Prospective Teachers’ Understanding of Graphs

Year 2011, Volume: 10 Issue: 4, 1325 - 1346, 01.12.2011

İbrahim Bayazıt

Abstract

This study examines prospective teachers’ understanding of graphical representations. The research findings indicate that prospective teachers have difficulties in understanding the relationships between the variables in the graphical contexts. The participants were successful in dealing with the graphs that required quantitative approach, such as dealing with a graph point-by-point or making algebraic manipulations to tease out information embedded in the situation. They were also quite competent to deal with the graphs in a global way providing that the graphs represented real life situations. Nevertheless, very few participants were able to interpret graphs in a global way when the graphs required qualitative approaches, such as an understanding of how changes in the algebraic form of a function could affect the graph of that function

Keywords

Prospective teachers, graphs, iconic interpretation, quantitative interpretation, qualitative interpretation

Öğretmen Adaylarının Grafikler Konusundaki Bilgi Düzeyleri

Abstract

Bu çalışmada Fen Bilgisi ve Sınıf Öğretmenliği bölümlerinde okuyan öğretmen adaylarının grafikler konusundaki bilgi düzeyleri incelenmektedir. Bulgular öğretmen adaylarının değişkenler arasındaki ilişkileri grafiksel ortamda anlama ve yorumlamada ciddi sıkıntılar yaşadıklarını göstermektedir. Katılımcılar noktasal bağlamda grafik okuma veya cebirsel formüller yardımıyla işlemler yapma gibi nicel bilgiler gerektiren ve gerçek yaşamla alakalı durumları temsil eden grafikleri yorumlamada daha başarılı olmuşlardır. Ancak, ‘bağımız değişkende yapılan değişimin grafiğin genel gelişimini nasıl etkileyeceğini anlama’ ve ‘verilen grafiklerin cebirsel/aritmetiksel işlemler yapmadan yorumlanması’ gibi nitel algılar ve global yaklaşımlar gerektiren sorularda katılımcıların başarısız olduğu görülmüştür

Keywords

Öğretmen adayları, grafiksel gösterimler, görsel algı, nicel algı, nitel algı

References

• Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics, 2(1), 34-42.
• Brasell, H. M., & Rowe, M. B. (1993). Graphing skills among high school physics students. School Science and Mathematics, 93(2), 63-70.
• Capraro, M. M., Kulm, G., & Capraro, R. M. (2005). Middle grades: Misconceptions in statistical thinking. School Science and Mathematics, 105(4), 165-174.
• Clement, J. (1989). The concept of variation and misconceptions in cartesian graphing. Focus on Learning Problems in Mathematics, 11(2), 77-87.
• Connery, K. F. (2007). Graphing predictions. Science Teacher, 74(2), 42-46.
• Dugdale, S. (1993). Functions and graphs: Perspectives on students thinking. In T. A. Romberg, E. Fennema, and T. P. Carpenter (Eds.) Integrating Research on the Graphical Representation of Functions (pp. 101-130). Hillsdale, NJ: Lawrence Erlbaum Associates.
• Dunham, P. H., & Osborne, A. (1991). Learning how to see: Students’ graphing difficulties. Focus on Learning Problems in Mathematics, 13(4), 35-49.
• Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105-121.
• Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32, 124–158.
• Gray, E., Pinto, M., Pitta, D., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary and advanced mathematics. Educational Studies in Mathematics, 38(1), 111-133.
• Kaput, J. J. (1995). Creating cybernetic and psychological ramps from the concrete to the abstract: Examples from multiplicative structures. In D. N. Perkins, J. L. Schwartz, M. M. West, & M. S. Wiske (Eds.), Software Goes to School: Teaching for Understanding with New Technologies (pp. 130-154). New York: Oxford University Press.
• Keller, B. A., & Hirsch, C. R. (1998). Student preferences of representations of functions. International Journal of Mathematical Education in Science and Technology, 29(1), 117.
• Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York: Macmillan Publishing Company.
• Kramarski, B. (2004). Making sense of graphs: Does metacognitive instruction make a difference on students’ mathematical conceptions and alternative conceptions? Learning and Instruction, 14, 593-619.
• Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1-64.
• Markovits, R., Eylon, B. S., & Brukheimer, M. (1986). Function’s today and yesterday. For the Learning of Mathematics, 29(1), 18-28.
• MEB (2005). Orta öğretim matematik (9,10,11 ve 12. sınıflar) dersi öğretim programı. Ankara: Milli Eğitim Bakanlığı.
• Mevarech, Z. R., & Kramarsky., B. (1997). From verbal descriptions to graphic representations: Stability and change in students’ alternative conceptions. Educational Studies in Mathematics, 32, 229-263.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis (An Expanded Sourcebook). London: Stage Publication.
• Monk, S. (1992). Students’ understanding of a function given by a physical model. In G. Harel and E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy (pp. 175-194). Washington, DC: Mathematical Association of America.
• Roth, W. M., & Bowen, G. M. (2001). Professionals read graphs: A semiotic analysis. Journal for Research in Mathematics Education, 32(2), 159-194.
• Schwarz, B., & Dreyfus, T. (1995). New actions upon old objects: A new ontological perspective on functions. Educational studies in mathematics, 29(3), 259-291.
• Sfard, A. (1992). Operational origins of mathematical objects and quandary of reification – The case of function. In G. Harel & Ed. Dubinsky (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy (pp. 59-85). United States of America: Mathematical Association of America.
• Shah, P., & Hoeffner, J. (2002). Review of graph comprehension research: Implications for instruction. Educational Psychology Review, 14(1), 47-69.
• Slavit, D. (1994). The effect of graphing calculators on students’ conceptions of function. (ERIC Document Reproduction Service No. ED 374 811).
• Smart, T. (1995). Visualising quadratic functions: A study of thirteen years old girls studying mathematics with graphic calculators. In L. Meira & D. Carraher (Eds.), Proceeding of the 19th International Conference for the Psychology of Mathematics Education (v. 2, pp. 272-279). Brazil: Atual Editors Ltd.
• Stake, R. E. (1995). The Art of Case Study Research. London: Stage Publication.
• Tairab, H. H. & Al-Naqbi, A. K. (2004). How do secondary school science students interpret and construct scientific graphs? Journal of Biology Education, 38(3), 127- 132.
• Yin, R. K. (2003). Case Study research: Design and methods. United Kingdom: Sage Publications Ltd.