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Journals / Türk Bilgisayar ve Matematik Eğitimi Dergisi / 2015 / Cilt: 6 - Sayı: 1

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

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

Eyüp SEVİMLİ
Ali DELİCE
Pages
68–92
Publication Date
2015-04-07
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Analizin Temel Teoremi · teknoloji · teorik farkındalık

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

Özet

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

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Cite This Article

SEVİMLİ, E., DELİCE, A. (2015). Can Technology-Assisted Instruction Improve Theoretical Awareness? The Case of Fundamental Theorem of Calculus. Türk Bilgisayar ve Matematik Eğitimi Dergisi, Cilt: 6 - Sayı: 1, 68–92. https://ajindex.com/articles/241158

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References (7)

  1. 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.
  2. 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.
  3. 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:
  4. 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.
  5. 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).
  6. 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.
  7. Gonzalez-Martin, A. S., & Camacho, M. (2004).