learning environment on secondary school students’ mathematical reasoning: A mixed method design
Abstract
The purpose of this study is to examine the effect of a technology-enhanced collaborative learning environment on secondary school students’ mathematical reasoning in the concept of triangle. The participants of the study are 30 secondary school ...
Making mathematical reasoning fun: web-integrated, collaborative, and "hands-on" techniques
ACMSE '13: Proceedings of the 51st annual ACM Southeast Conference

Is it possible to excite students about learning the mathematical principles that underlie high-quality software? Can they use a development environment for "hands-on" experimentation with reasoning? Is this possible without displacing existing content? ...
Making mathematical reasoning fun: web-integrated, collaborative, and "Hands-On" Techniques (abstract only)
SIGCSE '13: Proceeding of the 44th ACM technical symposium on Computer science education

Is it possible to excite students about learning the mathematical principles that underlie high-quality software? Can they use a development environment for "hands-on" experimentation with reasoning? Is this possible without displacing existing content? ...

Comments

Information & Contributors

Information

Published In

cover image Education and Information Technologies

Education and Information Technologies Volume 27, Issue 2

Mar 2022

1514 pages

ISSN:1360-2357

Issue’s Table of Contents

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 March 2022

Accepted: 20 July 2021

Received: 30 November 2020

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 13 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Zengin Y(2023)Effectiveness of a professional development course based on information and communication technologies on mathematics teachers' skills in designing technology-enhanced taskEducation and Information Technologies10.1007/s10639-023-11728-228:12(16201-16231)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10639-023-11728-2
Demir MZengin Y(2023)The effect of a technology-enhanced collaborative learning environment on secondary school students’ mathematical reasoning: A mixed method designEducation and Information Technologies10.1007/s10639-023-11587-x28:8(9855-9883)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1007/s10639-023-11587-x

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents