Türev ve İntegral Problemlerinin Çözümünde Görsel, Analitik ve Harmonik Çözüm Tercihleri

Yıl 2014, Sayı: 22, 108 - 119, 01.06.2014

Güney Hacıömeroğlu Erhan Selçuk Hacıömeroğlu Esra BUKOVA Güzel Semiha Kula

Öz

Öğrencilerin türev ve integral sorularını çözüm tercihlerini incelemek amacıyla Haciomeroglu ve Chicken (2011) tarafından geliştirilen Matematik İşlem Testi-Analiz (MİT-A) ölçme aracının Türkçe’ye uyarlama çalışması yapılmıştır. Buna ek olarak, bu çalışma ortaöğretim matematik öğretmenliği programında öğrenim gören öğrencilerin türev ve integral sorularını çözme tercihlerini belirlemeyi amaçlamıştır. Elde edilen bulgular, Matematik İşlem Testi-Analiz’in Türk kültüründe kullanılabilecek geçerli ve güvenilir bir ölçme aracı olduğunu göstermektedir. Cronbach alfa güvenirlik katsayısı MİT-A-türev için 0.83 ve MİT-A-integral için 0.86 olarak hesaplanmıştır. Testin bütünü için bu değer 0.91 olarak hesaplanmıştır. Elde edilen bulgular, öğrencilerin çoğunun türev ve integral sorularını analitik çözmeyi tercih ettiklerini göstermiştir. Öğrenciler soru tipi değiştiğinde çözüm tercihini değiştirmediğini göstermektedir.

Anahtar Kelimeler

görsel, analitik, harmonik, türev, integral, analiz.

Visual, Analytic and Harmonic Problem Solving Preferences for Derivative and Antiderivative Tasks

Öz

The purpose of this present study was to adapt the Mathematical Processing Instrument for Calculus (MPI-C) developed by Haciomeroglu and Chicken (2011) to Turkish. In addition, the study aimed at examining students’ preferences for problem solving strategies regarding derivative and antiderivative tasks. Results of the study revealed that the MPI-C is a valid and reliable instrument that can be used to reliably measure Turkish students’ preference for visual or analytic solution strategies. The cronbach alpha coefficients of the MPIC derivative and antiderivative tests were 0.83 and 0.86, respectively. The Cronbach alpha coefficient for the overall instrument was 0.91. Most of the students in this study preferred analytic solution strategies for the derivative and antiderivative tasks, and the mode of representations of the tasks did not affect their preference for visual or analytic solution strategies.

Anahtar Kelimeler

visual, analytic, harmonic, derivative, antiderivative, calculus.

Kaynakça

• Akbulut, K. ve Işık, A. (2005). Limit kavramının anlaşılmasın- da etkileşimli öğretim stratejisinin etkinliğinin incelenmesi ve bu süreçte karşılaşılan kavram yanılgıları. Kastamonu Eğitim Fakültesi Dergisi, 13 (2), 497-512.
• Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
• Aspinwall. L., & Shaw, K. L. (2002). Representations in Calculus: Two contrasting cases. Mathematics Teacher, 95, 434-439.
• Brown, D. L., & Wheatley, G. H. (1989). Relationship between spatial ability and mathematics knowledge. In A. C. Maher, G. A. Goldin, & R. B. Davis (Eds.), Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 143-148). New Brunswick, NJ.
• Bukova-Güzel, E. (2007). The effect of a constructivist learning environment on the limit concept among mathematics student teachers. Educational Sciences: Theory & Practice, 7, 1189-1195.
• Clements, K. (1984). Terence Tao. Educational Studies in Mathematics, 15, 213-238.
• Cruz, I., Febles, M., & Diaz, J. (2000). Kevin: A visualizer pupil. For the Learning of Mathematics, 20, 30-36.
• Çetin, N. (2009). The performance of undergraduate students in the limit concept. Journal of Mathematical Education in Science and Technology, 40 (3), 323-330.
• Duru, A. (2011). Pre-service teachers’ perception about the concept of limit. Educational Sciences: Theory & Practice, 11(3), 1710-1715.
• Eisenberg, T., & Dreyfus, T. (1991). On the reluctance to visualize in mathematics. In W. Zimmermann & S. Cunningham (Eds.), Visualization in Teaching and Learning Mathematics (pp. 127 – 138). Washington, DC: MAA.
• Field, A. (2005). Discovering Statistics Using SPSS (2. baskı). Thousand Oaks, CA: Sage Publications, Inc.
• Guy, R.K. (1984). How can we lead in an up-to-date and fair fashion?. The College Mathematics Journal, 15, 396-397.
• Guzman, M. (2002). The role of visualization in the teaching and learning of mathematical analysis. In D. Hughes-Hallett, & C. Tzanakis (Eds.), Proceedings of the International Conference on the Teaching of Mathematics (pp. 2-25). Crete, Greece: ERIC
• Haciomeroglu, E.S. (2007). Calculus students’ understanding of derivative graphs: Problems of representaions in calculus. Unpublished Ph.D. dissertation, Florida State Universitesi, Amerika Birleşik Devletleri.
• Haciomeroglu, E. S., & Chicken, E. (2011). Investigating relations between ability, preference, and calculus performance. Proceedings of the 33rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education–PME-NA (pp. 61-69). Reno, Nevada.
• Haciomeroglu, E.S. & Chicken, E. (2012). Visual thinking and gender differences in high school calculus. International Journal of Mathematical Education in Science and Technology, 43(3), 303–313.
• Hamming, R.W. (1984). Calculus and discrete mathematics. The College Mathematics Journal, 15, 388-389.
• Hughes-Hallett, D. (1991). Visualization and calculus reform. In W. Zimmermann, & S. Cunningham (Eds.), Visualization in Teaching and Learning Mathematics (pp. 127 – 138). Washington, DC: MAA.
• Hughes-Hallett, D., McCallum, W. G., Gleason, A. M., Pasquale, A., Flath, D. E., Quinney, D., Lock, P. F., Raskind, W., Gordon, S. P., Rhea, K., Lomen, D. O., Tecosky-Feldman, J., Lovelock, D., Thrash, J. B., Osgood, B. G., & Tucker, T. W. (2002). Calculus: Single Variable. Danvers, MA: John Wiley & Sons, Inc.
• Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren. In J. Kilpatrick & I. Wirszup (Eds.). Chicago: The University of Chicago Press.
• Janvier, C. (1987). Translation processes in mathematics education. In C. Janvier (Eds.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 27-32). Hillsdale, NJ: Lawrence Erlbaum Associates.
• Kleitman, D.J. (1984). Calculus defended. The College Mathematics Journal, 15, 377-378.
• Lax, P. (1984). In praise of calculus. The College Mathematics Journal, 15, 378-380.
• Lowrie, T. (2000). A case of an individual’s reluctance to visualize. Focus on Problems in Mathematics, 22, 17-26.
• MacLane, S. (1984). Calculus is a discipline. The College Mathematics Journal, 15, 373.
• Matthews, D. M. (1996). Mathematics Education: A response to Andrews. The College Mathematics Journal, 27, 349-353.
• National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards forTeaching Mathematics. Reston, VA.: NCTM.
• Porzio, D. (1999). Effects of differing emphases in the use of multiple representations and technology on students’ understanding of calculus concepts. Focus on Learning Problems in Mathematics, 21, 1-29.
• Presmeg, N. C. (1985). The role of visually mediated processes in high school mathematics: A classroom investigation. Unpublished Ph.D. dissertation, University of Cambridge.
• Presmeg, N. C. (1986a). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297–311.
• Presmeg, N. C. (1986b). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42–46.
• Presmeg, N. C. (1989). Visualization in multicultural mathematics classrooms. Focus on Learning Problems in Mathematics, 11, 17-24.
• Presmeg, N. C. (2006). Research on visualization in learning and teaching mathematics: Emergence from psychology. In A. Gutierrez & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (pp. 205-235). Rotterdam, The Netherlands: Sense Publishers.
• Ralston, A. (1984). Will discrete mathematics surpass calculus in importance? The College Mathematics Journal, 15, 371-373.
• Roberts, F.S. (1984). The introductory mathematics curriculum: Misleading, outdated, and unfair. The College Mathematics Journal, 15, 383-385.
• Sağlam, Y. & Bülbül, A. (2012). Üniversite Öğrencilerinin Görsel ve Analitik Stratejileri.
• Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 43, 398–409.
• Sawyer, W. W. (1961). What is Calculus About?. The New Mathematical Library, Vol. 2. New York: Random House.
• Schwarzenberger, R. L. E. (1980). Why calculus cannot be made easy. The Mathematical
• Gazette, 64, 158-166.
• Sevimli, E. & Delice, A. (2011). The influence of teacher candidates' spatial visualization ability on the use of multiple representations in problem solving of definite integrals: A qualitative analysis. Research in Mathematics Education, 1(13), 93-94.
• Sevimli, E. & Delice, A. (2012). The relationship between students' mathematical thinking types and representation preferences in definite integral problems. Research in Mathematics Education. 3(14), 295-96.
• Shilgalis, T. W. (1979). One answer to “What Is Calculus?” Mathematics Teacher, 72, 224 - 226.
• Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh grade students. Unpublished Ph.D. dissertation, Monash Üniversitesi, Avustralya.
• Stylianou, D. A. (2002). On the interaction of visualization and analysis: The negotiation of a
• visual representation in expert solving. Journal of Mathematical Behavior, 21, 303-317.
• Stylianou, D. A., & Dubinsky, E. (1999). Determining linearity: the use of visual imagery in problem solving. In F. Hitt, & M. Santos (Eds.), Proceedings of the Twenty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) (pp. 245-252). Columbus, OH: ERIC/CSMEE.
• Tall, D. (1984). Continuous mathematics and discrete computing are complementary, not alternatives. The College Mathematics Journal, 15, 389-391.
• Tall, D. (1985). Understanding the calculus. Mathematics Teaching, 110, 49-53.
• Tall, D. (1991). Intuition and rigour: The role of visualization in the calculus. In W. Zimmermann & S. Cunningham (Eds.), Visualization in Teaching and Learning Mathematics (pp. 105-119). Washington, DC: MAA.
• Ubuz, B. (2007). Interpreting a graph and constructing its derivative graph: stability and change in students’ conceptions. International Journal of Mathematical Education in Science and Technology, 38 (5), 609-637.
• Vinner, S. (1989). The avoidance of visual considerations in calculus students. Focus on Learning Problems in Mathematics, 11, 149-156.
• Webb, N. L. (1979). Processes, conceptual knowledge, and mathematical problem-solving ability. Journal for Research in Mathematics Education, 10, 83-93.
• Zimmerman, W. (1991). Visual Thinking in Calculus. In W. Zimmermann & S. Cunningham (Eds.), Visualization in Teaching and Learning Mathematics (pp. 127-137). Washington, DC: MAA.