Uzamsal Yönelim Becerilerini İçeren Bir Gerçek Yaşam Probleminin Çözüm Sürecinden Yansımalar: Badana Problemi

Öz Araştırmanın amacı, öğrencilerin gerçek yaşamdaki bir problemin çözüm sürecindeki uzamsal yönelim becerilerini de içeren modelleme yaklaşımlarını incelemektir. Daha önceden modelleme deneyimi olmayan katılımcılara bir gerçek yaşam problemi verilmiş ve çözümlerini posterler hazırlayarak sunmaları istenmiştir. Öğrencilerin çözümleri probleme özgü bir rubrik ile analiz edilmiş ve çözüm yaklaşımları gerçek model oluşturma, matematiksel model oluşturma, matematiksel olarak çalışma ve sonuçları gerçek yaşama göre yorumlamayı içeren modelleme basamaklarına göre değerlendirilmiştir. Çalışmanın bulguları öğrencilerin gerçek modellerinin kişisel deneyimlerinden ve uzamsal yönelim becerilerinden doğrudan etkilendiğini göstermiştir. Oluşturulan matematiksel modeller gerçek modellere dayalı olmuş ve öğrencilerin matematiksel modelleri oluştururken matematiksel bilgilerini ve farklı gösterimleri göz önünde bulundurdukları görülmüştür. Matematiksel olarak çalışırken, modelleri doğru bir şekilde çözmüşler ancak çoğunlukla birimleri ifade etmekte zorlanmışlardır. Modelleme deneyimi olmayan öğrencilerin matematiksel sonuçları gerçek yaşam bağlamında yorumlayabilmeleri dikkat çekici bir sonuç olmuştur. Bunun nedenleri, hepsi için anlamlı bir gerçek yaşam bağlamında çalışmış olmaları, okul dışında araştırma yapmış olmaları ve böylece gerçek verilere ulaşabilmeleri olarak belirlenmiştir.

Kaynakça

Berry J, & O’Shea T. (1982). Assessing mathematical modelling. International Journal of Mathematical Education in Science and Technology, 13(6). 715-724.

Blomhøj, M. (2008). Different perspectives on mathematical modelling in educational research - Categorising the TSG21 papers. Electronic Proceedings of the Eleventh International Congress on Mathematical Education ICME 11(pp. 1-13). Mexico.

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 (ICTMA 12): Education, Engineering and Economics (pp. 222-231). Chichester: Hollywood

Blum, W. & Niss, M. (1991). Applied Mathematical problem solving, modelling, applications, and links to other subjects - State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37-68.

Blum, W. (1991). Applications and modelling in mathematics teaching – A review of arguments and instructional aspects. In M. Niss, W. Blum, & I. Huntley (Eds.), Teaching of Mathematical Modelling and Applications (pp. 10-29). Chichester: Ellis Horwood.

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., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be thought or learned?. Journal Of Mathematical Modelling And Application, 1(1), 45-58.

Borromeo Ferri, R. (2006). Theoretical and Empirical Differentiations of Phases in the Modelling Process. Zentralblatt für Didaktik der Mathematik-ZDM, 38 (2), 86-95.

Borromeo Ferri, R., Kaiser, G., & Blum, W. (2011). Mit dem taxi durch die welt des mathematischen modellierens. In T. Krohn, E. Malitte, G. Richter, K. Richter, S. Schöneburg, & R. Sommer (Eds.), Mathematik für Alle. Wege zum Öffnen von Mathematik – Mathematikdidaktische Ansätze (pp. 35-47). Franzbecker: Hildesheim. Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating a Models and Modeling Perspective with Existing Research and Practice. In R. Lesh & H. M. Doerr (Eds.). Beyond Constructivism: Models and Modeling Perspective on Mathematics Problem Solving, Learning and Teaching (pp. 465-478). Mahwah, NJ: Lawrence Erlbaum Associates.

Chan, C. M. E., Ng, K. E. D., Widjaja, 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.

Clements, D. (1998). Geometric and spatial thinking in young children. State University of New York, Buffalo, New York.

Clements, D. H., & Mcmillen, S. (1996). Rethinking “concrete” manipulatives. Teaching Children Mathematics, 2(5), 270-279.

Dicksons, L. (1989). Area of a rectangle. In K. Hart, D. Johnson, M. Brown, L. Dickson, & R. Clarkson (Eds), Children’s mathematical frameworks 8-13 (pp. 89-125). Slough, England: NFER-Nelson.

Diezmann, C. M., & Lowrie, T. (2011). Learning to think spatially: What do students ‘see’ in numeracy test items?. International Journal of Science and Mathematics Education, 10, 1469-1490.

Doig, B., Cheeseman, J., & Lindsay, J. (1995). The medium is the message: Measuring area with different media. In B. Atweh, & S. Flavel (Eds.), Galtha: Proceedings of the 18th Annual Conference of the Mathematics Education Research Group of Australia, Vol. 1 (pp. 229-240). Darwin, Australia: Mathematics Education Research Group of Australia.

English, L. D., & Watters, J. J. (2005). Mathematical modeling in third-grade classrooms. Mathematics Education Research Journal, 16, 59–80.

Eryaman, Z. (2009). A study on sixth grade students’ spatial reasoning regarding 2D representations of 3D objects. Unpublished masters’ thesis, Middle East Technical University, Ankara.

Galbraith, P. L., & Clatworthy, N. J. (1990). Beyond standard models: meeting the challenge of modelling. Educational Studies in Mathematics, 21(2), 137-163.

Guilford, J. P., & Zimmerman, W. S. (1948). The Guilford-Zimmerman aptitude survey. Journal of Applied Psychology, 32(1), 24-35.

Hegarty, M., & Waller, D. (2004). A dissociation between mental rotation and perspective-taking spatial abilities. Intelligence, 32, 175–191.

Kaiser, G. & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik-ZDM, 38(3), 302-310.

Kaiser, G. (2005). Introduction to the working group “Applications and Modelling”. In M. Bosch (Ed.), Proceedings of the 4th Congress of the European Society for Research in Mathematics Education CERME 4 (pp. 1611-1622). Spain: FUNDEMI IQS – Universitat Ramon Llull.

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.

Kalay, H. (2015). 7. sınıf öğrencilerinin uzamsal yönelim becerilerini geliştirmeye yönelik tasarlanan öğrenme ortamının değerlendirilmesi. Yayımlanmamış Yüksek Lisans Tezi. Karadeniz Teknik Üniversitesi, Trabzon.

Keck, H. L. (1996). The development of an analytic scoring scale to assess mathematical modelling projects. Unpublished doctoral dissertation. Missoula (MT): University of Montana.

Kozhevnikov, M., & Hegarty, M. (2001). A dissociation between object manipulation spatial ability and spatial orientation ability. Memory & Cognition, 29, 745–756.

Krippendorff, K. (1980). Content Analysis: An Introduction to its Methodology. Beverly Hills, CA: Sage Publications.

Kurtuluş, A., & Yolcu, B. (2013). A Study on Sixth-grade Turkish Students’ Spatial Visualization Ability. The Mathematics Educator, 22(2), 82-117.

Leong, K. E. (1998). Assessment of mathematical modeling. Journal of Mathematics Education at Teachers College, 3(1), 61-65.

Lesh, R. & Caylor, B. (2007). Introduction to special ıssue: modeling as application versus modeling as a way to create mathematics. International Journal of Computers for Mathematical Learning, 12(3), 173-194.

Lesh, R. Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum.

Lesh, R., Doerr, H. M., Carmona, G. & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking and Learning, 5 (2), 211–234.

Lesh, R., Young, R., & Fennewald, T. (2010). Modeling in K-16 mathematics classrooms and beyond. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling Students’ Mathematical Modeling Competencies (pp. 275 –283). New York: Springer.

Lin, C.-H., Chen, C.-M., & Lou, Y.-C. (2014). Developing spatial orientation and spatial memory with a treasure hunting game. Educational Technology & Society, 17(3), 79–92.

Lohman, D. F. (1979). Spatial Ability: Individual Differences in Speed and Level (Technical Report No:9). Stanford, CA: Aptitude Research Project, School of Education, Stanford University.

Maaß, K.(2005). Barriers and Opportunities for the Integration of Modelling in Mathematic Classes- Results of an Empirical Study. Teaching Mathematics and its Applications, 2/3, 1-16.

Maaß, K., & Mischo, C. (2011). Implementing modelling into day-to-day teaching practice-the project STRATUM and its framework. Journal Für Mathematik-Didaktik, 32(1), 103-131.

Marshall, L. (1997). Year 7 students' understanding of the relationship between area and perimeter. Retrieved from http://ro.ecu.edu.au/ theses/900 Master of Education, Faculty of Education, Edith Cowan University

McGee, M. G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal and neurological ınfluences. Psychological Bulletin, 86(5), 889-918.

Miles, M. B., & Huberman, M. A. (1994). Qualitative Analysis: An Expanded Sourcebook. Thousand Oaks, CA: Sage.

Mousoulides, N. (2007). A modeling perspective in the teaching and learning of mathematical problem solving (Doctoral dissertation, University of Cyprus, Cyprus). Retrieved fromhttp://lekythos.library.ucy.ac.cy/handle/10797/5927

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

Nunes, T., Light, P., & Mason, J. (1993). Tools for thought: the measurement of length and area. Learning and Instruction, 3, 39-54.

Okagaki, L. R., & Frensch, P. A. (1996). Effects of video game playing on measures of spatial performance: Gender effects in late adolescents. In P. Greenfield & R. Cocking (Eds.), Interacting with video (pp. 115-140) Norwood, NJ: Ablex Corporation.

Olkun, S. (2003). Making connections: improving spatial abilities with engineering drawing activities. International Journal of Mathematics Teaching and Learning, 1–10.

Özaltun, A., Hıdıroğlu, Ç. N., Kula, S., & Bukova Güzel, E. (2013). Matematik Öğretmeni Adaylarının Modelleme Sürecinde Kullandıkları Gösterim Şekilleri. Turkish Journal of Computer and Mathematics Education, 4(2), 66-88.

Peter Koop, A. (2004). Fermi problems in primary mathematics classrooms: pupils’ interactive modelling processes. In I. Putt, R. Farragher, & M. McLean (Eds.), Mathematics Education for the Third Millennium: Towards 2010 (Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australia) (pp. 454-461). Townsville, Queensland: MERGA.

Pollak, H. (1979). The Interaction between Mathematics and other School Subjects. UNESCO (Ed.). New Trends in Mathematics Teaching IV. Paris.

Reys, R., Suydam, M., & Lindquist, M. (1984). Helping children learn mathematics. New Jersey: Prentice-Hall.

Schwarz, B., & Kaiser, G. (2007). Mathematical modelling in school – Experiences from a project integrating school and university. In D. Pitta-Pantazi, & G. Philippou (Eds.), CERME 5 – Proceedings of the fourth Congress of the European Society for Research in Mathematics Education (pp. 2180-2190). Larnaca, Cyprus.

Simon, M. A., & Blume, G. W. (1994). Building and Understanding Multiplicative Relationships: A Study of Prospective Elementary Teachers. Journal for Research in Mathematics Education, 25(5), 472-494.

Tan Şişman, G., & Aksu, M. (2016). A Study on Sixth Grade Students’ Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume. Internationa Journal of Science and Mathematics Education, 14, 1293–1319.

Turğut, M. (2007). İlköğretim II. kademede öğrencilerin uzamsal yeteneklerinin incelenmesi. Yayımlanmamış yüksek lisans tezi, Dokuz Eylül Üniversitesi, İzmir.

Verschaffel, L., Greer, B., & De Corte, E. (2000). Making Sense of Word Problems. Lisse: The Netherlands: Swets & Zeitlinger.

Weber, R. P. (1985). Basic Content Analysis, Quantitative Applications in the Social Sciences. Beverly Hills, CA: Sage Publications.

Yin, R. K. (1987). Case Study Research Design and Methods. London: Sage Publications Inc.

Yolcu, B., & Kurtuluş, A. (2010). A study on developing sixth-grade students’ spatial visualization ability. Elementary Education Online, 9(1), 256-274.

Kaynak Göster

APA Tekin Dede, A . (2018). Uzamsal Yönelim Becerilerini İçeren Bir Gerçek Yaşam Probleminin Çözüm Sürecinden Yansımalar: Badana Problemi . Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi , (46) , 176-198 . Retrieved from https://dergipark.org.tr/tr/pub/deubefd/issue/41774/459532