Can Technology-Assisted Instruction Improve Theoretical Awareness? The Case of Fundamental Theorem of Calculus

Year 2015, , 68 - 92, 07.04.2015

Eyüp Sevimli , Ali Delice

https://doi.org/10.16949/turcomat.44905

Abstract

The aim of this study is to evaluate the effect of technology-assisted instruction on theoretical awareness in terms of the Fundamental Theorem of Calculus (FTC), which is one of the important issues of undergraduate mathematics. In this study which is structured with regard to multi-method approach, the impact of the teaching experiment was assessed by using qualitative data on the basis of traditional environment. The research group consists of 84 students from a mathematics teacher training department at a state university; out of these students two groups have randomly been assigned, one as the experimental group and the other as control group. The tests which were carried out before and after implementations, used for determining instructional inputs-outputs and interviews conducted for evaluating students’ way of thinking. The findings show that the students in the experimental group, compared to the before treatment, solved integral problems considering with the necessary and sufficient condition of the FTC. Even though students in the control group achieved expressing the FTC, they failed to reflect their knowledge into practice. It has been concluded that a Computer Algebra System may enable to interpret the solution processes not only more analytical but also with a visual sense in the experimental group.

Keywords: Fundamental Theorem of Calculus, technology, awareness of theory

Keywords

Fundamental Theorem of Calculus, technology, awareness of theory

Teknoloji Destekli Öğretim Teorik Farkındalığı Geliştirebilir mi? Analizin Temel Teoremi Örneği

Abstract

Bu çalışmanın amacı, teknoloji destekli öğretimin teorik farkındalığa etkisini, yükseköğretim matematiğinin önemli teoremlerinden biri olan Analizin Temel Teoremi (ATT) bağlamında değerlendirmektir. Çoklu yöntem modeline göre yapılandırılan araştırmada, bir öğretim deneyinin etkililiği nitel veri toplama süreçleri üzerinden, var olan durum ile karşılaştırmalı olarak değerlendirilmiştir. Bir devlet üniversitesinin ilköğretim matematik öğretmenliği 2. sınıf programına kayıtlı olan 84 öğrencisi yansız atama ile iki eşit gruba ayrılmış; bu işlem sonucunda deney grubunda Bilgisayar Cebiri Sistemi (BCS) destekli yaklaşım, kontrol grubunda ise geleneksel yaklaşım takip edilerek öğretim süreci yürütülmüştür. Öğretim süreci öncesi ve sonrasında uygulanan testler ile öğrenim girdi ve çıktıları değerlendirilmiş; sürecin katılımcı gözüyle değerlendirilmesi için görüşme bulgularından yararlanılmıştır. Bulgular, uygulama öncesine kıyasla deney grubundaki öğrencilerin ATT’nin gerek ve yeter şartlarını dikkate alarak integral hesabı gerçekleştirdiğini göstermiştir. Kontrol grubundaki öğrenciler, ATT’yi teorik olarak ifade edebilmelerine karşın, teorik bilgilerin gerekliliklerini çözüm sürecine yansıtamamışlardır. Çalışma sonuçları, sürecin sadece analitik değil aynı zamanda görsel çözümler ile desteklendiği durumlarda, öğrencilerin daha yüksek teorik farkındalığa sahip olabileceğini göstermiştir.

Anahtar Kelimeler: Analizin Temel Teoremi, teknoloji, teorik farkındalık

Keywords

Analizin Temel Teoremi, teknoloji, teorik farkındalık

References

• Alcock, L., & Inglis, M. (2010). Visual considerations in the presentation of mathematical proofs. Seminar.net-International Journal of Media, Technology and Lifelong Learning, 6, 43-59.
• Alcock, L., & Wilkinson, N. (2011). e-Proofs: Design of a resource to support proof comprehension in mathematics. educational designer, 1(4). http://www.educationaldesigner.org/ed/volume1/issue4/article14/pdf/ed_1_4_alcock_11.pdf adresinden 17 Mayıs 2014 tarihinde erişilmiştir.
• Alsina, C., & Nelsen R. (2010). An invitation to proofs without words. European Journal of Pure and Applıed Mathematıcs, 3(1), 118-127.
• Bajracharya, R. R., & Thompson, J. R. (2014). Student understanding of the fundamental theorem of calculus at the mathematics-physics ınterface. Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education. http://timsdataserver.goodwin.drexel.edu/RUME-2014/rume17_submission_46.pdf. adresinden 8 Temmuz 2014 tarihinde erişilmiştir.
• Balcı, M. (2008). Genel Matematik (5. Baskı). Ankara: Balcı yayınları.
• Bardelle, C. (2009). Visual proofs: an experiment. Proceedings of the Sixth Conference of European Research in Mathematics Education, Lyon:France.
• Bezuidenhout, J., & Olivier, A. (2000). Students’ conceptions of the integral. Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education. Hiroshima: Japan.
• Camacho, M., Depool, R., & Santos-Trigo, M. (2009). Students’ use of Derive software in comprehending and making sense of definite integral and area concepts. CBMS Issues in Mathematics Education, 16, 35-67.
• Carlson, M. P., Persson, J., & Smith, N. (2003). Developing and connecting calculus students’ notions of rate-of-change and accumulation: The fundamental theorem of calculus. In Proceedings of the 2003 Meeting of the International Group for the Psychology of Mathematics Education - North America (Vol 2, pp. 165-172). Honolulu, HI: University of Hawaii.
• Creswell, J. (2003). Research design. Qualitative, quantitative and mixed methods approaches, 2nd edt. Sage: Thousand Oaks.
• Ferrini-Mundy, J., & Graham, K. (1994). Research in calculus learning: Understanding of limits, derivatives, and integrals. In J. J. Kaput & E. Dubinsky (Eds.), Research issues in undergraduate mathematics learning. Washington, D. C.: Mathematical Association of America.
• Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139-162.
• Gonzalez-Martin, A. S., & Camacho, M. (2004). What is first-year mathematics students’ actual knowledge about improper integrals? International Journal of Mathematical Education in Science and Technology, 35(1), 73-89.
• Hughes-Hallett, D. (1991). Visualization and calculus reform. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics, MAA Notes.
• Hughes-Hallett, D., Gleason, A. M., McCallum, W. G. et al. (2008). Calculus: Single variable (5th Edition). New York: Wiley.
• Lavicza, Z. (2007). Factors influencing the integration of Computer Algebra Systems into university-level mathematics education. International Journal for Technology in Mathematics Education, 14(3) 121-129.
• Milli Eğitim Bakanlığı [MEB] (2013). Ortaöğretim matematik dersi 9-12. sınıflar öğretim programı. Ankara: MEB Talim Terbiye Başkanlığı Yayınları.
• Oberg, R. (2000). An investigation of under graudate calculus students understanding of the definite integral (Unpublished PhD Dissertation). The University of Montana.
• Özyurt, Ö., Özyurt, H., Baki, A. ve Güven, B. (2013). Integration into mathematics classrooms of an adaptive and intelligent individualized e-learning environment: implementation and evaluation of UZWEBMAT. Computers in Human Behavior, 29, 726–738.
• Ponce-Campuzano, J. C., & Maldonado-Aguilar, A. M. (2013). The fundamental theorem of calculus within a geometric context based on Barrow's work. International Journal of Mathematical Education in Science and Technology, 45(2), 293-303. doi:10.1080/0020739X.2013.822586.
• Presmeg, N. C. (2006). A semiotic view of the role of imagery and inscriptions in mathematics teaching and learning. In: Navotná J., Moraová H., Krátká M., & Stehliková N. (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol 1, pp. 19-34). Prague: Czech Republic.
• Rasslan, S., & Tall, D. (2002). Definitions and images for the definite integral concept. In Cockburn A.; Nardi, E. (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol 4, pp. 89-96). Norwich: England.
• Schnepp, M., & Nemirovsky, R. (2001). Constructing a foundation for the fundamental theorem of calculus. In A. A. Cuoco & F. Curcio (Eds.), The roles of representation in school mathematics (pp. 90-102). Reston, VA: NCTM.
• Sevimli, E. (2013). Bilgisayar cebiri sistemi destekli öğretimin farklı düşünme yapısındaki öğrencilerin integral konusundaki temsil dönüşüm süreçlerine etkisi (Yayımlanmamış doktora tezi). Marmara Üniversitesi, Türkiye.
• Sevimli, E. ve Delice, A. (2013). An investigation of students’ concept image and integration approaches to definite integral: Computer Algebra System. In Lindmeier A.; Heinze, A. (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol 4, pp. 201-209). Kiel: Germany.
• Swidan, O. (2013). Perceiving calculus ideas in a dynamic and multi- semiotic environment - The case of the antiderivative. CERME 8, Antalya, Turkey.
• Tall, D. O. (1997). Functions and Calculus. In A. J. Bishop et al (Eds.), International handbook of mathematics education (pp. 289-325, Dortrecht, Kluwer.
• Tall, D. O., Smith, D., & Piez, C. (2008). Technology and calculus. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics (pp. 207–258). USA: NCTM.
• Thompson, P. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2), 229-274.
• Thompson, P. W., & Silverman, J. (2008). The concept of accumulation in calculus. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics. Washington, DC: Mathematical Association of America.
• Thomas G. B., Weir M. D., Hass J., & Giordano F. R. (2009). Thomas' calculus. (11. Baskıdan çeviri: Recep Korkmaz). Boston: Pearson Education.