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Investigating History of Mathematics for Teaching Mathematics: The Case of Logarithm

Yıl 2021, , 208 - 220, 31.10.2021
https://doi.org/10.32433/eje.1004600

Öz

The role of the history of mathematics in understanding the concepts in mathematics is among the topics that have been given importance in recent years, however incorporating history of mathematical concept in teaching is still limited. Logarithm is one of the most fundamental concepts in mathematics, it is frequently used in the fields of science and technology. However, studies show that students have difficulty in understanding the concept of logarithm, and they have difficulty in comprehending the meaning of logarithm even if they can perform operations on logarithmic expressions. As with other concepts in mathematics, it is known that the way in which the concept of logarithm is introduced and structured in teaching is closely related to how students understand it. How a mathematical concept is structured in the textbook significantly affects how teachers teach the concept in the classroom. Therefore, how mathematical concepts are structured in textbooks is one of the important parameters in mathematics teaching. In Turkey, the concept of logarithm is introduced to students in the 12th grade. When the 12th grade mathematics textbook is examined, it is seen that the concept of logarithm is defined as the inverse of the exponential function. It is also understood that the algebraic approach is heavily utilized in the teaching of logarithms. In this study on the history of the concept of logarithm, it is revealed that the historical development of the concept of logarithm is different from the way the concept is structured in textbooks. This study aims to propose an alternative way of defining and introducing the logarithm by making use of the historical development of logarithm. It is expected that the findings of the study will facilitate the understanding of the relationship between the numerical, algebraic, and geometric expressions of the logarithm, thus helping to comprehend the meaning of the logarithm.

Kaynakça

  • Anglin, W. S. (1994). Mathematics: A Concise History and Philosophy, Springer, Berlin.
  • Berezovski, T & Zazkis, R. (2006). Logarithms: Snapshot from two tasks. Proceedings on 30th International Conference for Psychology of Mathematics Education. Praque, CZ.
  • Bednarz, N., Kieran, C., Lee, L. (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht: Kluwer, 364.
  • Burton, D. M. (2007). The history of mathematics: an introduction. (sixth edition). The McGrow-Hill.
  • Boyer, C. B. (1968). A history of mathematics: Wiley New York.
  • Cajori, F. (1913). History of exponential and logarithmic concepts. The American Mathematical Monthly, 20(1), 5-14.
  • Confrey, J. (1991). The concept of exponential functions: A student’s perspective. In L. Steffe (Ed.). Epistemological foundations of mathematical experience, (p.124-159). New York: Springer-Verlag.
  • Cooke, R. (2005). The history of mathematics. A Brief course. Hoboken, N. J.: Willey-Interscience.
  • Confrey, J. & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for research in mathematics education, 26(1), 66-8.
  • Eves, H. (1980). Great moments in mathematics (before 1650). The Mathematical Association of America (MAA).
  • Fauvel, J. (1995). Revisiting the history of logarithms. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson, & V. Katz (Eds.), Learn from the masters (p.43-48). Washington, DC: Mathematical Association of America.
  • Filloy, E., Rojano, T., Puig, L., & Rojaho, T. (2008). Educational algebra: a theoretical and empirical approach, New York: Springer.
  • Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science and Education, 10, 391-408.
  • Kastberg, S. E. (2002). Understanding mathematical concepts: The case of logarithmic function. Unpublished Doctoral Dissertation, University of Georgia.
  • Hairer, E., & Wanner, G. (1996). Analysis by its history. Springer.
  • Katz, V. (1995). Napier’s logarithms adapted for today’s classroom. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson, & V. Katz (Eds.), Learn from the masters (p.49-56). Washington, DC: Mathematical Association of America.
  • Katz, V. J. (2004). The history of mathematics: Brief version. Boston, MA: Pearson Education.
  • MEB (2018). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı, Millî Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
  • Millî Eğitim Bakanlığı [MEB] (2019). Ortaöğretim Matematik 12 Ders Kitabı. Millî Eğitim Bakanlığı Yayınları.
  • Pierce, R. C. (1977). A brief history of logarithms. The two-Year College Mathematics Journal 8(1), 22-26.
  • Radford, L., & Puig, L. (2006). Syntax and meaning as sensuous, visual, historical forms of algebraic thinking. Educational Studies in Mathematics, 66(2), 145-164.
  • Smith, E., & Confrey, J. (1994). Multiplicative structures and the development of logarithms: What was lost by the invention of function. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics, 333-364, State University of New York Press.
  • Schubring, G., Furinghetti, F. & Siu, M.K. (2012). Introduction: the history of mathematics teaching. Indicators for modernization processes in societies. 44(4), 457-459.
  • Swetz, F., Fauvel, J., Katz, V., Bekken, O, & Johansson, B (1995). Learn from the masters!. The Mathematical Association of America.
  • Toumasis (1993). Teaching logarithms via history. School Science and Mathematics, 93(8), 428-34.
  • Villarreal-Calderon, R. (2008). Chopping Logs: A Look at the History and Uses of Logarithms. The Montana Mathematics Enthusiast, 5(2/3), 337-344.
  • Weber, K. (2002). Developing students' understanding of exponents and logarithms. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Athens, GA: University of Georgia.

Matematik Öğretimi İçin Matematik Tarihini İncelemek: Logaritma Örneği

Yıl 2021, , 208 - 220, 31.10.2021
https://doi.org/10.32433/eje.1004600

Öz

Matematik tarihinin matematikteki kavramların anlaşılmasındaki rolü son yıllarda önem verilen konular arasındadır, ancak matematik tarihinin matematik öğretimine dahil edilmesinde hala bazı kısıtlar mevcuttur. Logaritma, matematikteki en temel kavramlardan biridir, bilim ve teknoloji alanlarında sıklıkla kullanılmaktadır. Ancak, araştırmalar öğrencilerin logaritma kavramını anlamakta zorlandıklarını, kimi zaman logaritmik ifadelerle ilgili işlemlerde kimi zaman ise logaritmik ifadelerle ilgili işlemleri yapabildikleri halde logaritmanın anlamını kavramakta güçlük çektiklerini göstermektedir. Matematikteki diğer kavramlarda olduğu gibi, logaritma kavramının öğretiminde öğrencilere tanıtılma ve yapılandırılma şeklinin öğrencilerin onu nasıl anladığı ile yakından ilişkili olduğu bilinmektedir. Bir matematiksel kavramın ders kitabında nasıl yapılandırıldığı öğretmenlerin kavramı sınıfta nasıl öğrettiğini önemli oranda etkilemektedir. Dolayısıyla, ders kitaplarında matematiksel kavramların nasıl ele alındığı matematik öğretimindeki önemli parametrelerden biridir. Türkiye'de logaritma kavramı öğrencilere 12. sınıfta tanıtılmaktadır. 12. sınıf matematik ders kitabı incelendiğinde logaritma kavramının üstel fonksiyonun tersi olarak tanımlanarak öğretilmeye başlandığı görülmektedir. Logaritma öğretiminde yoğunluklu olarak cebirsel yaklaşımdan faydalanıldığı anlaşılmaktadır. Logaritma kavramının tarihi ile ilgili yapılan bu çalışmada, logaritma kavramının tarihsel gelişiminin kavramın ders kitaplarında ele alınma şeklinden farklı olduğu ortaya konulmaktadır. Bu çalışma, logaritmanın tarihsel gelişiminden faydalanarak logaritmayı tanımlamanın ve tanıtmanın alternatif bir yolunu önermeyi amaçlamaktadır. Çalışmanın bulgularının logaritmanın sayısal, cebirsel ve geometrik ifadeleri arasında ilişkinin anlaşılmasını kolaylaştırması, böylelikle logaritmanın anlamının kavratılmasına faydası olması beklenmektedir.

Kaynakça

  • Anglin, W. S. (1994). Mathematics: A Concise History and Philosophy, Springer, Berlin.
  • Berezovski, T & Zazkis, R. (2006). Logarithms: Snapshot from two tasks. Proceedings on 30th International Conference for Psychology of Mathematics Education. Praque, CZ.
  • Bednarz, N., Kieran, C., Lee, L. (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht: Kluwer, 364.
  • Burton, D. M. (2007). The history of mathematics: an introduction. (sixth edition). The McGrow-Hill.
  • Boyer, C. B. (1968). A history of mathematics: Wiley New York.
  • Cajori, F. (1913). History of exponential and logarithmic concepts. The American Mathematical Monthly, 20(1), 5-14.
  • Confrey, J. (1991). The concept of exponential functions: A student’s perspective. In L. Steffe (Ed.). Epistemological foundations of mathematical experience, (p.124-159). New York: Springer-Verlag.
  • Cooke, R. (2005). The history of mathematics. A Brief course. Hoboken, N. J.: Willey-Interscience.
  • Confrey, J. & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for research in mathematics education, 26(1), 66-8.
  • Eves, H. (1980). Great moments in mathematics (before 1650). The Mathematical Association of America (MAA).
  • Fauvel, J. (1995). Revisiting the history of logarithms. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson, & V. Katz (Eds.), Learn from the masters (p.43-48). Washington, DC: Mathematical Association of America.
  • Filloy, E., Rojano, T., Puig, L., & Rojaho, T. (2008). Educational algebra: a theoretical and empirical approach, New York: Springer.
  • Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science and Education, 10, 391-408.
  • Kastberg, S. E. (2002). Understanding mathematical concepts: The case of logarithmic function. Unpublished Doctoral Dissertation, University of Georgia.
  • Hairer, E., & Wanner, G. (1996). Analysis by its history. Springer.
  • Katz, V. (1995). Napier’s logarithms adapted for today’s classroom. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson, & V. Katz (Eds.), Learn from the masters (p.49-56). Washington, DC: Mathematical Association of America.
  • Katz, V. J. (2004). The history of mathematics: Brief version. Boston, MA: Pearson Education.
  • MEB (2018). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı, Millî Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
  • Millî Eğitim Bakanlığı [MEB] (2019). Ortaöğretim Matematik 12 Ders Kitabı. Millî Eğitim Bakanlığı Yayınları.
  • Pierce, R. C. (1977). A brief history of logarithms. The two-Year College Mathematics Journal 8(1), 22-26.
  • Radford, L., & Puig, L. (2006). Syntax and meaning as sensuous, visual, historical forms of algebraic thinking. Educational Studies in Mathematics, 66(2), 145-164.
  • Smith, E., & Confrey, J. (1994). Multiplicative structures and the development of logarithms: What was lost by the invention of function. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics, 333-364, State University of New York Press.
  • Schubring, G., Furinghetti, F. & Siu, M.K. (2012). Introduction: the history of mathematics teaching. Indicators for modernization processes in societies. 44(4), 457-459.
  • Swetz, F., Fauvel, J., Katz, V., Bekken, O, & Johansson, B (1995). Learn from the masters!. The Mathematical Association of America.
  • Toumasis (1993). Teaching logarithms via history. School Science and Mathematics, 93(8), 428-34.
  • Villarreal-Calderon, R. (2008). Chopping Logs: A Look at the History and Uses of Logarithms. The Montana Mathematics Enthusiast, 5(2/3), 337-344.
  • Weber, K. (2002). Developing students' understanding of exponents and logarithms. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Athens, GA: University of Georgia.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Eğitim Üzerine Çalışmalar
Bölüm Derleme
Yazarlar

Duygu Ören Vural 0000-0002-1676-6348

Yayımlanma Tarihi 31 Ekim 2021
Gönderilme Tarihi 4 Ekim 2021
Kabul Tarihi 5 Ekim 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Ören Vural, D. (2021). Investigating History of Mathematics for Teaching Mathematics: The Case of Logarithm. Erciyes Journal of Education, 5(2), 208-220. https://doi.org/10.32433/eje.1004600

ERCİYES JOURNAL OF EDUCATION [EJE]

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