Ortaokul Matematik Öğretmeni Adaylarının Cebirsel İfade ve Denklemlere Yönelik Kurdukları Problemlerin İncelenmesi

Yıl 2017, , 161 - 187, 04.04.2017

Melihan Ünlü , Gülfem Sarpkaya-aktaş

https://doi.org/10.16949/turkbilmat.303966

Cited By: 3

Öz

Bu araştırmanın amacı, ortaokul matematik
öğretmeni adaylarının cebirsel ifade ve denklemlere ilişkin kurdukları
problemlerin incelenerek sınıflandırılmasıdır. 
Araştırmaya ait veri 2012- 2013 bahar döneminde bir devlet
üniversitesinin ilköğretim matematik öğretmenliği programında öğrenim görmekte
olan 96 öğretmen adayından toplanmıştır. Veri toplama aracı olarak
araştırmacılar tarafından geliştirilen ve beş açık uçlu maddeden oluşan Problem
Kurma Testi kullanılmıştır. Öğretmen adaylarından verilen cebirsel ifade ve
denklemlere uygun problem kurmaları istenmiştir. Kurulan problemler betimsel
analiz yöntemine uygun olarak sınıflandırılmıştır. Yapılan analizler sonucunda,
öğretmen adaylarının cebirsel ifade ve denklemlere yönelik genel olarak sözel
ve çözülebilen problemler kurdukları, kurulan problemlerde genellikle günlük
dili kullandıkları tespit edilmiştir.

Anahtar Kelimeler

Cebirsel ifade ve denklemler, problem kurma, öğretmen adayı

Examination of Pre-service Elementary Mathematics Teachers’ Problems Posed about Algebraic Expressions and Equations

Öz

The purpose of this study is to examine pre-service elementary mathematics teachers’ problems posed about algebraic expressions and equations. Data was collected from 96 pre-service elementary mathematics teachers in the spring semester of 2012- 2013 who were enrolled in a teacher education program at a public university.  Problem Posing Test consists 5 open ended items which were developed by researchers was used as a data collection tool. Pre-service elementary mathematics teachers were asked to pose problems corresponding to the algebraic expressions and equations. Problems were examined and classified. Descriptive statistics were used to determine pre-service elementary mathematics teachers’ problem types. Findings of the study indicated that in general problem types were classified as story and solvable problems, they used daily language for posing problems.

Anahtar Kelimeler

Algebraic expressions and equations, problem posing, pre-service teacher

Kaynakça

• Akkan, Y., Çakıroğlu, Ü. ve Güven, B. (2009). Equation forming and problem posing abilities of 6th and 7th grade primary school students. Mehmet Akif Ersoy University Journal of Education Faculty, 17, 41- 55.
• Aydoğdu-İskenderoğlu T. ve Güneş G. (2016). Pedagojik formasyon eğitimi alan matematik bölümü öğrencilerinin problem kurma becerilerinin incelenmesi. Sakarya University Journal of Education, 6, 26-45.
• Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. (3. baskı). Trabzon: Derya Kitapevi.
• Brown, S. I., & Walter, M. I. (2005). The art of problem posing. New Jersey: Lawrence Erlbaum Associates, Inc.
• Brown, C., Carpenter, T., Kouba, V., Lindquist, M., Silver, E., & Swafford, J. (1988). Secondary school results from the fourth NAEP mathematics assessment: Algebra, geometry, mathematical methods, and attitudes. Mathematics Teacher, 81(5), 337-347.
• Büyüköztürk, Ş., Çakmak Kılıç, E., Akgün, Ö., Karadeniz, Ş. ve Demirel, F. (2011). Bilimsel araştırma yöntemleri (10. baskı). Ankara: Pegem Akademi Yayıncılık.
• Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401–421.
• Cortes, A., & Pfaff, N. (2000). Solving equations and inequations: operational invariants and methods constructed by students. Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. II, pp. 193-200). Hiroshima, Japan: Nishiki Print Co., Ltd.
• Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
• Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395–415.
• Dede, Y. (2004). Öğrencilerin cebirsel sözel problemleri denklem olarak yazarken kullandıkları çözüm stratejilerinin belirlenmesi. Educational Secience and Practice, 4(6), 175-192.
• Dede Y. ve Yaman S. (2005). Matematik öğretmen adaylarının matematiksel problem kurma ve problem çözme becerilerinin belirlenmesi. Eğitim Araştırmaları, 5, 41- 56.
• Eisenberg, T., & Dreyfus, T., (1991). On the reluctance to visualize in mathematics. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 25–37). Washington DC: Mathematical Association of America.
• English, L. D. (2003). Engaging students in problem posing in an inquiry-oriented mathematics classroom. In F. Lester & R. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten-grade 6 (pp.187-198). Reston, Virginia: National Council of Teachers of Mathematics.
• Graham, A. T., & Thomas M. O. J. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41, 265- 282.
• Güveli, E. (2015). Prospective elementary mathematics teachers’ problem posing skills about absolute value. Turkish Journal of Teacher Education, 4(1), 1-17.
• Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
• Işık, C., Işık, A. ve Kar, T. (2011). Matematik öğretmeni adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30, 39-49.
• Işık, C., & Kar, T. (2012a). The analysis of the problems posed by the pre- service teachers about equations. Australian Journal of Teacher Education, 37(9), 93-113.
• Işık, C. ve Kar, T. (2012b). Matematik dersinde problem kurmaya yönelik öğretmen görüşleri üzerine nitel bir çalışma. Milli Eğitim Dergisi, 194, 199-215.
• Kılıç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22, 1-10.
• Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
• Korkmaz, E. ve Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(1), 64–74.
• Lavy, I., & Bershadsky, I. (2003). Problem posing via ‘‘what if not?’’ strategy in solid geometry a case study. Journal of Mathematical Behavior, 22, 369–387.
• Lee, F. (2002, Aralık). Diagnosing students’ algebra errors on the web. Paper presented at Proceedings of the International Conference on Computers in Education (ICCE’02), Auckland, New Zeland: The Printing House.
• MEB. (2013). Ortaokul (5-8. sınıflar) matematik öğretim programı. Ankara: MEB Basımevi.
• Miles, B. M., & Huberman, A. M. (1994). Qualitative data analvsis (2nd ed.). London: Sage Publications.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, Va: National Council of Teachers of Mathematics.
• Polya, G. (1962). Mathematical discovery: On understanding, teaching, and learning problem solving. New York: John Wiley.
• Sheffield, L. J., & Cruikshank, D. E. (2005). Teaching and learning mathematics pre-kindergarten through middle school. Hoboken, N.J.: Wiley Jossey Bass Education.
• Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing, International Journal of Mathematical Education in Science and Technology, 48(2), 163-184
• Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics. 14(1), 19–28.
• Stacey, K., & MacGregor, M. (1997). Ideas about symbolism that students bring to algebra. Mathematics Teacher, 90, 110-113.
• Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14, 503–518.
• Steinberg, R., Sleeman, D., & Ktorza D. (1990). Algebra students’ knowledge of equivalence of equations. Journal for Research in Mathematics Education, 22(2), 112-121.
• Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia.
• Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. The Australian Mathematics Teacher, 59(2), 32–40.
• Şandır, H., Ubuz, B. ve Argün, Z. (2002, Eylül). Ortaöğretim 9. sınıf öğrencilerinin mutlak değer kavramındaki öğrenme hataları ve kavram yanılgıları. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi’nde sunulan bildiri. Orta Doğu Teknik Üniversitesi, Ankara.
• Şengül, S. & Katrancı, Y. (2012). Problem solving and problem posing skills of prospective mathematics teachers about the ‘sets’ subject. Procedia - Social and Behavioral Sciences, 69, 1650 – 1655.
• Şengül, S. & Katrancı, Y. (2015). Free problem posing cases of prospective mathematics teachers: Difficulties and solutions. Procedia - Social and Behavioral Sciences, 174, 1983 – 1990.
• Ticha, M., & Hošpesová, A. (2009, Ocak). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at Congress of European Research in Mathematics Education (CERME 6), Lyon, France.
• Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175.
• Tsamir P., & Bazzini, L. (2004). Consistencies and inconsistencies in students’ solutions to algebraic ‘single-value’inequalities. International Journal of Mathematical Education in Science and Technology, 35(6), 793–812.
• Ünlü, M. & Ertekin, E. (2012). Why do pre-service teachers pose multiplication problems instead of division problems in fractions? Procedia - Social and Behavioral Sciences, 46, 490 – 494.
• Van de Walle, J., Karp, K., & Bay-Williams, J. (2012). İlkokul ve ortaokul matematiği: gelişimsel yaklaşımla öğretim. (S. Durmuş, Çev. Ed.). Ankara: Nobel Yayıncılık.
• Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82, 201-221.
• Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers' content knowledge on their evaluation of students' strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319-351.
• Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in ‘negativity’. Learning and Instruction, 14, 469–484.
• Yenilmez, K. ve Ev-Çimen (2014). Matematik öğretmeni adaylarının “örnek, alıştırma, problem” oluşturma çalışmalarının incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 3(3), 76-84.
• Yıldız, A. ve Baltacı, V. (2015). İlköğretim matematik öğretmen adaylarının problem kurma etkinlikleri ile olasılığa yönelik bilgilerinin incelenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD), 16(1), 201-213.