Bilgisayar cebiri sistemleri ortamlarında öğretmen adaylarının problem çözme stratejilerinin incelenmesi

Bu çalışmanın amacı, üniversite öğrencilerinin problem çözme stratejilerini bir bilgisayar yazılımı ortamında incelemektir. Çalışmaya, Matematik Öğretmenliği, II. Sınıfında eğitim gören ve 2006-2007 Bahar Dönemi içinde bilgisayar programlama dersine devam eden üç erkek ve iki kız öğrenci dahil edilmiştir. Veri toplama yöntemi olarak klinik, yarı-yapılandırılmış görüşme ve katılımcı gözlem teknikleri kullanılmıştır. Toplanan veriler, içerik analizi kullanılarak Nvivo7 programında analiz edilmiştir. Araştırma sonuçlarına göre öğrencilerin Maple’da problem çözmek için en sık kullandığı stratejiler ayrıştırma ve sadeleştirme, benzer problem bulma döngüsel olmayan strateji ile araç amaç analizi olarak belirlenmiştir.

Investigation of preservice teachers' problem solving strategies in computer algebra systems environments

The purpose of the study was to investigate undergraduate students’ problem solving strategies in a computer software envoriment. The participants of this study consist of three male and two female students attending Computer Programming II course in a mathematics teacher training program during the Spring Semester of 2006–2007. In this study, data were collected through clinical interviews, semi structered interviews and observations. Data were analyzed using content analysis by Nvivo7. According to study findings, most frequently used strategy by the students are decomposing and simplifying, analogy, anti looping strategy and means-end analysis at Maple.

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  • Aksoy, Y. (2007). “Türev Kavramının Öğretilmesinde Bilgisayar Cebiri Sistemlerinin Etkisi.” Yayımlanmamış doktora tezi, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.
  • Altun, M. (2000). “İlköğretimde Problem Çözeme Öğretimi.” Milli Eğitim Dergisi, 147.
  • Aktümen, M. (2007). “Belirli İntegral Kavramının Öğretiminde Bilgisayar Cebiri Sistemlerinin Etkisi.” Yayımlanmamış doktora tezi, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.
  • Arsham, H. & Oblak, M. (1996). Matrix inversion: a computational algebra approach. International Journal of Mathematical Education in Science and Technology, 27(4), 599–605.
  • Baki, A., Karataş, İ. & Güven, B. (16-18 Eylül 2002). Klinik Mülakat Yöntemi İle Problem Çözme Becerilerinin Değerlendirilmesi. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresinde sunulmuş bildiri, Ankara.
  • Boulter, D. R. & Kirby, J. R. (1994). Identification of stratejies used in solving transformational geometry problems. Journal of Educational Research, 87(5), 298-303.
  • Brody, J. & Rosenfield, S. (1996). Problem posing/solving and linear algebra. International Journal of Mathematical Education in Science and Technology, 27(1), 103-121.
  • Bruning, R. H., Schraw, G. J.& Roning, R.R. (1995). Cognitive Physchology and Instruction(2ndEd.). Prentice-Hall:New Jersey
  • Bulut, M. (2009). “İşbirliğine Dayalı Yapılandırmacı Öğrenme Ortamlarında Kullanılan Bilgisayar Cebir Sistemlerinin Matematiksel Düşünme, Öğrenci Başarısına Ve Tutumuna Etkisi.” Yayımlanmamış doktora tezi, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.
  • Carvalho, M. J.& D'Agostino S. (2001).A MAPLE program for calculations with Schur functions. Computer Physics Communications, 141(2), 282-295.
  • Cheung, Y.L. (1996). Learning number theory with a computer algebra system. International Journal of Mathematical Education, 27(3), 379-385.
  • Crocker, D. A. (1991). “A qualitative study of interactions, concept development and problem-solving in a calculus class immersed in the computer algebra system Mathematica(TM).” Yayımlanmamış doktora tezi, The Ohio State University.
  • Davies, S.P. (2000). Memory and planning processes in solutions to wellstructured problems. The Quarterly Journal of Experımental Psychology, 53A(3), 896-927.
  • Diezmann, C, M. & English, L. D. (2001). Promoting the use of diagrams as tools for thinking. In A. A. Cuoco & F.R. Curcio (Eds.), The roles of representation in school mathematics (pp. 77–89). Reston, VA: NCTM.
  • Gander, W. & Gruntz, D. (1999). Derivation of Numerical Methods Using Computer Algebra. Society for Industrial and Applied Mathematics, 41(3), 577-593.
  • Gorgorió, N. (1998). Exploring the funtionalitly of visual and non-visual strategies in solving rotation problems. Educational Studies in Mathematics, 35, 207-231.
  • Ghusayni, B. (2005). Maple explortions, perfect numbers and Mersenne primes. International Journal of Mathematical Education in Science and Technology, 36(6), 643-654.
  • Hammouri, H. A. M. (2003). An Investigation of Undergraduates’ Transformational Problem Solving Strategies: cognitive/metacognitive processes as predictors of holistic/analytic strategies. Assessment & Evaluation in Higher Education, 28(6).
  • Harmon, M., G. & Morse, L.,W. (1995, Summer). Strategies and knowledge in problem solving: Results and implication for education. Education, 115, 4, 580-589.
  • Houstis, E. N. (2003). “The Role of Problem Solving Environments in Engineering and Mathematics Education.” Published in the Proceedings of the 6th International Conference on “Technology in Mathematics Teaching” .
  • Jonassen, D. H. (1997). Instructional Design Models for Well-Structured and Ill-Structured Problem-Solving Learning Outcomes. ETR&D, 45, 1, 65-94.
  • Kabaca, T. (2006). “Limit Kavramının Öğretiminde Bilgisayar Cebiri Sistemlerinin Etkisi.” Yayımlanmamış doktora tezi, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.
  • Leinbach, C; Pountney, D. C. & Etchells, T. (2002). Appropriate use of a CAS in the teaching and learning of mathematics. International Journal of Mathematical Education in Science & Technology, 33, 1, 1–14.
  • Lu, J. & Ye, Z. (2000). Application of CASs to iterative solution of nonlinear analysis of shallow conical shell. Computer Methods in Applied Mechanics and Engineering, 181, 1-3, 345-361.
  • McCoy, L. P. (1996). Computer-based mathematics learning. Journal of Research on Computing in Education,28(4), 438-461.
  • MEB, Talim Terbiye Kurulu Başkanlığı (2005). Ortaöğretim Matematik Dersi Öğretim Programı. http://ttkb.meb.gov.tr/ogretmen/modules.php? name=Downloads&d_op=viewdownload&cid=75 adresinden erişilmiştir.
  • Malloy, C. & Jones, M. (1998). An investigation of African American students’ mathematical problem solving, Journal for Research in Mathematics Education, 29(2), 143–164.
  • Mayer, R. E. (1983). Thinking, problem solving, congnition. New York: W.H. Freeman and Company
  • Nunokawa, K. (2006). Using drawings and generating information in mathematical Problem solving processes. Eurasia Journal of Mathematics, Science and Technology Education, 2, (3).
  • Patton, M. Q. (2002). Qualitative research and evaluation methods, Sage Publication: USA
  • Pierce, R., & Stacey, K. (2001). Observations on Students' Responses to Learning in a CAS Environment. Mathematics Education Research Journal, 13(1), 28-46.
  • Póyla, G.(1997). Nasıl Çözmeli?. (Çev. F. Halatçı). İstanbul: Sistem Yayıncılık. (Özgün kitap 1945’de yayımlandı.)
  • Pountney, D. C.; Leinbach, C. & Etchells, T. (2002). The issue of appropriate assessment in the presence of a CAS. International Journal of Mathematical Education in Science & Technology, 33, 1, 15–36.
  • Reed, S. K. (2007). Cognition: Theory and application. USA: Thomson Wadsworth
  • Rosengrant, D., Heuvelen, A. V.& Etkina, E. (2006). “Case Study: Students’ Use of Multiple Representations in Problem Solving.” Paper presented at Physic Education Research Conference.
  • Srinivasan, V. K. (1997). Three perspective on the limit of a function. International Journal of Mathematical Education in Science and Technology, 28(2), 185-196.
  • Stenphens, L. J. & Konvalina, J. (1998). The use of computer algebra software in teaching intermediate and college algebra. International Journal of Mathematical Education in Science and Technology, 30(4), 483-488.
  • Strauss, A. L & Corbin, J. (1990). Basic of qualitative research: Grounded theory procedures and tecniques. Newbury Park, CA: Sage
  • Stylianou, D. A. & Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: An examination of expertnovice similarities and differences. Mahtematical Thinking and Learning, 6(4), 353–387.
  • Waters, M. S. (2003). “How and why students select, apply, and translate among mathematical representations in problem solving while learning algebra in a computer algebra system learning environment.” Yayımlanmamış doktora tezi, Ohio University.
  • Weigand, H. G. & Weller, H. (2001). Changes of working styles in a computer algebra environment – the case of functions. International Journal of Computers for Mathematical Learning, 6.
  • Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P.S. Wilson (Eds.), Research ideas for the classroom: High school mathematics, New York, NY: Macmillian.