Yıl: 2018 Cilt: 26 Sayı: 1 Sayfa Aralığı: 219 - 230 Metin Dili: Türkçe DOI: 10.24106/kefdergi.378181 İndeks Tarihi: 30-10-2020

Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi

Öz:
Bu çalışmanın amacı ikinci dereceden denklemlerin öğrenme veöğretiminde matematik tarihinin özellikle Hârezmî’nin tam kareyetamamlama metodunun bir öğretim aracı olarak kullanılmasına ilişkinilköğretim matematik öğretmen adaylarının görüşlerinin belirlenmesidir.Yapılan çalışmada nitel araştırma yöntemlerinden olan durum çalışmasıkullanılmıştır. Araştırmanın verileri ilköğretim matematik öğretmenliğibölümünde okuyan 10 öğretmen adayıyla yapılan yarı-yapılandırılmışgörüşme tekniğiyle toplanmıştır. Araştırma kapsamında elde edilen bulgular,ikinci dereceden denklemlerin öğretiminde matematik tarihinin özellikleHârezmî’nin tam kareye tamamlama metodunun öğretmen adaylarınınbu konudaki mevcut matematik bilgilerine etkisi hakkındaki görüşleriylegelecekte yapacakları öğretmenlik mesleğinde bu metodunun bir öğretimaracı olarak kullanılmasına ilişkin görüşlerini ortaya koymuştur. Harezmîyöntemi gibi matematik tarihindeki çalışmaları matematik öğretimindekullanmak öğretmen adaylarının ikinci dereceden denklemlerin içeriğinidaha iyi anlamalarını sağlamış ve onlara, matematik tarihindeki materyalleriikinci dereceden denklemlerin öğretimine dâhil etmek için farklı yöntemler veteknikler sunmuştur.
Anahtar Kelime:

Integrating History of Mathematics into Mathematics Teaching: Al-Khwarizmi’s Completing The Square Method

Öz:
The purpose of this study is to explore preservice elementary mathematics teachers’ conceptions regarding the use of history of mathematics as a teaching tool, especially Al-Khwarizmi’s method of completing the square in the learning and teaching of quadratic equations. The case study of qualitative research methods was used. The data were collected through semi-structured interviews with 10 teacher candidates. The results of the study revealed the conceptions of the influences of the use of history of mathematics, specifically Al-Khwarizmi’s method of completing the square, in the teaching of quadratic equations on preservice elementary mathematics teachers’ current mathematical knowledge, as well as the conceptions of the influences of the use of this method as a teaching instrument on their future teaching professions. It has been seen that using Al-Khwarizmi’s method in mathematics teaching has provided prospective teachers with better understanding of the second-order equations by presenting different techniques to integrate them into teaching quadratic equations.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Allaire, P. R., & Bradley, R. E. (2001). Geometric approaches to quadratic equations from other times and places. Mathematics Teacher, 94(4), 308-319
  • Arcavi, A., & Isoda, M. (2007). Learning to listen: From historical sources to classroom practice. Educational Studies in Mathematics, 66(2), 111-129.
  • Arzarello, F., Bazzini, L., & Chiappini, G. (2000). A model for analysing algebraic thinking. In Sutherland R., Roiano T., & Bell A. (Eds.), Perspectives on school algebra (pp. 61-81). Washington, Kluwer Academic Publishers, Dordrecht.
  • Avital, S. (1995). 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, Washington, DC.
  • Bachelard, G. (1938). La formation de l’esprit scientifique. Vrin, Paris.
  • Baki, A. (2008). Kuramdan Uygulamaya Matematik Eğitimi (Genişletilmiş 4. Basım). Ankara: Harf Eğitim Yayıncılığı.
  • Baki, A., & Bütüner, S. Ö. (2010). Matematik tarihi etkinlikleriyle zenginleştirilmiş sınıf ortamından yansımalar. IX. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi Bildiri Özetleri içinde (s. 104), Dokuz Eylül Üniversitesi, İzmir.
  • Baki, A., & Bütüner, S. Ö. (2013). 6, 7 ve 8. sınıf matematik ders kitaplarında matematik tarihinin kullanım şekilleri. İlköğretim Online, 12(3), 849-872.
  • Baki, A., & Yıldız, C. (2010). Matematik tarihi etkinlikleriyle zenginleştirilmiş sınıf ortamından yansımalar. II. Uluslararası Türkiye Eğitim Araştırmaları Kongre Kitabı içinde (ss. 563-577), Eğitim Araştırmaları Birliği, Antalya.
  • Barbin, E., & Menghini, M. (2000). On potentialities, limits, and risks. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI book, (pp. 86-90). Dordrecht, the Netherlands: Kluwer Academic Publishers.
  • Barbin, E. (1996). The role of problems in the history and teaching of mathematics. In R. Calinger (Ed.), Vita mathematica: Historical research and integration with teaching, (pp. 17-25). Washington, DC: The Mathematical Association of America.
  • Barbin, E. (2000). Integrating history: Research perspectives. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI book, (pp. 63-90). Dordrecht, the Netherlands: Kluwer Academic Publishers.
  • Bossé, M. J., & Nandakumar, N. R. (2005). The factorability of quadratics: motivation for more techniques (section A). Teaching Mathematics and its Applications, 24(4), 143-153.
  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Kluwer, Dordrecht.
  • Brown, S. I. (1993). Towards a pedagogy of confusion. In A. White (Ed.), Essays in humanistic mathematics (pp. 107-122). The Mathematical Association of America, Washington, DC.
  • Carter, C. S., & Yackel, E. (1989). A constructivist perspective on the relationship between mathematical beliefs and emotional acts. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
  • Charalambous, C. Y., Panaoura, A., & Philippou, G. (2009). Using the history of mathematics to induce changes in pre-service teachers’ beliefs and attitudes: Insights from evaluating a teacher education program. Educational Studies in Mathematics, 71, 161-180.
  • Cheung, Y. L. (1980). Learning ideas for mathematics teacher education. Journal of Science and Mathematics Education in S. E. Asia, 3(2), 12-19.
  • Clark, K. M. (2011). History of mathematics: Illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educational Studies in Mathematics, 81(1), 67-84.
  • Conference Board of the Mathematical Sciences [CBMS] (2001). The mathematical education of teachers: Vol. 11. Issues in mathematics education. Providence, RI: American Mathematical Society.
  • Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Los Angeles: SAGE Publications.
  • Didiş, M. G., Baş, S., & Erbas, A. K. (2011). Students’ reasoning in quadratic equations with one unknown. The Seventh Congress of the European Society for Research in Mathematics Education (CERME-7), pp. 479-489.
  • Ernest, P. (1998). The history of mathematics in the classroom. Mathematics in School, 27(4), 26-31.
  • Estrada, M. F. (1993). A história no ensino da matemática [History in the teaching of mathematics]. Educação e Matemática, 27(3), 17-20.
  • Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3-6.
  • Fauvel, J., & Gray, J. (1987). The history of mathematics: A reader. The Open University, London.
  • Fauvel, J., & van Maanen, J. (Eds.). (2000). History in mathematics education-The ICMI study. Dordrecht: Kluwer Academic.
  • Fidel, R. (1984). The case study method: A case study. Library and Information Science Research, 6(3), 273-288.
  • Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science & Education, 10(4), 391-408.
  • Furinghetti, F. (1997). History of mathematics, mathematics education, school practice: Case studies linking different domains. For the Learning of Mathematics, 17(1), 55-61.
  • Furinghetti, F. (2000). The long tradition of history in mathematics teaching. In V. Katz (Ed.), Using history to teach mathematics: An international perspective, (pp. 49-58). Washington, DC: The Mathematical Association of America.
  • Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131-143.
  • Gagne, R. M. (1983). Some issues in the psychology of mathematics instruction. Journal for Research in Mathematics Education, 14(1), 7-18.
  • Garner, M. (1996). The importance of history in mathematics teaching and learning. A paper presented at Interface’ 96, Atlanta.
  • Glaisher, J. W. L. (1890). Presidential address British association for the advancement of science. (Section A), Nature 42, no. 1089, 464-468.
  • Gray, R., & Thomas, M. O. J. (2001). Quadratic equation representations and graphic calculators: Procedural and conceptual interactions. In J. Bobis, B. Perry & M. Mitchelmore (Eds.), Numeracy and beyond. Proceedings of the 24th Conference for the Mathematics Education Research Group of Australasia, Sydney, (pp. 257-264). Sydney: MERGA
  • Grugnetti, L., & Rogers, L. (2000). Philosophical, multicultural, and interdisciplinary issues. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI book, (pp. 39-62). Dordrecht, the Netherlands: Kluwer Academic Publishers.
  • Grugnetti, L. (2000). The history of mathematics and its influence on pedagogical problems. In V. Katz (Ed.), Using history to teach mathematics: An international perspective, (pp. 29-35). Washington, DC: The Mathematical Association of America.
  • Hilton, P. (1980). Math anxiety: Some suggested causes and cures: Part 1. The Two-Year College Mathematics Journal, 11(3), 174-188.
  • Hoffman, N. (1976). Factorisation of quadratics. Mathematics teaching, 76, 54-55.
  • Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in teaching mathematics education. Educational Studies in Mathematics, 71(3), 235-261. Katz, V. J. (1993). Using the history of calculus to teach calculus. Science & Education, 2, 243-249.
  • Katz, V. J. (1997). Some ideas on the use of history in the teaching of mathematics. For the Learning of Mathematics, 17(1), 62-63.
  • Katz, V., & Barton, B. (2007). Stages in the history of algebra with implications for teaching. Educational Studies in Math, 66(2), 185-201.
  • Kelley, L. (2000). A mathematical history tour. Mathematics Teacher, 93(1), 14-17.
  • Kleiner, I. (1993). Functions: Historical and pedagogical aspects. Science & Education, 2, 183-209.
  • Kotsopoulos, D. (2007). Unravelling student challenges with quadratics: A cognitive approach. Australian Mathematics Teacher, 63(2), 19-24.
  • Lakatos, I. (1976). Proofs and refutations. Cambridge University Press, Cambridge.
  • Lefort, X. (1990). History of mathematics in adult continuing education. In J. Fauvel (Ed.), History in the mathematics classroom: The IREM papers (vol. 1). (pp. 85-96). Leicester, England: The Mathematical Association.
  • Leng, W. N. (2006). Effects of an ancient Chinese mathematics enrichment programme on secondary school students’ achievement in mathematics. International Journal of Science and Mathematical Education, 4, 485-511.
  • Liu, P. H. (2003). Do teachers need to incorporate the history of mathematics in their teaching? Mathematics Teacher, 96(6), 416-421.
  • MacDonald, T. H. (1986). Problems in presenting quadratics as a unifying topic. The Australian Mathematics Teachers, 42(3), 20-22.
  • Marshall, G. (2000). Using history of mathematics to improve secondary students’ attitudes towards mathematics. Unpublished doctoral dissertation, Illinois State University, Bloomington−Normal, IL, USA.
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass.
  • National Council for the Accreditation of Teacher Education. [NCATE]. (2003). NCATE/NCTM Program standards: Programs for initial preparation of mathematics teachers. Washington, DC: Author.
  • Ness, H. (1993). Mathematics: An integral part of our culture. In A. M. White (ed.), Essays in humanistic mathematics, (pp. 49-52). The Mathematical Association of America, Washington, DC.
  • Noss, R., & Baki, A. (1996). Liberating school mathematics from procedural view. Journal of Hacettepe Education (Ankara), 12, 179-182.
  • Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers` attitudes toward mathematics. Educational Studies in Mathematics, 35, 189-206.
  • Radford, L. (2000). Historical formation and student understanding of mathematics. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: The ICMI study (pp. 143-170). Dordrecht, the Netherlands: Kluwer Academic.
  • Reimer, L., & Reimer, W. (1995). Connecting mathematics with its history: A powerful, practical linkage. In A. House & A. F. Coxford (Eds.), Connecting
  • mathematics across the curriculum, 1995 Yearbook of the National Council of Teachers of Mathematics (pp. 104 -114). Reston, VA: National Council of Teachers of Mathematics.
  • Rice, A. (1998). A Platonic stimulation: Doubling the square or why do I teach maths? Mathematics in School, 27(4), 23-24.
  • Rickey, V. F. (1996). The necessity of history in teaching mathematics. In R. Calinger (Ed.), Vita mathematica: Historical research and integration with teaching, (pp. 251-256). Washington, DC: The Mathematical Association of America.
  • Rubinstein, R. N., & Schwartz, R. K. (2000). Word histories: Melding mathematics and meanings. Mathematics Teacher, 93(8), 664-669.
  • Schubring, G. (2000). History of mathematics for trainee teachers. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI book, (pp. 91-142). Dordrecht, the Netherlands: Kluwer Academic Publishers.
  • Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228. Reprinted in P. Cobb (Ed.), Learning Mathematics-Constructivist and Interactionist theories of mathematical development. (pp. 87-124). Dordrecht: Kluwer Academic Publishers.
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
  • Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematical Behavior, 14(1), 15-39.
  • Simonson, S. (2000). The mathematics of Levi ben Gershon. Mathematics Teacher, 93(8), 659-663.
  • Siu, M. K. (2000). The ABCD of using history of mathematics in the (undergraduate) classroom. In V. Katz (Ed.), Using history to teach mathematics: An international perspective (pp. 3-9). Washington, DC: Mathematical Association of America.
  • Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
  • Skemp, R. R. (1982). Communicating mathematics: Surface structures and deep structures. Visible Language, 16, 281-288.
  • Swetz, F. (1984). Seeking relevance? Try the history of mathematics. Mathematics Teacher, 77(1), 54-62.
  • Swetz, F. (1989). Using problems form the history of mathematics in classroom instruction. Mathematics Teacher, 82(5), 370-377.
  • Swetz, F. (1995). Using problems from the history of mathematics in classroom instruction. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. Katz (Eds.), Learn from the Masters (pp. 25-38). The Mathematical Association of America, Washington, DC.
  • Thomaidis, Y. (1991). Historical digressions in Greek geometry lessons. For the Learning of Mathematics, 11(2), 37-43.
  • Thomaidis, Y. (1993). Aspects of negative numbers in the early 17th century: An approach for didactic reasons. Science & Education, 2, 69-86.
  • Tobias, S. (1978). Overcoming maths anxiety. Boston: Houghton Mifflin Company.
  • Tzanakis, C., & Arcavi, A. (2000). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI book, (pp. 201-240). Dordrecht, the Netherlands: Kluwer Academic Publishers.
  • Tzanakis, C., & Thomaidis, Y. (2000). Integrating the close historical development of mathematics and physics in mathematics education: Some methodological and epistemological remarks. For the Learning of Mathematics, 20(1), 44-55.
  • Vaiyavutjamai, P., & Clements, M. A. (2006). Effects of classroom instruction on students’ understanding of quadratic equations. Mathematics Education Research Journal, 18(1), 47-77.
  • van Maanen, J. (1991). LHôpitals weight problem. For the Learning of Mathematics, 11(2), 44-47.
  • van Maanen, J. (1997). New maths may profit from old methods. For the Learning of Mathematics, 17(2), 39-46.
  • Vinogradova, N. (2007). Solving quadratic equations by completing squares. Mathematics Teaching in the Middle School, 12(7), 403-405.
  • Wilson, P. S., & Chauvot, J. B. (2000). Who? How? What? A strategy for using history to teach mathematics. Mathematics Teacher, 93(8), 642-645.
  • Yıldırım, A., & Şimşek, H. (2005). Sosyal bilimlerde nitel araştırma yöntemleri. (2. baskı). Ankara: Seçkin yayıncılık.
  • Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Applied Social Research Series, Vol. 5, Sage Publications.
APA GENÇ V, Karataş İ (2018). Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. , 219 - 230. 10.24106/kefdergi.378181
Chicago GENÇ Veysel Murat İstemihan,Karataş İlhan Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. (2018): 219 - 230. 10.24106/kefdergi.378181
MLA GENÇ Veysel Murat İstemihan,Karataş İlhan Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. , 2018, ss.219 - 230. 10.24106/kefdergi.378181
AMA GENÇ V,Karataş İ Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. . 2018; 219 - 230. 10.24106/kefdergi.378181
Vancouver GENÇ V,Karataş İ Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. . 2018; 219 - 230. 10.24106/kefdergi.378181
IEEE GENÇ V,Karataş İ "Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi." , ss.219 - 230, 2018. 10.24106/kefdergi.378181
ISNAD GENÇ, Veysel Murat İstemihan - Karataş, İlhan. "Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi". (2018), 219-230. https://doi.org/10.24106/kefdergi.378181
APA GENÇ V, Karataş İ (2018). Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi, 26(1), 219 - 230. 10.24106/kefdergi.378181
Chicago GENÇ Veysel Murat İstemihan,Karataş İlhan Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi 26, no.1 (2018): 219 - 230. 10.24106/kefdergi.378181
MLA GENÇ Veysel Murat İstemihan,Karataş İlhan Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi, vol.26, no.1, 2018, ss.219 - 230. 10.24106/kefdergi.378181
AMA GENÇ V,Karataş İ Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi. 2018; 26(1): 219 - 230. 10.24106/kefdergi.378181
Vancouver GENÇ V,Karataş İ Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi. Kastamonu Üniversitesi Kastamonu Eğitim Dergisi. 2018; 26(1): 219 - 230. 10.24106/kefdergi.378181
IEEE GENÇ V,Karataş İ "Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi." Kastamonu Üniversitesi Kastamonu Eğitim Dergisi, 26, ss.219 - 230, 2018. 10.24106/kefdergi.378181
ISNAD GENÇ, Veysel Murat İstemihan - Karataş, İlhan. "Matematik Tarihinin Matematik Öğretimine Entegrasyonu: Hârezmî’nin Tam Kareye Tamamlama Yöntemi". Kastamonu Üniversitesi Kastamonu Eğitim Dergisi 26/1 (2018), 219-230. https://doi.org/10.24106/kefdergi.378181