Matematiksel Modelleme Problemlerinin Yapılandırılması Üzerine Tasarım Tabanlı İnceleme: Finansal İçerik Örneği

Year 2017, Volume: 5 Issue: 10, 218 - 240, 03.12.2017

Melike Tural Sönmez

https://doi.org/10.18009/jcer.307314

Cited By: 5

Abstract

Bu çalışmada
yedinci sınıf seviyesinde finansal içerikte matematiksel modelleme
problemlerinin yapılandırma sürecinin incelenmesi amaçlanmıştır. Matematiksel
modelleme problemlerinin yapılandırılmasına yönelik tasarım önerisi
oluşturulması hedeflenmiştir. Araştırmada tasarım tabanlı araştırma yöntemi
kullanılmıştır. Çalışmanın katılımcıları üç yedinci sınıf öğrencisi, altı
finans uzmanı ve dokuz matematik eğitimi uzmanından oluşmaktadır. Çalışmanın
veri toplama araçları yedinci sınıf öğrencilerinin matematiksel modelleme
etkinlikleri süresinde videolarının ve ses kaydının transkiribi, öğrenci
çalışma dokümanları, uzman katılımcıların görüş alma formlarıdır. Çalışma üç
aşamadan oluşmaktadır. Birinci aşama ön uygulamanın yapılması aşamasıdır. Bu
aşama, matematiksel modelleme problemlerin sınıf seviyesine uygunluğu,
öğrencilerin zamanlamaları, problemlerin anlaşılırlığı ve öğrencilerin bağlam
hakkındaki bilgileri konusunda değerlendirmeler sunmuştur. İkinci aşamada
finans konusunda uzman kişilerden; matematiksel modelleme problemlerin finansal
okuryazarlık standartlarına uygunluğu konusunda görüş alınmıştır. Üçüncü
aşamada ise matematik eğitimi uzmanları matematiksel modelleme problemlerin
sınıf seviyesine, matematiksel modelleme ilkelerine ve yedinci sınıf matematik
dersi kazanımlarına uygunluğu konusunda görüş bildirmişlerdir. Görüş alma
formundaki maddelerin frekans değerleri hesaplanmış ve uzmanların ifadelerinden
alıntılar yapılmıştır. Araştırmada tasarım rehberinin aşamalandırılmasına ve
uygulanmasına yönelik önerilerde bulunulmuştur.

Keywords

Tasarım araştırması, matematiksel modelleme, finansal okuryazarlık

Design based Investigation on Construction of Mathematical Modelling Problems: Example of Financial Content

Abstract

The purpose of this study is to examine the
construction of mathematical modelling problems process in the content of
financial literacy. It is also aimed to create design proposals for
construction of mathematical modelling problems. A design based research method
was used in this study. The participants were three seventh grade students, six
finance experts and nine mathematics education experts. Data collection tools
were transcription of video and tapes group discussions, presentations and
worksheets during mathematical modelling activities, and participant experts’
feedback form about mathematical modelling problems. There were three stages in
this study. First stage was application of preliminary study. This stage gave
information about convenience of problems to grade level, students’ timing for
solution of problems, clarity of problems and students’ background about
content. In second stage, finance experts commented on convenience of
mathematical modelling problems to financial literacy standards.  In third stage, mathematics education experts
commented on convenience of problems to students’ grade level, mathematical
modelling principles and seventh grade mathematics lesson objectives. They also
gave suggestion on progress. The frequency value of theme in feedback forms was
calculated and experts’ expressions were given as citation. It was given
suggestion about stages and application of the design guide.

Keywords

Design based research, mathematical modelling, financial literacy, mathematics education

References

• Aztekin, S. & Şener, Z.T. (2015). The content Analysis of Mathematical Modelling Studies in Turkey: A Meta-synthesis Study. Education and Science, 40 (178) Bernheim, D., Garrettand D., & Maki D., (2001). Education and saving: The long-term effects of high school financial curriculum mandates. Journal of Public Economics, 85, 435-565. Berry, J. & Houston, K. (1995) Students Using Posters as a Means of Communication and Assessment. Educational Studies in Mathematics, 29, (1), 21-27 Published by: Springer Stable URL: http://www.jstor.org/stable/3482829 . Blomhøj, M. & Jensen, T. H. (2003). Developing mathematical modelling competence: conceptual clarification and educational planning. Teaching Mathematics and Its Applications , 22(3), 123-139 Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating models and modeling perspective with existing research and practice. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 465-478). Mahwah, NJ: Lawrence Erlbaum. Cobb, P., Confrey, J., diSessa, A., Lehrer, R. ve Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13. Cobb, P., Confrey, J., diSessa, A., Lehrer, R. ve Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13. Cole, S., T. & Sampsonand B. Z. (2011). Pricesor knowledge? What drives demand for financial services in emerging markets?. The Journal of Finance, 66 (6),1933-1967. Creswell, J. W. (2003). Research design: qualitative, quantitative, and mixed method approaches. Thousand Oaks, Calif, Sage Publications. Crouch, R., & Haines, C. (2004). Mathematical modelling: Transitions between the real world and mathematical model. International Journal of Mathematical Education in Science and Technology , 35(2), 197-206. Gravemeijer, K. (1999). Emergent Models May Foster the Constitution of Formal Mathematics. Mathematical Thinking and Learning, 1(2), 155-177. Greer, B. (1993). The mathematical modelling perspective on world problems. Journal of Mathematical Behaviour, 12, 239-250. Haines, C. & Crouch, R. (2001). Recognising constructs within mathematical modelling. Teaching Mathematics and its Applications, 20 (3): 129-138. Haines, C., Crouch, R., & Davis, J. (2000). Mathematical modelling skills: A research instrument (Technical Report No. 55). Hatfield, UK: University of Hertfordshire, Department of Mathematics INFE. (2009). Financial education programmes in schools: draft comparative analysis of selected financial education learning frameworks: international network on financial education. Jensen, T. H. (2007). Assessing Mathematical Modelling Competency. In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical Modelling Education, Engineering and Economics (ICTMA12). pp. 141-148. Chichester: Horwood. Kuzu, A.,Çankaya, S., Mısırlı, Z. A. (2011).Tasarım Tabanlı Araştırma ve Öğrenme Ortamlarının Tasarımı ve Geliştirilmesinde Kullanımı. Anadolu Journal of Educational Sciences International, July 2011, 1(1) Lawshe, C. H. (1975). A quantitative approach to content validity. Personnel Psychology, 28, 563–575. Lesh , R.A., & Doerr, H. (2003). Foundations of model and modeling perspectives on mathematic teaching and learning. In R.A. Lesh and H. Doerr (Eds.), Beyond constructivism: A models and modeling perspectives on mathematics teaching, learning, and problem solving. Mahwah, NJ: Lawrance Erlbaum. Lusardi, A. (2009), U.S. Household savings behavior: the role of financial literacy, information and financial education programs, InC. Foote, L. Goetteand S. Meier (eds.), Policy making Insights from Behavioral Economics, Federal Reserve Bank of Boston, pp. 109-149. Milli Eğitim Bakanlığı. (2009). İlköğretim matematik dersi 6-8. sınıflar öğretim programı ve kılavuzu, Ankara: Yazar. Merriam, S. B. (1998). Qualitative Researchand Case Study Applications in Education (second edition). San Francisco: Jossey-BassPublishers Miles MB, Huberman M. (1994).Qualitative Data Analysis: A Sourcebook of New Methods. 2. Beverly Hills, CA: Sage Publications Niss, M. & Jensen, T. H. (eds) (2002). Kompetencer og matematiklæring – Ideer og inspiration til udvikling af matematikundervisning i Danmark, number 18 in Uddannelsesstyrelsens temahæfteserie, The Ministry of Education, Copenhagen, Denmark. Cf. http://nyfaglighed.emu.dk/kom. OECD, (2005). Improving Financial Literacy Analysis of Issue and Policies. OECD, (2012). Guidelines on financial education at school and guidance on learning framework. Schoenfeld, A. H. (1982). Some thoughts on problem-solving research and mathematics education. In F. K. Lester And J. Garofalo (Eds.) Mathematical problem solving: issues in research (Pp. 27-37). Philadelphia: Franklin Institute Press. Veneziano L. ve Hooper J. (1997). A method for quantifying content validity of health-related questionnaires. American Journal of Health Behavior, 21(1):67-70. Wang, F. & Hannafin, M. (2005). Design-based research and technology-enhanced learning environments. Educational Technology Research and Development, 53(4), 5-23. Wang, F. ve Hannafin, M.J. (2005). Design-based research and technology-enhanced learning environments. Educational Technology Research and Development, 53(4), 5-23. Yurdugül, H. (2005). Ölçek Geliştirme Çalışmalarında Kapsam Geçerliği İçin Kapsam Geçerlik İndekslerinin Kullanılması XIV. Eğitim Bilimleri Kurultayı, 28-30 Eylül, Pamukkale Üniversitesi, Denizli Zbiek, R. M. & Conner, A. (2006). Beyond Motivation: Exploring mathematical modelling as a context for deepening students’ understandings of curricular mathematics. Educational Studies in Mathematics, 63, 89–112.