Conceptualizing Technology-Enhanced Mathematical Modeling Process

Year 2023, , 1213 - 1248, 28.12.2023

Çağlar Naci Hıdıroğlu , Esra Bukova Guzel

https://doi.org/10.51460/baebd.1366450

Abstract

The aim of the study is to elucidate the mental actions employed in technology-enhanced mathematical modeling process. Within the framework this grounded theory study, participant selection was based on criterion sampling and theoretical sampling methods. The study was conducted with seven study groups comprised of 21 prospective mathematics teachers. The data consisted of video analyses depicting the solution processes of the groups for three mathematical modeling problems, GeoGebra solution files, written responses, and scratch papers, as well as the researcher's reflective/observational notes. The data analysis adhered to theory-building data analysis procedures, employing constant comparative analysis technique and open, axial, and selective coding processes. At the end of the theory-building data analysis, the technology-enhanced mathematical modeling process was explained through two basic and one subsidiary world, nine basic components, four subcomponents and nine basic steps. The study is one of the most comprehensive studies in the literature conducted on both the mathematical modeling process and technology integration in mathematical modeling.

Keywords

Mathematical modeling, Technology integration, GeoGebra, Grounded theory

Teknoloji ile Zenginleştirilmiş Matematiksel Modelleme Sürecinin Kavramsallaştırılması

Abstract

Çalışmanın amacı, teknoloji ile zenginleştirilmiş matematiksel modelleme sürecindeki zihinsel eylemleri açıklamaktır. Kuram oluşturma çalışması çerçevesinde yürütülen araştırmanın katılımcıları seçilirken ölçüt örnekleme ve kuramsal örnekleme yöntemleri dikkate alınmıştır. Çalışma 21 ortaöğretim matematik öğretmeni adayının oluşturduğu yedi birlikte çalışma grubu ile gerçekleştirilmiştir. Veriler; tasarlanan üç matematiksel modelleme problemine yönelik grupların çözüm süreçlerini içeren video çözümlemeleri, GeoGebra çözüm dosyaları, yazılı yanıt ve karalama kağıtlarından, araştırmacıların hatırlatıcı/gözlem notlarından oluşmaktadır. Verilerin analizinde kuram oluşturma veri analizi sürecine bağlı kalınarak sürekli karşılaştırmalı analiz tekniği, açık, eksensel ve seçici kodlama süreci dikkate alınmıştır. Kuram oluşturma veri analizi sonunda, teknoloji destekli matematiksel modelleme süreci iki temel ve bir yardımcı dünya, dokuz temel bileşen, dört yardımcı bileşen ve dokuz temel basamak ile açıklanmıştır. Çalışma alanyazında hem matematiksel modelleme sürecine hem de matematiksel modellemede teknoloji entegrasyonuna yönelik gerçekleştirilmiş en kapsamlı çalışmalardan biridir.

Keywords

Matematiksel modelleme, Teknoloji entegrasyonu, GeoGebra, Kuram oluşturma

References

• Abramovich, S. (2010). Topics in mathematics for elementary teachers: A Technology-enhanced experiential approach. Information Age Publishing.
• Abrams, J. P. (2001). Mathematical modeling: Teaching the open-ended application of mathematics. http://inst-mat.utalca.cl/~cdelpino/modelos/previos/libro/numbers3.pdf
• Ang, K. C. (2001). Teaching mathematical modelling in Singapore schools. The Mathematics Educator, 6(1), 63-75.
• Ang, K. C. (2010). Teaching and learning mathematical modelling with technology. Nanyang Technological University. 20.03.2012 tarihinde http://atcm.mathandtech.org/ep2010/invited/3052010_18134.pdf adresinden erişilmiştir.
• Ärlebäck, J. B. & Bergsten, C. (2010). On the use of realistic Fermi Problems in introducing mathematical modelling in upper secondary mathematics. R. Lesh, P. L. Galbraith, W. Blum & A. Hurford (Eds) Modeling students' mathematical modeling competencies- ICTMA 13 (ss. 597-609) içinde. Springer.
• Bazoune, A. (2010). Systems dynamics & control- Chapter 1: Introduction to system dynamics. 27.1.2012 tarihinde http://faculty.kfupm.edu.sa/ME/qahtanih/ME413Note/Chapter1.pdf adresinden erişilmiştir.
• Berry, J. & Davies, A. (1996). Written reports. C. R. Haines & S. Dunthorne (Eds) Mathematics learning and assessment: Sharing innovative practices (ss. 3.3-3.11). London: Arnold.
• Berry, J. & Houston K. (1995). Mathematical modelling. Bristol: J. W. Arrowsmith Ltd.
• Biccard, P. & Wessels, D. C. J. (2011). Documenting the Development of Modelling Competencies of Grade 7 Mathematics Students. International Perspectives on the Teaching and Learning of Mathematical Modelling, 1(5), 375-383.
• Blomhøj, M. & Jensen T. H. (2006). What’s all the fuss about competencies? Experiences with Using a Competence Perspective on Mathematics Education to Develop the Teaching of Mathematical Modelling. W.
• Blum, P.L. Galbraith and M. Niss (Eds) Modelling and applications in mathematics education (ss. 45-56) içinde. New York: Springer.
• Blomhøj, M. (1993). Modelling of dynamical systems at O-level. J. de Lange, C. Keitel, I. Huntley, & M. Niss (Eds) Innovation in mathematics education by modelling and applications (ss. 257-268) içinde. Ellis Horwood.
• Blum, W. & Leiß, D. (2007). How Do students and teachers deal with mathematical modelling problems? The example “Sugarloaf”. C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds) Mathematical modelling (ICTMA 12): Education, engineering and economics (ss. 222-231) içinde. Horwood Publishing.
• Blum, W. & Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. M. Niss, W. Blum & I. Huntley (Ed.) Modelling applications and applied problem solving (ss.1-19) içinde. England: Halsted Pres.
• Blum, W. (1985). Anwendungsorientierter mathematikunterricht in der didaktischen diskussion. Mathematische Semesterberichte, 32, 195-232.
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. G. Kaiser, W.
• Blum, R. Borromeo Ferri & G. Stillman (Eds.) Trends in the teaching and learning of mathematical modelling- Proceedings of ICTMA14 (ss. 15-30) içinde. New York: Springer.
• Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can, we do?. S. J. Cho (Ed.), The proceedings of the 12th ınternational congress on mathematical education-Intellectual and attitudinal challenges (ss. 73–96) içinde. Springer.