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Lineer Cebir Ders Kitaplarının Öğretici Unsurlar Açısından İncelenmesi

Year 2013, Volume: 2 Issue: 2, 376 - 394, 10.12.2013

Abstract

Lineer cebir ile ilgili ders kitaplarının ele alındığı bu araştırmada 1977-2010 tarihleri arasında
Türkçe’ye çevrilmiş ve Türkçe yazılmış kitaplardan oluşan toplam 20 kitap incelenmiştir. Bu lineer cebir ders
kitapları, öğrenmeye rehberlik eden öğretici unsurları içerme açısından ele alınmıştır. Buna yönelik olarak
kitaplar lineer cebir bilgi yapısına uygun öğretici unsurları dikkate alan bazı temalar boyutunda incelenmiştir.
Bu temalar önsöz için; genel tanıtım, yönerge, güdüleyici unsurlar, içindekiler kısmı için; içerik sırası, bölümler
için; güdüleyici unsurlar, sunum şekli ve pedagoji şeklindedir. Belirtilen bu temalar çalışmada kendi içlerinde
daha özel kategorilere ayrılmış ve bunlar; kitapların önsözleri ve içindekiler kısmından başlanılarak elementer
lineer cebir konuları olarak anılan; lineer denklem sistemleri, matrisler, determinantlar, vektör uzayları, lineer
dönüşümler, özdeğerler ve özvektörler kısımlarında incelenmiştir. Çalışmada nitel araştırma yaklaşımı
kullanılmış olup veriler doküman incelemesi yapılarak toplanmış ve betimsel olarak analiz edilmiştir. Betimsel
analiz için yukarıda belirtilen temalar, literatürde ki lineer cebir öğrenimi-öğretimi çalışmaları dikkate alınarak
belirlenmiştir. Çalışma sonucunda elde edilen bulgular, lineer cebir ders kitaplarının genelde bilgi aktarmaya
dayalı hazırlandığını, kitaplarda öğretici unsurlara çok az yer verildiğini ve genellikle formalizme bağlı
kalındığını işaret etmektedir

References

  • Artigue, M. (1999). The teaching and learning of mathematics at the university level: Crucial questions for contemporary research in education. Notices of the American Matematical Society, 46 (11), 1377-1385.
  • Avital, S. (1994). History of mathematics can help improve instruction and learning. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz, (Eds.), Learn from the masters (pp. 3-12). The Mathematical Association of America Publishing.
  • Baer, R. (1952). Linear algebra and projective geometry, New York: Acedemic Press.
  • Carlson, D. (1993). Teaching linear algebra: must the fog always roll in ?. College Mathematics Journal, 24 (1), 29-40.
  • Cornu, B. (1991). Limits. In D.Tall (Ed.), Advanced Mathematics Thinking. Netherlands: Kluwer Academic Publ. Dordrecht.
  • Çakmak, M. (2001). Matematik Ders Kitaplarının Nitelikleri. L. Küçükahmet (Ed.) Konu Alanı Ders Kitabı İnceleme Kılavuzu (Matematik 1-8) (s.123-153). Ankara: Nobel Yayın Dağıtım.
  • Dorier, J.-L., Robert, A., Robinet, J. & Rogalski, M. (1994). The teaching of linear algebra in first year of French science university. Proceedings of the 18 th Conference of The International Group for The Psychology of Mathematics Education, Lisbonne,14, 137- 144.
  • Dorier, J.-L. (1998). The role of formalism in the teaching of the theory of vector spaces. Linear Algebra and Its Applications, 275-276, 141-160.
  • Dorier, J.-L. & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra, In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study, 255-273, Netherland, Kluwer Aca. Publ.
  • Dorier, J.-L. 2002, Teaching linear algebra at university. In Li Tatsien (ed.), Proc. Int.Congr. Mathematician, Beijing 2002, August 20–28, Vol III.1-3. pp. 875–884.
  • Ertekin, E., Solak, S. & Yazici, E. (2010), The effects of formalism on teacher trainees’ algebraic and geometric interpretation of the notions of linear dependency/independency. International Journal of Mathematical Education in Science and Technology, 41(8),1015- 1035.
  • Harel, G. (1987). Variations in linear algebra content presentations, For the Learning of Mathematics, 7 (3), 29-32.
  • Harel, G. (1989). Learning and teaching linear algebra: diffuculties and an alternative approach to visualizing concepts and processes. Focus on Learning Problems in Mathematics, 11(2), 139-148.
  • Harel, G. (1999). Students' understanding of proofs: a historical analysis and implications for the teaching of geometry and linear algebra. Linear Algebra and Its Applications, 302- 303. 601-613
  • Harel, G. (2000). Principles of learning and teaching mathematics, with particular reference to the learning and teaching of linear algebra, In J-L. Dorier (Ed.), On The Teaching of Linear Algebra, 177-189, Dordrecht, Kluwer Academic Publishers.
  • Hestenes, D. (1991). The design of linear algebra and geometry, Acta Applicandae Mathematicae, 23(1), 65-93.
  • Herrero, M. P. (2000). Strategies and computer projects for teaching linear algebra, International Journal of Mathematical Education in Science and Technology, 31(2), 181- 186.
  • Hillel, J., (2000). Modes of description and the problem of representation in linear algebra. In J- L. Dorier (Ed.), On The Teaching of Linear Algebra, 191-207, Dordrecht, Kluwer Ac., Publ.
  • Hristovitch, S. P. (2001). Students’ conception of introductry linear algebra notions: The role of metaphors, analogies, and symbolization. Unpublished Doctoral Thesis. Purdue University, Purdue, USA.
  • Işık, C. (2003). İlköğretim Okullarının 7. Sınıflarında Okutulan Matematik ders Kitaplarının İçerik, Öğrenci Seviyesine Uygunluk ve Anlamlı Öğrenmeye Katkısı Yönünden Değerlendirilmesi. Yayınlanmamış doktora tezi, Atatürk Üniversitesi, Erzurum, Turkey.
  • Kaplan, T. (2011). Lineer denklem sistemleri ve uygulama alanları. Yayınlanmamış yüksek lisans tezi, Atatürk Üniversitesi, Erzurum, Turkey.
  • Karasar, N. (1999). Bilimsel Araştırma Yöntemi (9. Basım). Ankara: Nobel Yayın Dağıtım.
  • Konyalıoğlu, A. C., İpek, A. S., & Işık, A. (2003). On the teaching linear algebra at the university level: the role of visualization in the teaching vector spaces. Journal of the Korea Society of Mathematical Education Series, 7(1), 59-67.
  • Konyalıoğlu, A. C. (2003). Üniversite Düzeyinde Vektör Uzayları Konusundaki Kavramların Anlaşılmasında Görselleştirme Yaklaşımının Etkinliğinin İncelenmesi. Yayınlanmamış doktora tezi, Atatürk Üniversitesi, Erzurum, Turkey.
  • Konyalıoğlu, S., Konyalıoğlu, A.C., İpek, A.S. & Işık, A. (2005). The role of visualization approach on studentís conceptual learning. International Journal for Mathematics Teaching and Learning, Sept. 21.
  • Konyalıoğlu, A.C., Konyalıoğlu, S. & Işık. A. (2008). Effectiveness of visualization approach on student’s conceptual learning. Journal of Qafqaz University, 24, 245-249.
  • Konyalıoğlu, A. C. (2009). An evaluation from students’ perspective on visualization approach used in linear algebra instructions. World Applied Science Journal, 6(8), 1046-1052.
  • Lapp, D. A., Nyman, M. A., & Berry, J. S. (2010). Student connections of linear algebra concepts: an analysis of concept maps. International Journal of Mathematical Education in Science and Technology. 41(1),1-18.
  • Mallet, D. G. (2007). Multiple representations for systems of linear equations via computer algebra system maple. International Electronic Journal of Mathematics Education. 2 (1). 16-31.
  • Mirsky, L. (1963). An introduction to linear algebra, London: Oxford Universty Press.
  • Nef, W. (1967). Linear algebra, London: Mcgraw-Hill Publ. Com. Limited.
  • Swetz, F., Fauvel, J., Bekken, O., Johansson, B. & Katz, V. (1994). History in higher mathematics. In F. Swetz, J.Fauvel, O.Bekken, B.Johansson & V.Katz, (Eds.) Learn from the masters (pp.103) The Mathematical Association of America Publshing.
  • Yıldırım, A. & Şimşek, H. (2011). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (8.Baskı). Ankara: Seçkin Yayıncılık.
  • Wang, Tse-Wei, (1989). A course on applied linear algebra, Chemical Engineering Education, 23 (4), 236-241.
  • Wu, H. (2004). Computer aided teaching in linear algebra. The China Papers. July 2004. 100- 102.

An Evaluation of Linear Algebra Textbooks from an Instructive Factors Perspective

Year 2013, Volume: 2 Issue: 2, 376 - 394, 10.12.2013

Abstract

In this study in which the coursebooks an linear algebra are evaluated, 20 books that have
been translated into Turkish or written in Turkish between the years 1977-2010 were analyzed. For this, the
textbooks were evaluated with respect to some themes that take account of the instructive factors suitable to
the nature of linear algebra knowledge. These themes are, for the preface, a general introduction,
instructions, and motivating factors; for the list of contents, sequence of the contents; for the chapters,
motivating factors, the way of presentation, and pedagogy. The themes mentioned were also grouped into
more specific categories: and, they were evaluated, starting from the prefaces and contents of the textbooks,
in the chapters of linear equation systems, matrices, determinants, vector spaces, linear transforms,
eigenvalues and eigenvectors, which are regarded as the elementary linear algebra subjects. In the study a
qualitative approach was adopted and the data were collected through a document analysis and descriptively
analyzed. For the descriptive analysis, the subjects given above were determined considering the studies on
linear algebra learning and teaching. The findings obtained through this study indicate that linear algebra
textbooks are prepared on the basis of conveying knowledge, involve instructive factors only to a very small
extent, and the generally rely on formalism.

References

  • Artigue, M. (1999). The teaching and learning of mathematics at the university level: Crucial questions for contemporary research in education. Notices of the American Matematical Society, 46 (11), 1377-1385.
  • Avital, S. (1994). History of mathematics can help improve instruction and learning. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz, (Eds.), Learn from the masters (pp. 3-12). The Mathematical Association of America Publishing.
  • Baer, R. (1952). Linear algebra and projective geometry, New York: Acedemic Press.
  • Carlson, D. (1993). Teaching linear algebra: must the fog always roll in ?. College Mathematics Journal, 24 (1), 29-40.
  • Cornu, B. (1991). Limits. In D.Tall (Ed.), Advanced Mathematics Thinking. Netherlands: Kluwer Academic Publ. Dordrecht.
  • Çakmak, M. (2001). Matematik Ders Kitaplarının Nitelikleri. L. Küçükahmet (Ed.) Konu Alanı Ders Kitabı İnceleme Kılavuzu (Matematik 1-8) (s.123-153). Ankara: Nobel Yayın Dağıtım.
  • Dorier, J.-L., Robert, A., Robinet, J. & Rogalski, M. (1994). The teaching of linear algebra in first year of French science university. Proceedings of the 18 th Conference of The International Group for The Psychology of Mathematics Education, Lisbonne,14, 137- 144.
  • Dorier, J.-L. (1998). The role of formalism in the teaching of the theory of vector spaces. Linear Algebra and Its Applications, 275-276, 141-160.
  • Dorier, J.-L. & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra, In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study, 255-273, Netherland, Kluwer Aca. Publ.
  • Dorier, J.-L. 2002, Teaching linear algebra at university. In Li Tatsien (ed.), Proc. Int.Congr. Mathematician, Beijing 2002, August 20–28, Vol III.1-3. pp. 875–884.
  • Ertekin, E., Solak, S. & Yazici, E. (2010), The effects of formalism on teacher trainees’ algebraic and geometric interpretation of the notions of linear dependency/independency. International Journal of Mathematical Education in Science and Technology, 41(8),1015- 1035.
  • Harel, G. (1987). Variations in linear algebra content presentations, For the Learning of Mathematics, 7 (3), 29-32.
  • Harel, G. (1989). Learning and teaching linear algebra: diffuculties and an alternative approach to visualizing concepts and processes. Focus on Learning Problems in Mathematics, 11(2), 139-148.
  • Harel, G. (1999). Students' understanding of proofs: a historical analysis and implications for the teaching of geometry and linear algebra. Linear Algebra and Its Applications, 302- 303. 601-613
  • Harel, G. (2000). Principles of learning and teaching mathematics, with particular reference to the learning and teaching of linear algebra, In J-L. Dorier (Ed.), On The Teaching of Linear Algebra, 177-189, Dordrecht, Kluwer Academic Publishers.
  • Hestenes, D. (1991). The design of linear algebra and geometry, Acta Applicandae Mathematicae, 23(1), 65-93.
  • Herrero, M. P. (2000). Strategies and computer projects for teaching linear algebra, International Journal of Mathematical Education in Science and Technology, 31(2), 181- 186.
  • Hillel, J., (2000). Modes of description and the problem of representation in linear algebra. In J- L. Dorier (Ed.), On The Teaching of Linear Algebra, 191-207, Dordrecht, Kluwer Ac., Publ.
  • Hristovitch, S. P. (2001). Students’ conception of introductry linear algebra notions: The role of metaphors, analogies, and symbolization. Unpublished Doctoral Thesis. Purdue University, Purdue, USA.
  • Işık, C. (2003). İlköğretim Okullarının 7. Sınıflarında Okutulan Matematik ders Kitaplarının İçerik, Öğrenci Seviyesine Uygunluk ve Anlamlı Öğrenmeye Katkısı Yönünden Değerlendirilmesi. Yayınlanmamış doktora tezi, Atatürk Üniversitesi, Erzurum, Turkey.
  • Kaplan, T. (2011). Lineer denklem sistemleri ve uygulama alanları. Yayınlanmamış yüksek lisans tezi, Atatürk Üniversitesi, Erzurum, Turkey.
  • Karasar, N. (1999). Bilimsel Araştırma Yöntemi (9. Basım). Ankara: Nobel Yayın Dağıtım.
  • Konyalıoğlu, A. C., İpek, A. S., & Işık, A. (2003). On the teaching linear algebra at the university level: the role of visualization in the teaching vector spaces. Journal of the Korea Society of Mathematical Education Series, 7(1), 59-67.
  • Konyalıoğlu, A. C. (2003). Üniversite Düzeyinde Vektör Uzayları Konusundaki Kavramların Anlaşılmasında Görselleştirme Yaklaşımının Etkinliğinin İncelenmesi. Yayınlanmamış doktora tezi, Atatürk Üniversitesi, Erzurum, Turkey.
  • Konyalıoğlu, S., Konyalıoğlu, A.C., İpek, A.S. & Işık, A. (2005). The role of visualization approach on studentís conceptual learning. International Journal for Mathematics Teaching and Learning, Sept. 21.
  • Konyalıoğlu, A.C., Konyalıoğlu, S. & Işık. A. (2008). Effectiveness of visualization approach on student’s conceptual learning. Journal of Qafqaz University, 24, 245-249.
  • Konyalıoğlu, A. C. (2009). An evaluation from students’ perspective on visualization approach used in linear algebra instructions. World Applied Science Journal, 6(8), 1046-1052.
  • Lapp, D. A., Nyman, M. A., & Berry, J. S. (2010). Student connections of linear algebra concepts: an analysis of concept maps. International Journal of Mathematical Education in Science and Technology. 41(1),1-18.
  • Mallet, D. G. (2007). Multiple representations for systems of linear equations via computer algebra system maple. International Electronic Journal of Mathematics Education. 2 (1). 16-31.
  • Mirsky, L. (1963). An introduction to linear algebra, London: Oxford Universty Press.
  • Nef, W. (1967). Linear algebra, London: Mcgraw-Hill Publ. Com. Limited.
  • Swetz, F., Fauvel, J., Bekken, O., Johansson, B. & Katz, V. (1994). History in higher mathematics. In F. Swetz, J.Fauvel, O.Bekken, B.Johansson & V.Katz, (Eds.) Learn from the masters (pp.103) The Mathematical Association of America Publshing.
  • Yıldırım, A. & Şimşek, H. (2011). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (8.Baskı). Ankara: Seçkin Yayıncılık.
  • Wang, Tse-Wei, (1989). A course on applied linear algebra, Chemical Engineering Education, 23 (4), 236-241.
  • Wu, H. (2004). Computer aided teaching in linear algebra. The China Papers. July 2004. 100- 102.
There are 35 citations in total.

Details

Primary Language Turkish
Subjects Studies on Education
Journal Section Articles
Authors

Tuba Kaplan This is me

Solmaz Gedik This is me

Alper Konyalıoğlu

Ahmet Işık

Publication Date December 10, 2013
Published in Issue Year 2013 Volume: 2 Issue: 2

Cite

APA Kaplan, T., Gedik, S., Konyalıoğlu, A., Işık, A. (2013). Lineer Cebir Ders Kitaplarının Öğretici Unsurlar Açısından İncelenmesi. Bartın University Journal of Faculty of Education, 2(2), 376-394.

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