The Classification of Development and Assessment Approaches for Mathematical Modelling Competencies

Year 2016, Volume: 7 Issue: 3, 621 - 645, 13.12.2016

Funda Aydın Güç , Adnan Baki

https://doi.org/10.16949/turkbilmat.277876

Abstract

The main goal of
mathematics education is to train individuals as have reasoning and connection
skills, well-adjusted with their environment, productive and can solve problems
that faced throughout in their lives. Modeling competencies take place in the
center of this goal.  When the literature
examined, it can be seen that there are many studies on developing and
assessing mathematical modeling competencies and it is seen that the adopted
approaches are different from each other. However, systematic classifications
of the relevant approaches, how it can be improve and how mathematical modeling
can be integrated into learning environment are not dealt with in detail in the
literature. In this study, studies on developing and assessing mathematical
modeling competencies were examined and studies were classified by analyzing
comparative in terms of integration mathematical modeling on the learning
environment approaches and mathematical modeling competencies assessment
approaches. The classifications set out in this study depending on the
approaches and examples are thought to shed light on the discussions and
studies on developing and assessing mathematical modeling competencies.

Keywords

Mathematical modeling, modeling competencies, competency development, competency assessment, development and assessment approaches on competencies

Matematiksel Modelleme Yeterliklerini Geliştirme ve Değerlendirme Yaklaşımlarının Sınıflandırılması

Abstract

Muhakeme ve ilişkilendirme becerisine sahip,
çevresiyle uyumlu, üreten ve yaşamı boyunca karşılaştığı problemleri çözebilen
bireylerin yetiştirilmesi okul matematiğinin en temel amacıdır. Bu amacın tam
merkezinde matematiksel modelleme yeterlikleri yer almaktadır. İlgili alan
yazın incelendiğinde matematiksel modelleme yeterliklerinin geliştirilmesine ve
değerlendirilmesine yönelik birçok çalışmaya rastlanmaktadır ve benimsenen
yaklaşımların birbirinden farklı olduğu anlaşılmaktadır. Ancak ilgili alan yazında
söz konusu bu farklı yaklaşımların sistematik sınıflandırılması, nasıl
geliştirilebileceği ve matematiksel modellemenin öğrenme ortamlarına nasıl
entegre edilebileceği ayrıntılı olarak ele alınmamıştır. Bu çalışmada, kapsamlı
bir alan yazın taraması yapılarak matematiksel modelleme yeterliklerini
geliştirme, matematiksel modellemeyi öğrenme ortamına entegre etme ve
değerlendirme yaklaşımları karşılaştırmalı olarak çözümlenerek
sınıflandırılmıştır. Bu çalışma sonunda, yaklaşımlara ve örnek uygulamalara bağlı
olarak ortaya koyulan sınıflandırmaların matematiksel modelleme yeterliklerini
geliştirme ve değerlendirme çalışmalarına ve tartışmalarına ışık tutacağı
düşünülmektedir. 

Keywords

Matematiksel modelleme, modelleme yeterlikleri, yeterlik gelişimi, yeterlik değerlendirme, yeterlik geliştirme ve değerlendirme yaklaşımları

References

• Australia Ministry of Education. (2008). Australian curriculum. Retrieved from http://www. australiancurriculum.edu.au/mathematics/rationale
• Bal, A. P. ve Doğanay, A. (2014). Sınıf öğretmenliği adaylarının matematiksel modelleme sürecini anlamalarını geliştirmeye yönelik bir eylem araştırması. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1363-1384.
• Berry, J., & Haouston, K. (1995). Mathematical modelling. Bistrol: J. W. Arrowsmith Ltd.
• Biccard, P. (2010). An investigation into the development of mathematical modelling competencies of grade 7 learners. (Unpublished master’s thesis). Stellenbosh University, Stellenbosh.
• Blomhøj, M. (2007). Developing mathematical modelling competency through problem based project work - experiences from Roskilde University. Paper presented at Philosophy and Science Teaching Conferance. Retrieved from http://www. ucalgary. ca/ihpst07/proceedings/ıhpst07% 20papers/125% 20blomhoj. pdf.
• Blomhøj, M. & Jensen, T. H. (2003). Developing mathematical modelling competence: conceptual clarification and educational planning. Teaching Mathematics and Its Applications , 22(3), 123-139.
• Blomhøj, M., & Jensen, T. H. (2007). What's all the fuss about competencies? Experiences with using a competence perspective on mathematics education to develop the teaching of mathematical modelling. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 45-56). New York: Springer.
• Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical modelling and application, 1(1), 45-58.
• Blum, W., & Leiß, D. (2007). How do students’ and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222-231). Chichester: Horwood Publishing.
• Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. The International Journal on Mathematics Education, 38(2), 86-95.
• Braun, E. A. (2014). Designing a learning environment for elementary students based on a real life context. In S. Oesterle, C. Nicol, P. Liljedahl & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, 6 (pp. 26). Vancouver, Canada: PME.
• Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to cunstruct and solve mathematical modelling problems. Teaching Modelling and Its Applications, 39, 19-36.
• Bukova-Güzel, E. ve Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 69-90.
• 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.
• Dan, Q., & Xie, J. (2011). Mathematical modelling skills and creative thinking levels: An experimental study. In G. Kaiser, W. Blum, R. Borromeo-Ferri, and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 457-466). New York: Springer.
• Department for Education and Employment. (1999). Mathematics: The national curriculum for England. London: HMSO.
• 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.
• Eric, C. C., Dawn, N. K., Wanty, W., & Seto, C. (2012). Assessment of primary 5 students' mathematical modelling competencies. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 146-178.
• Galbraith, P., & Clatworthy, N. J. (1990). Beyond standard models – Meeting the challenge of modelling. Educational Studies in Mathematics, 21(2), 137-163.
• García, F. J. G., Maaß, K. & Wake, G. (2010). Theory meets practice—Working pragmatically within different cultures and traditions. In R. Lesh, P. Galbraith, C. Haines & A. Hurford (Eds.), Modelling students’ modelling competencies (pp. 445–457). New York: Springer.
• Gravemeijer, K. (2002). Preamble: From models to modelling. In K. Gravemeijer, R. Lesrer, B. Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 7-22). Dordrecht, The Netherlands: Kluwer Academic Publishers.
• Grünewald, S. (2012). Acquirement of modelling competencies – First results of an empırical comparison of the effectıveness of o holistic respectıvely an atomistic approach to the development of (metacognition) modelling competencies of students. Paper presented at 12th International Congress on Mathematical Education Program. COEX, Seoul, Korea. Retrieved from http://icme12.org/upload/UpFile2/TSG/0629.pdf
• Haines, C., & Crouch, R. (2001). Recognizing constructs within mathematical modelling. Teaching Mathematics and Its Applications, 20(3), 129-138.
• Henning, H., & Keune, M. (2007). Levels of modelling competencies. In W. Blum, P. L. Galbraith, H. Henn & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 225-232). US: Springer.
• Hıdıroğlu, Ç. N., Tekin-Dede, A., Kula, S. ve Bukova-Güzel, E. (2014). Öğrencilerin kuyruklu yıldız problemi’ne ilişkin çözüm yaklaşımlarının matematiksel modelleme süreci çerçevesinde incelenmesi. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 31, 1-17.
• Huang, C. H. (2011). Assessing the modelling competencies of engineering students. World Transactions on Engineering and Technology Education, 9(3), 172-177.
• Izard, J., Haines, C., Crouch, R., Houston, K., & Neil, N. (2003). Assessing the impact of teachings mathematical modeling: Some implications. In S. J. Lamon, W. A. Parker & K. Houston (Eds.), Mathematical modelling: A way of life (pp. 165-177). Chichester, UK: Horwood Publishing.
• Jensen, T. H. (2007). Assessing mathematical modelling competency. In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 141-148). Chichester: Horwood.
• Ji, X. (2012). A quasi-experimental study of high school students’ mathematics modelling competence. Paper presented at 12th International Congress on Mathematical Education Program, COEX, Seoul, Korea. Retrieved from http://www.icme12.org/upload/upfile2/tsg/0266.pdf
• Jorgensen, L., & Ryan, S. (2004). Relativism, values and morals in the New Zealand curriculum framework. Science and Education, 13, 223- 233.
• Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, M. Niss & H. W. Henn (Eds.), Modelling and applications in mathematics education (pp. 503-510). New York, NY: Springer.
• Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical Modelling Education, Engineering And Economics (pp. 110-119). Chichester: Horwood.
• Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. The International Journal on Mathematics Education, 38(3), 302-310.
• Kaiser, G., Schwarz, B., & Tiedemann, S. (2010). Future teachers’ professional knowledge on modeling. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 433-444). New York: Springer.
• Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi (Yayınlanmamış doktora tezi). Marmara Üniversitesi, İstanbul.
• Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri (Yayınlanmamış doktora tezi). Balıkesir Üniversitesi, Balıkesir.
• Kösa, T. ve Aydın-Güç, F. (2014). Matematik öğretmeni adaylarının matematiksel modelleme becerilerini geliştirmeye yönelik tasarlanan öğrenme ortamının değerlendirilmesi. (Araştırma Raporu, Proje Kod No: 9962), Karadeniz Teknik Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi, Trabzon.
• Lesh, R. A., & Doerr, H. (2003). Foundations of model and modelling perspectives on mathematic teaching and learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: Amodels and modelling perspectives on mathematics teaching, learning and problem solving (pp. 3-33). Mahwah, NJ: Lawrance Erlbauum.
• Ludwig, M., & Xu, B. (2010). A comparative study of modelling competencies among Chinese and German students. Journal for Didactics of Mathematics, 31(1), 77-97.
• Maaß, K. (2006). What are modelling competencies? The International Journal on Mathematics Education, 38(2), 113-142.
• Maaß, K., & Mischo, C. (2011). Implementing modelling into day-to-day teaching practice - the project stratum and its framework. Journal for Didactics of Mathematics, 32(1),103-131.
• Mason, J. (1988). Modelling: What do we really want pupils to learn? In D. Pimm (Ed.), Mathematics, teachers and children (pp. 201-215). London: Hodder and Stoughouton.
• Mehraein, S., & Gatabi, A. R. (2014a). Gender and mathematical modelling competency: primary students’ performance and their attitude. Procedia - Social and Behavioral Sciences, 128, 198-203.
• Mehraein, S., & Gatabi, A. R. (2014b). Sixth grade Iranian students engage in mathematical modelling activities. In S. Oesterle, C. Nicol, P. Liljedahl & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education. Vancouver, Canada.
• Milli Eğitim Bakanlığı [MEB]. (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12. Sınıflar) öğretim programı. Ankara.
• Ministry of Education. (1992). Mathematics in the nz curriculum. Wellington: Author.
• Mischo, C., & Maaß, K. (2012). Which personal factors affect mathematical modelling? The effect of abilities, domain specific and cross domain-competences and beliefs on performance in mathematical modelling. Journal of Mathematical Modelling and Application, 1(7), 3-19.
• Mischo, C., & Maaß, K. (2013). The effect of teacher beliefs on student competence in mathematical modeling – an intervention study. Journal of Education and Training Studies, 1(1), 19-38.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In M. Niss, W. Blum, H. Henn & P. L. Galbraith (Eds.), Modelling and applications in mathematics education (pp. 3-32). New York: Springer.
• Niss, M, & Højgaard, T. H. (2011). Competencies and mathematical learning: Ideas and inspiration for the development of mathematics teaching and learning in Denmark (English edition). Roskilde, Denmark: IMFUFA.
• Organisation for Economic Co-operation and Development [OECD], (2003). The PISA 2003 assessment framework: Mathematics, reading, science and problem solving knowledge and skills. Paris: Author
• Özdemir, E. ve Üzel, D. (2013). A case study on teacher instructional practices in mathematical modeling. The Online Journal of New Horizons in Education, 3(1), 1-14.
• Plath, J., Leiss, D., & Schwippert, K. (2014). Characteristics of comprehension processes in mathematical modelling. In S. Oesterle, C. Nicol, P. Liljedahl & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (6, pp. 198). Vancouver, Canada: PME.
• Queensland Board of Senior Secondary School Studies [QBSSSS]. (2000). Mathematics b senior syllabus 2001. Brisbane, QLD: Author.
• Rensaa, R. J. (2011). A task based two-dimensional view of mathematical competency used to analyse a modelling task. International Journal of Innovation in Science and Mathematics Education, 19(2), 37-50.
• Schwarz, B., & Kaiser, G. (2007). Mathematical modelling in school-experiences from a project ıntegrating school and university. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2180-2189). Larnaca: University of Cyprus.
• Sekerak, J. (2010). Phases of mathematical modelling and competence of high school students. The Teaching of Mathematics, 13(2), 105-112.
• Stillman, G. (2012). Applications and modelling research in secondary classrooms: What have we learnt? Paper presented at 12th International Congress on Mathematical Education Program, COEX, Seoul, Korea. Retrieved from http://www.icme12.org/upload/submission/1923_f.pdf
• Tekin-Dede, A. ve Yılmaz, S. (2013). İlköğretim matematik öğretmeni adaylarının modelleme yeterliklerinin incelenmesi. Turkish Journal of Computer and Mathematics Education, 4(3), 185-206.
• Victorian Curriculum and Assessment Authority [VCAA]. (2005). Victorian essential learning standards: Discipline-based learning strand mathematics. Melbourne: Author.
• Zöttl, L., Ufer, S., & Reiss, K. (2011). Assessing modelling competencies using a multidimensional IRT approach. In G. Kaiser, W. Blum, R. Borromeo-Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 427-437). New York: Springer.