Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach

Şule Deniz; Gamze Kurt

doi:10.17275/per.22.34.9.2

EN

Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach

Abstract

This study aimed to reveal mathematical modeling processes and difficulties encountered in model-eliciting activities (MEAs) of 8th-grade students in a STEM education setting. This qualitative research is a case study conducted at a public school located in the central districts of a large province in the Mediterranean Region. The participants of the study are groups of 8th-grade middle school students in a classroom (five groups of students), which were selected with the purposeful sampling method in the 2019-2020 academic year. The student groups were applied an MEA according to a certain plan, and the students’ model-eliciting processes were recorded. Then, the participants’ modeling activity process and the cognitive activities they put forward through documents and interviews were examined by considering the stages in a mathematical modeling process. For this purpose, each group’s modeling process was analyzed qualitatively using the modeling cycle of Blum and Borromeo Ferri (2009). The results of the study revealed that these 8th-grade students faced some difficulties in the process of modeling. These difficulties were identified in 7 categories: understanding the problem, establishing a model, using mathematics, and explaining the results, - which are the four stages of the modeling process- working within a group, verifying the created model, and time management.

Keywords

Stem Education, model-eliciting activities, mathematical modelling, mathematical modelling activities, middle school students

Supporting Institution

Mersin University Scientific Research Projects (BAP) Unit

Project Number

2019-3-TP2-3736

References

Balakrıshnan, G., Yen, Y.P. ve Goh, E. L. E. (2010). Mathematical modelling in the Singapore secondary school mathematics curriculum. In Mathematical Applications And Modelling: Yearbook 2010, Association of Mathematics Educators (pp. 247-257).
Ben-Chaim, D., Fey, J., Fitzgerald, W., Benedetto, C. ve Miller, J. (1997). Development of proportional reasoning in a problem-based middle school curriculum. Annual Meeting of the American Educational Research Association, Chicago, IL. Erişim adresi: https://files.eric.ed.gov/fulltext/ED412091.pdf
Berry, J. S. ve Houston, K. (1995). Mathematical modelling. Gulf Professional Publishing. Erişim adresi:https://books.google.com.tr/books?id=yWmnj4nNBcgC&printsec=frontcover&hl=tr&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 15-30). New York: Springer.
Blum, W. ve Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
Blum, W. ve Leiß, D. (2007). How Do Students and Teachers Deal With Modeling Problems? In C. R. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical Modeling Education, Engineering and Economics (pp. 222–231). Chichester: Horwood Publishing. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 86-95
Bryan, L. A., Moore, T. J., Johnson, C. C., ve Roehrig, G. H. (2015). Integrated STEM education. In STEM road map (pp. 23-37). Routledge.
Bulgar, S. (2008). Enabling more students to achieve mathematical success. Creativity, giftedness and talent development in mathematics, 133-154.
Chan, E. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
Corlu, M. S., Capraro, R. M., ve Capraro, M. M. (2014). Introducing STEM education: Implications for educating our teachers in the age of innovation. Eğitim ve Bilim, 39(171), 74-85.

Creswell, J. W. (2019). Eğitim araştırmaları: nicel ve nitel araştırmanın planlanması, yürütülmesi ve değerlendirilmesi (H. Ekşi, Çev.). İstanbul: EDAM Yayıncılık.
Creswell, J. W. (2018). Nitel Araştırma Yöntemleri (M. Bütün ve S. B. Demir, Çev.). Ankara: Siyasal Kitabevi.
Dede, Y. ve Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir? Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(24), 180-185.
Doerr, H. M. (1997). Experiment, simulation and analysis: An integrated instructional approach to the concept of force. International journal of science education, 19(3), 265-282.
Doğan, M. F., Gürbüz, R., Çavuş Erdem, Z. ve Şahin, S. (2019a). STEM eğitimine geçişte bir araç olarak matematiksel modelleme. R. Gürbüz ve M. F. Doğan (Ed.). Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı (3. Baskı) içinde (s. 43-56). Ankara: Pegem Akademi.
Doğan, M. F., Gürbüz, R., Çavuş Erdem, Z. ve Şahin, S. (2019b). Using Mathematical Modeling for Integrating STEM Disciplines: A Theoretical Framework. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(3), 628-653.
Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin Etkisi. Doktora Tezi, Hacettepe Üniversitesi Sosyal Bilimler Enstitüsü, Ankara
English, L. D. (2002). Development of 10-Year-Olds' Mathematical Modelling. Document Reproduction Service, No: ED 476 094.
English, L. D. (2006). Mathematical modeling in the primary school: Children's construction of a consumer guide. Educational studies in mathematics, 63(3), 303-323.
English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling. Zentralblatt für Didaktik der Mathematik -ZDM, 41(1-2), 161-181.
English, L. D. ve Kirshner, D. (Eds.). (2015). Handbook of international research in mathematics education. Routledge.
English, L. D. ve Mousoulides, N. G. (2011). Engineering-based modelling experiences in the elementary and middle classroom. In Models and modeling (pp. 173-194). Springer, Dordrecht.
Eraslan, A. ve Kant, S. (2015). Modeling processes of 4th-year middle-school students and the difficulties encountered. Educational Sciences: Theory & Practice, 15(3).
Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., ve Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1-21.
Eş, H., Özdemir, A. ve Kaplan, M. (2019). Matematik Bir Bilim Dalı Mıdır? Matematik Öğretmen Adaylarının Bilim-Matematik İlişkisine Dair Algıları. Kastamonu Eğitim Dergisi, 27(1), 407-419.
Fraenkel, J.R., Wallen, N.E. ve Hyun, H.H. (2012). Eğitimde araştırma nasıl tasarlanır ve değerlendirilir (8. baskı). New York: McGram-Hill Şirketleri.
Galbraith, P. ve Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 143-162.
Gilbert, J. K. (2010). The role of visual representations in the learning and teaching of science: An introduction. In Asia-Pacific Forum on Science Learning ve Teaching 11(1).
Gonzalez, H. B. ve Kuenzi, J. J. (2012). Science, technology, engineering, and mathematics (STEM) education: A primer. Washington, DC: Congressional Research Service, Library of Congress.
Greefrath, C. (2013). Analysis of modelling problem solutions with methods of problem solving. In Lesh, R., Galbraith, P. L., Haines, C. R., & Hurford, A (Eds.), Modeling students' mathematical modeling competencies: The 13th. ICTMA study (pp. 265-271). Springer, Dordrecht.
Guba, E. G. ve Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication and Technology Journal, 30 (4), 233-252
Hestenes, D. (2010). Modeling theory for math and science education. In Modeling students' mathematical modeling competencies (pp. 13-41). Springer, Boston, MA.
Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıklama. Yüksek Lisans Tezi. Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi. Yüksek Lisans Tezi. Marmara Üniversitesi, Eğitim Bilimleri Enstitüsü, İstanbul.
Kertil, M. ve Gurel, C. (2016). Mathematical modeling: A bridge to STEM education. International Journal of Education in Mathematics Science and Technology, 4(1), 44-55.
Kuenzi, J. J. (2008). Science, technology, engineering, and mathematics (STEM) education: Background, federal policy, and legislative action. Erişim adresi (25.03.2020): http://digitalcommons.unl.edu/crsdocs/35/
Kurt-Birel, G., Deniz, Ş. ve Önel, F. (2020). Analysis of Primary School Teachers’ Knowledge of Geometry. International Electronic Journal of Elementary Education, 12(4), 303-309.
Lesh, R. ve Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, 3-33.
Lesh, R. ve English, L. (2017). Case Study for Kids. Erişim adresi (25. 03. 2020): https://engineering.purdue.edu/ENE/Research/SGMM/CASESTUDIESKIDSWEB/index.htm
Lesh, R. ve Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical thinking and learning, 5(2-3), 157-189.
Merriam, S. B. (2018). Nitel araştırma: Desen ve uygulama için bir rehber (S. Turan, Çev.) (3.Basımdan çeviri). Ankara: Nobel Akademik Yayıncılık (Eserin orijinali 2009 yılında basılmıştır).
Meyrick, K.M. (2011). How STEM education improves student learning. Meridian K12 School Computer Technologies Journal, 14 (1), 1-6.
Millî Eğitim Bakanlığı. (2016). STEM Eğitimi Raporu. Ankara: Millî Eğitim Bakanlığı Yenilik ve Eğitim Teknolojileri Genel Müdürlüğü (YEĞİTEK). Erişim adresi (20.04.2020): http://yegitek.meb.gov.tr/STEM_Egitimi_Raporu.pdf .
Millî Eğitim Bakanlığı (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1,2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: MEB Yayınları
Moore, T.J., Doerr, H.M., Glancy, A.W. ve Ntow, F.D. (2015). Preserving pelicans with models that make sense. Mathematics Teaching in the Middle School, 20(6), 358-364.
Mousoulides, N., Pittalis, M. ve Christou, C. (2006). Improving Mathematical Knowledge through Modeling in Elementary School. In Proc. 30 th Conf. Of the PME (Vol. 4, pp. 201-208).
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (1). Erişim adresi (18.03.2020): http://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf
Olkun, S. ve Uçar, Z. T. (2009). İlköğretimde etkinlik temelli matematik öğretimi. Ankara: Eğiten Kitap Yayınevi
Organisation for Economic Co-operation and Development (2010). Education at a glance 2010: OECD indicators. Paris: OECD.
Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri (M. Bütün ve S.B. Demir, Çev. Ed.). Ankara: Pegem Akademi.
Şahin, A., Ayar, M. C. ve Adiguzel, T. (2014). STEM Related After-School Program Activities and Associated Outcomes on Student Learning. Educational Sciences: Theory and Practice, 14(1), 309-322.
Sol, M., Giménez, J. ve Rosich, N. (2011). Project Modelling Routes in 12–16-Year-Old Pupils. In G. Kaiser, W. Blum, R. B. Ferri, G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modellin: The 14. ICMTA Study (pp. 231–240). New York: Springer.
Sriraman, B. (2006). Conceptualizing the model-eliciting perspective of mathematical problem solving. In Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1686-1695).
Sriraman, B., ve Lesh, R. A. (2006). Modeling conceptions revisited. Zentralblatt für Didaktik der Mathematik-ZDM, 38(3), 247-254.
Stillman, G., Galbraith, P., Brown, J. ve Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. Mathematics: Essential research, essential practice, 2, 688-697.
Swan, M., Turner, R., Yoon, C. ve Muller, E. (2007). The roles of modelling in learning mathematics. In W. Blum, P. Galbraith, H.-W. Henn & M. Niss (Eds.) Modelling and applications in mathematics education: The 14th ICMI study (pp. 275-284). Springer, Boston, MA.
Şencan, H. (2005). Sosyal ve davranışsal ölçümlerde güvenilirlik ve geçerlilik. Ankara: Seçkin Yayıncılık.
Şimşek, H. ve Yıldırım, A. (2011). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
Turner, R. (2007). Modelling and applications in PISA. In Modelling and applications in mathematics education (pp. 433-440). Springer, Boston, MA.
Umay, A. (1996). Matematik öğretimi ve ölçülmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 12, 145-149
Van De Walle, J., Karp, K. S. ve Bay-Williams, J. M. (2012). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim. (S. Durmuş Çev. Ed, 7. Basımdan Çeviri). Ankara: Nobel Akademik Yayıncılık.
Yamak, H., Bulut, N. ve Dündar, S. (2014). 5. sınıf öğrencilerinin bilimsel süreç becerileri ile fene karşı tutumlarına FeTeMM etkinliklerinin etkisi. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 34(2), 249-265. Doi: 10.17152/gefd.15192
Yanık, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78 (2), 231-260.
Yin, R. K. (2017). Durum çalışması araştırması uygulamaları (İ. Günbayı, Çev.). Ankara: Nobel Akademik Yayıncılık.
Zawojewski, J. S., Lesh, R. A. ve English, L. D. (2003). A models and modeling perspective on the role of small group learning activities. In Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 337-358). Lawrence Erlbaum Associates.

Details

Primary Language

English

Subjects

Other Fields of Education

Journal Section

Research Article

Authors

Şule Deniz
0000-0002-3119-7403
Türkiye

Gamze Kurt ^*
0000-0002-4976-5069
Türkiye

Publication Date

March 1, 2022

Submission Date

March 25, 2021

Acceptance Date

June 2, 2021

Published in Issue

Year 2022 Volume: 9 Number: 2

DOI

https://doi.org/10.17275/per.22.34.9.2

IZ

https://izlik.org/JA43TM85LD

APA

Deniz, Ş., & Kurt, G. (2022). Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach. Participatory Educational Research, 9(2), 150-177. https://doi.org/10.17275/per.22.34.9.2

AMA

1.Deniz Ş, Kurt G. Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach. PER. 2022;9(2):150-177. doi:10.17275/per.22.34.9.2

Chicago

Deniz, Şule, and Gamze Kurt. 2022. “Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach”. Participatory Educational Research 9 (2): 150-77. https://doi.org/10.17275/per.22.34.9.2.

EndNote

Deniz Ş, Kurt G (March 1, 2022) Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach. Participatory Educational Research 9 2 150–177.

IEEE

[1]Ş. Deniz and G. Kurt, “Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach”, PER, vol. 9, no. 2, pp. 150–177, Mar. 2022, doi: 10.17275/per.22.34.9.2.

ISNAD

Deniz, Şule - Kurt, Gamze. “Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach”. Participatory Educational Research 9/2 (March 1, 2022): 150-177. https://doi.org/10.17275/per.22.34.9.2.

JAMA

1.Deniz Ş, Kurt G. Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach. PER. 2022;9:150–177.

MLA

Deniz, Şule, and Gamze Kurt. “Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach”. Participatory Educational Research, vol. 9, no. 2, Mar. 2022, pp. 150-77, doi:10.17275/per.22.34.9.2.

Vancouver

1.Şule Deniz, Gamze Kurt. Investigation of Mathematical Modeling Processes of Middle School Students in Model-Eliciting Activities (MEAs): A STEM Approach. PER. 2022 Mar. 1;9(2):150-77. doi:10.17275/per.22.34.9.2