Bilgisayar Destekli Soyut Cebir Öğretiminin Başarıya ve Matematiğe Karşı Tutuma Etkisi: ISETL Örneği

Year 2019, , 260 - 289, 10.04.2019

Serpil Yorgancı

https://doi.org/10.16949/turkbilmat.473030

Abstract

Araştırma, bilgisayar
destekli soyut cebir öğretiminin, ilköğretim matematik öğretmeni adaylarının
akademik başarılarına ve matematiğe karşı tutumları üzerine etkisini
belirlemeyi amaçlamaktadır. Çalışmanın örneklemini, bir devlet üniversitesinin
eğitim fakültesi ilköğretim matematik öğretmenliği lisans programında öğrenim
gören toplam 30 öğrenci oluşturmaktadır. Eşit olmayan kontrol gruplu ön
test-son test deneysel desenin benimsendiği çalışmada kontrol grubunda
geleneksel öğretim yöntemi, deney grubunda ise APOS teorisine dayalı olarak
geliştirilen ACE (activities, class discussion, exercices) öğretim döngüsü
kullanılmıştır. Bu çerçevede deney grubunda ACE döngüsünün ilk adımı olan
bilgisayar aktivitelerinde ISETL programlama dili kullanılmıştır. Araştırmanın
verileri akademik başarı testi, matematik tutum ölçeği ve görüşmeler yoluyla
elde edilmiştir. Elde edilen sonuçlar, deney ve kontrol grubunun başarı ve
tutum puanları arasında deney grubu lehine anlamlı farklar olduğunu
göstermiştir. Görüşmelerden elde edilen bulgular; deney grubu öğrencilerinin
normal alt grup ve bölüm grubu kavramlarına ilişkin anlamalarının, kontrol
grubu öğrencilerine göre daha ileri düzeyde olduğunu göstermiştir.

Keywords

Başarı, tutum, bilgisayar destekli matematik, APOS teorisi, ACE döngüsü

The Impact of Computer-Assisted Abstract Algebra Instruction on Achievement and Attitudes Toward Mathematics: The Case of ISETL

Abstract

The research aims to test
whether a computer-assisted abstract algebra instruction has significant
influence on students’ achievement levels and their attitudes toward the
mathematics. The sample of the study consists of a total of 30 students
studying in the elementary mathematics teacher training program of the faculty
of education of a state university in Turkey. The methodology of this study is
nonequivalent pretest-posttest control group experimental design. The
traditional teaching method was used in the control group and the ACE
(activities, class discussion, exercises) teaching cycle based on the APOS
theoretical framework was used in the experimental group. In this framework,
ISETL programming language was used in the computer activities which was the
first step of ACE cycle in the experimental group. The data were collected
through academic achievement test, math attitude scale and interviews. The
results showed that the use of ISETL programming language in abstract algebra
teaching increased academic achievement and attitudes towards mathematics
course. Findings from interviews showed that the experimental group students'
understanding of the concepts of normal subgroup and quotient group was more
advanced than the control group students.

Keywords

Achievement, attitudes, computer-assisted mathematics, APOS theory, ACE cycle

References

• Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2013). APOS theory: A framework for research and curriculum development in mathematics education. New York: Springer.
• Asiala, M., Dubinsky, E., Mathews, D. M., Morics, S., & Oktac, A. (1997). Development of students' understanding of cosets, normality, and quotient groups. Journal of Mathematical Behavior, 16(3), 241-309.
• Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Ankara: Harf Eğitim Yayıncılık.
• Blyth, R. D., & Rainbolt, J. G. (2010). Discovering theorems in abstract algebra using the software GAP. Primus, 20(3), 217-227.
• Brenton, L., & Edwards, T. G. (2003). Sets of sets: A cognitive obstacle. The College Mathematics Journal, 34(1), 31-38.
• Büyüköztürk, Ş. (2005). Sosyal bilimler için veri analizleri el kitabı. Ankara: Pegem Yayıncılık.
• Capaldi, M. (2014). Non-traditional methods of teaching abstract algebra. Primus, 24(1), 12–24.
• Clark, J. M., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D. J., St John, D., & Vidakovic, D. (1997). Constructing a schema: The case of the chain rule? The Journal of Mathematical Behavior, 16(4), 345- 364.
• Clark, J. M., Hemenway, C., St. John, D., Tolias, G., & Vakil, R. (1999). Student attitudes toward abstract algebra. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 9(1), 76-96.
• Cetin, I., & Dubinsky, E. (2017). Reflective abstraction in computational thinking. Journal of Mathematical Behavior, 47, 70-80.
• Çetin, İ. ve Top, E. (2014). Programlama eğitiminde görselleştirme ile ACE döngüsü. Turkish Journal of Computer and Mathematics Education, 5(3), 274-303.
• Duatepe, A. ve Çilesiz, Ş. (1999). Matematik tutum ölçeği geliştirilmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 16, 45-52.
• Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. O. Tall (Ed.), Advanced Mathematical Thinking (pp. 95-126). Dordrecht: Kluwer.
• Dubinsky, E. (2001). Using a theory of learning in college mathematics courses. MSOR Connections, 1(2), 10-15.
• Dubinsky, E., Dautermann, J., Leron, U., & Zazkis, R. (1994). On learning fundamental concepts of group theory. Educational studies in Mathematics, 27(3), 267-305.
• Dubinsky, E., & Leron, U. (1994). Learning abstract algebra with ISETL. New York: Springer‐Verlag.
• Dubinsky, E., & Schwingendorf, K. (1991). Constructing calculus concepts: Cooperation in a computer laboratory. In L. C. Leinbach (Ed.), The laboratory approach to teaching calculus (pp. 47-70). Washington, DC: The Mathematical Association of America.
• Dubinsky, E., & Tall, D. (2002). Advanced mathematical thinking and the computer. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 231-248). Dordrecht: Kluwer.
• Fenton, W. E., & Dubinsky. E. (1996). lntroduction to discrete matheıııatics with ISETL. New York: Springer‐Verlag.
• Galois, E. (1831). Mémoire sur les conditions de résolubilité des équations par radicaux. Journal de Mathématiques Pures et Appliquées, 9, 417–433.
• Gilbert, W. (1976). Modern algebra with applications. New York: John Wiley & Sons.
• Gordon, G. (1996). Using wallpaper groups to motivate group theory. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 6(4), 355-365.
• Grassl, R., & Mingus, T. T. Y. (2007). Team-teaching and cooperative groups in abstract algebra: Nurturing a new generation of confident mathematics teachers. International Journal of Mathematical Education in Science and Technology, 38(5), 581–597.
• Hazzan, O. (1999). Reducing abstraction level when learning abstract algebra concepts. Educational Studies in Mathematics, 40, 71–90.
• Hazzan, O. (2001). Reducing abstraction: The case of constructing an operation table for a group. The Journal of Mathematical Behavior, 20(2), 163–172.
• Hirsch, J. (2008). Tracking changes in teaching and learning abstract algebra: Beliefs and ability to abstract (Unpublished doctoral dissertation). Colombia University, USA.
• Hoffman, A. J. (2017). Abstract algebra for teachers: An evaluative case study (Unpublished doctoral dissertation). Purdue University, USA.
• Ioannou, M., & Iannone, P. (2011). Students’ affective responses to the inability to visualize cosets. Research in Mathematics Education, 13(1), 81–82.
• Kleiner, I. (2007). A History of abstract algebra. Boston: Birkhäuser.
• Konyalıoğlu, S. (2006). A study on teaching group and subgroup concepts. Journal of Qafqaz University, 18, 155-158.
• Konyalıoğlu, S. (2009). Escher’s tessellations in understanding group theory. World Applied Sciences Journal, 6(11), 1521-1524.
• Kulich, L. T. (2000). Ideas for teaching and learning: Computer algebra in abstract algebra. The International Journal of Computer Algebra in Mathematics Education, 7(3), 213–219.
• Leron, U., & Dubinsky, E. (1995). An abstract algebra story. The American Mathematical Monthly, 102(3), 227-242.
• Leron, U., Hazzan, O., & Zazkis, R. (1995). Learning group isomorphism: A crossroads of many concepts. Educational Studies in Mathematics, 29(2), 153-174.
• Melhuish, K. M. (2015). The design and validation of a group theory concept inventory. (Unpublished doctoral dissertation). Portland State University, USA.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded source book (2nd ed.). California: Sage Publications.
• Nardi, E. (2000). Mathematics undergraduates’ responses to semantic abbreviations, “geometric” images and multi-level abstractions in group theory. Educational Studies in Mathematics, 43(2), 169–189.
• Nicholson, J. (1993). The development and understanding of the concept of quotient group. Historia Mathematica, 20(1), 68-88.
• Nwabueze, K. K. (2004). Computers in abstract algebra. International Journal of Mathematical Education in Science and Technology, 35(1), 39-49.
• Papert, S. (1980). Mindstorms: Computers and powerful ideas. London: Harvester.
• Quoc, N. A. (2018). An epistemological analysis of the concept of quotient group. Tạp Chí Khoa Học, 15(5b), 139-152.
• Rainbolt, J. G. (2002). Using GAP in an abstract algebra class. In A. C. Hibbard, & E. J. Maycock (Eds.), Innovations in teaching abstract algebra (pp. 77-84). Washington, DC: Mathematical Association of America.
• Schubert, C., Gfeller, M., & Donohue, C. (2013). Using Group Explorer in teaching abstract algebra. International Journal of Mathematical Education in Science and Technology, 44(3), 377-387.
• Senechal, M. (1988). The algebraic escher. Structural Topology, 15, 31-42.
• Shilin, I. A. (2014). Some programming problems for teaching foundations of group theory. International Journal of Mathematical Education in Science and Technology, 45(3), 438-445.
• Smith, R. S. (1993, November). ISETL and cooperative learning-vehicles for learning calculus. Paper presented at the Proceedings of the Fourth Annual International Conference on Technology in Collegiate Mathematics, Portland.
• Smith, R. S. (1997). A collaborative learning constructivist approach to abstract algebra using ISETL (Unpublished master’s thesis). Miami University, USA.
• Şenay, Ş. C. ve Özdemir, A. Ş. (2014). Matematik öğretmen adaylarının lineer kongrüanslara ilişkin soyutlamayı indirgeme eğilimleri. Eğitim ve İnsani Bilimler Dergisi: Teori ve Uygulama, 5(10), 59-72.
• Van der Waerden, B. L. (1939). Nachruf auf Otto Hölder. Mathematische Annalen, 116(1), 157-165.
• Weber, K., & Larsen, S. (2008). Teaching and learning abstract algebra. In M. Carlson, & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 137-149). Washington, DC: Mathematical Association of America.
• Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M. A., & Merkovsky, R. (2000). An examination of student performance data in recent RUMEC studies. Washington, DC: Mathematical Association of America.
• Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.