Analysis of The Problems Related to Verbal and Visual Representations Posed by Pre-service Teachers

Yıl 2011, Cilt: 30 Sayı: 30, 39 - 49, 01.02.2011

Ahmet Işık Tuğrul Kar

Öz

In this study, it was aimed to analyze the problems related to verbal and visual representations posed by pre-service mathematics teachers. This study was conducted with 70 pre-service teachers studying in Primary Education in Mathematics Department in a public university during 2010-2011 academic year autumn term. Data were gathered through a problem posing test prepared appropriate to verbal and visual representations. Problem sentences written by pre-service teachers were classified as “problem,” “not problem,” and “blank.” As a result of this classification, answers evaluated as “problem” were characterized as “assignment”, “relational”, and “conditional”. Findings of the study indicated that the success of the preservice teachers were generally low in problem posing appropriate to different representations. Besides,it was determined that pre-service teachers gave more place to “assignment” type of problems posed appropriate to verbal and visual representations.

Anahtar Kelimeler

problem posing, representations, pre-service teachers

Öğretmen Adaylarının Sözel ve Görsel Temsillere Yönelik Kurdukları Problemlerin Analizi

Öz

Bu çalısma, matematik ögretmeni adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizini amaçlamıstır. Çalısma 2010-2011 güz döneminde bir devlet üniversitesinin Ilkögretim Matematik Ögretmenligi Bölümü’nde ögrenim gören 70 ögretmen adayı ile yürütülmüstür. Veri toplama aracı olarak sözel ve görsel temsillere yönelik hazırlanan Problem Kurma Testi kullanılmıstır. Ögretmen adaylarının yazmıs oldukları problem cümleleri “problem”, “problem degil” ve “bos” seklinde sınıflandırılmıstır. Bu sınıflama sonucunda “problem” olarak degerlendirilen yanıtlar ise “ödev”, “iliskisel” ve “kosullu” olarak sınıflandırılmıstır. Çalısmanın bulgularına göre, adayların farklı temsillere yönelik problem kurma basarılarının genel olarak düsük oldugu belirlenmistir. Ayrıca ögretmen adaylarının sözel ve görsel temsillere yönelik her bir problem kurma maddesinde “ödev” seklindeki problem cümlelerine daha fazla yer verildikleri tespit edilmistir.

Anahtar Kelimeler

problem kurma, temsiller, öğretmen adayları.

Kaynakça

• Brown, S. I. & Walter, M. I. (1983). The art of problem posing. London: Lawrence Erlbaum Associates.
• Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37(2), 121–143.
• 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.
• 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 of Mathematics Teacher Education, 11, 395-415. Doi: 10.1007/s10857-008-9081-0
• Cunningham, R. (2004). Problem posing: an opportunity for increasing student responsibility. Mathematics and Computer Education, 38(1),83-89.
• Dickerson, V. M. (1999). The impact of problem- posing instruction on the mathematical problem solving achievement of seventh graders (Unpublished doctoral dissertation). University of Emory, Atlanta.
• Dreyfus, T. & Eisenberg, T. (1991). On the reluctance to visualize in mathematics. In W. Zimmermann & S. Cunningham (Eds.) Visualization in Teaching and Learning Mathematics, 19, 25–37.
• English, D. L. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
• English, L. D. & Halford, G. S. (1995). Mathematics education: Models and processes. New Jersey: Lawrence Erlbaum Associates.
• Gonzales, N. A. (1996). Problem formulation: Insights from student generated questions. School Science and Mathematics, 96(3), 152–157.
• Harries, T. & Barmby, P. (2008). Representing multiplication. Mathematics Teaching, 206, Research Library, pp. 37.
• Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535–540. Doi: 10.1007/s11858-009- 0214-4
• Henningsen, M. & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524–549.
• Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S.Wagner, & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167– 194). Hillsdale, NY: Erlbaum.
• Lavy, I. & Shriki, A. (2007, July). Problem posİng as a means for developing mathematical knowledge of prospective teachers. Paper presented at the meeting of 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul.
• Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.
• Leung, S. S. (1993). The relation of mathematical knowledge and creative things to the mathematical problems posing of prospective elementary school teachers on tasks differing in numerical information content (Unpublished doctoral dissertation). University of Pittsburg.
• Matz, K. & Leier, C. (1992). Word Problems and the language connection. Arithmetic Teacher, 39(8), 14-17.
• Mcmillan, H. J. & Schumacher, S. (2010). Research in education. Boston, USA: Pearson Education.
• Milli Eğitim Bakanlığı(MEB). (2006). İlköğretim matematik dersi(6-8. Sınıflar) öğretim programı ve kılavuzu. Ankara Devlet Kitapları Müdürlüğü.
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
• Nicol, C. (1999). Learning to teach mathematics: Questioning, listening, and responding. Educational Studies in Mathematics, 37(1), 45–66.
• Richards, L. (1990). Measuring things in words: Language for learning mathematics. Language Arts, 67(1), 14-25.
• Schloemer, C. G. (1994). Integrating problem posing into instruction in advanced algebra: feasibility and outcomes (Unpublished doctoral dissertation). University of Pittsburg.
• Silver, E. (1994). On mathematical problem posing. For The Learning of Mathematics, 14(1), 19–28.
• Silver, E. A. & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.
• Silver, E. A., Mamona-Downs, J., & Leung, S. S. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27, 293–309.
• Stein, M. K., Smith, M., Henningsen, M., & Silver, E. (2000). Implementing standards-based mathematics instruction : A casebook for professional development. NY: Teachers College Press.
• Stevenson, H. W. & Stigler. J. W. (1992). The learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. NY: Summit Books.
• Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.
• Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh, & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp. 164-185). Perth: MASTEC Publication.
• Vacc, N. (1993). Implementing the professional standards for teaching mathematics: Questioning in the mathematics classroom. Arithmetic Teacher, 41(2), 88– 91.
• Van den Heuvel-Panhuizen, M., Middleton, J., & Streefland, L. (1995). Student-generated problems: Easy and difficult problems on percentage. For the Learning of Mathematics,15(3), 21-27.
• Van De Walle, J. A. (2004). Elementary and middle school mathematics (5th Ed.). America: Person Education.