Effect Of Causal Stories In Solving Mathematical Story Problems

Yıl 2010, Cilt: 39 Sayı: 39, 284 - 295, 01.06.2010

GLENN GORDON Smıth HELEN Gerretson SİNAN Olkun JORMA Joutsenlahtı

Öz

Bu çalışmada sözel problemler içerisine yerleştirilen nedensel öykülerin öğrenci performansını etkileyipetkilemediği araştırılmıştır. İlki Amerika’da, ikincisi ise Amerika, Türkiye ve Finlandiya’da eş zamanlı olarak yapılan deneyselçalışmalarda sınıf öğretmeni adayları 3 farklı tipte 1) standart (minimum sözel matematiksel bilgi), 2) nedensel (hem nedenselhem de sözel matematiksel bilgi içeren, 3) olası sonuç da içeren (problemin olası etkileri ve sonuçları görülen bir şekilde)hazırlanmış sözel matematiksel problemleri çözmeye çalışmışlardır. Nedensel öykü unsurlarının eklenmesi Amerikalı ve Finliöğrencilerin uzamsal içerikli problemlerdeki performansını artırırken Türk öğrencilerde herhangi bir etki yapmamıştır.Nedensel öykü unsurlarının eklenmesinin farklı kültürlerde farklı etki yapabileceği bulgusundan hareketle sözel problemlerinçözümünde durumsal modellerin en az şema modelleri kadar öncelikli olabileceği sonucuna varılmıştır

Anahtar Kelimeler

sözel problemler, şema modelleri, durumsal modeller

Kaynakça

• Alwyn, O., & Wearne, D. (1996). Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics, Educational Researcher, 25(4), 12-21.
• Aydoğdu, T., Akbaba-Altun, S. & Olkun, S. (2004). İlköğretim 3, 4, ve 5. Sınıf Öğrencilerinin standart sözel problemlerde işlem seçimleri. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 27, 126-134.
• Awh, E., & Jonides, J. (2001). Overlapping mechanisms of attention and spatial working memory. Trends in Cognitive Sciences, 5, 119-126.
• Berends, I. E., & van Lieshout, E. C. D. M. (2009). The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load. Learning and Instruction, 19, 345-353.
• Boaler, J. (2000). Introduction: Intricacies of knowledge, practice, and theory. In Boaler, J. (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 1-18). Mahwah. NJ: Lawrence Erlbaum Associates.
• Chandler, P., & Sweller, J. (1996). Cognitive load while learning to use a computer program. Applied Cognitive Psychology, 10, 151-170.
• Chapman, O. (2003). Teachers’ conceptions of mathematical word problems: A basis for growth. In N. A. Pateman, B. J. Dougherty, & J. T. Zillox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (vol. 2), (pp. 197-204). Honolulu: University of Hawaii.
• Contreras, J.N., & Martinez-Cruz, A.M. (2003). Pre-service elementary teachers’ solution processes to problematic addition and subtraction word problems involving ordinal numbers and their interpretations of solutions. In N. A. Pateman, B. J. Dougherty & J. T. Zillox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (vol. 2), (pp. 236-244). Honolulu: University of Hawaii.
• Coquin-Viennot, D., & Moreau, S. (2003). Highlighting the role of the episodic situation model in the solving of arithmetical problems. European Journal of Psychology of Education, 3, 267-279.
• Cruz, I., Febles, M., & Díaz, J. (2000). Kevin: A visualiser pupil. For the Learning of Mathematics, 20(2), 30-36.
• de Vega, M. (1995). Backward updating of mental models during continuous reading of narratives. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, 373-385.
• Devidal, M., Fayol, M., & Barrouillet, P. (1997). Stratégies de lecture et résolution de problèmes arithmétiques. L’Année Psychologique, 97, 9-31.
• Divorce Rates Around the World. (2007). Retrieved July 16, 2009, from http://www.darndivorce.com/divorce-rates-around- the-world/
• Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer Academic Publishers.
• Greer, B. (1997). Modeling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307.
• Hakala, C. M. (1999). Accessibility of spatial information in a situation model. Discourse Processes, 27(3), 261-279.
• Hasher, L., & Zacks, R. T. (1979). Automatic and effortful processes in memory. Journal of Experimental Psychology: General, 3, 356-388.
• Hiebert, J., Thomas P., Carpenter, E., Fennema, K., Fuson, P., Hanlie, M.,
• Human Development Index. (2008). Retrieved July 16, 2009, fromhttp://en.wikipedia.org/wiki/Human_Development_Index
• Human Development Reports. (2008). Retrieved July 16, 2009, from http://hdr.undp.org/en/mediacentre/news/title,15493,en.html
• Human Development Reports. (2005). Retrieved July 16, 2009, from http://hdrstats.undp.org/countries/country_fact_sheets/cty_fs_TUR.html
• Jahn, G. (2004). Three turtles in danger: Spontaneous construction of causally relevant spatial situation models. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30(5), 969-987.
• Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92(1), 109- 129.
• Levine, W. H., & Klin, C. M. (2001). Tracking of spatial information in narratives. Memory & Cognition, 29, 327-335.
• Long, D. L., Golding, J. M., & Graesser, A. C. (1992). A test of the on-line status of goal-related inferences. Journal of Memory and Language, 31, 634-647.
• Lord, T., & Holland, M. (1997). Preservice secondary education majors and visual-spatial perception: An important cognitive aptitude in the teaching of science and mathematics. Journal of Science Teacher Education, 8(10), 43-53.
• Mandler, J. M, & Johnson, N. S. (1977). Remembrance of things parsed: Story structure and recall. Cognitive Psychology, 9, 111-151.
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• O'Brien, E. J., & Albrecht, J. E. (1992). Comprehension strategies in the development of a mental model. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18(4), 777-784.
• Paas, F., Tuovinen, J., Tabbers, H., & Van Gerven, P. W. M. (2003). Cognitive load measurement as a means to advance cognitive load theory. Educational Psychologist, 38, 63-71.
• Riley, M. S., Greeno, J. G., & Heller, J. I. (1983). Development of children’s problem solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153-196). New York: Academic Press.
• Rinck, M., Hahnel, A., & Becker, G. (2001). Using temporal information to construct, update and retrieve situation models of narratives. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 67-80.
• Rosales, J., Orrantia, J., Vicente, S., & Chamoso, J. (2008). Studying mathematics problem-solving classrooms: A comparison between the discourse of in-service teachers and student teachers. European Journal of Psychology of Education, 23(3), 275-294.
• Rumelhart, D. E. (1980). Schemata: The building blocks of cognition. In R. J. Spiro, B. C. Bruce, & W. F. Brewer (Eds.), Theorical issues in reading comprehension: Perspectives from cognitive psychology, linguistics, artificial intelligence, and education (pp. 33-58). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
• Schaer, B. B., Ley, T. C., Neal, K. S., & Wright, J. P. (1988). Evaluation and validation of the Mikulecky behavioral reading attitude measure. Educational and Psychological Measurement, 48, 181-186.
• Schank, R. C. (1975). Conceptual information processing. Amsterdam: North-Holland.
• Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. (Ch. 15) New York: Simon & Schuster Macmillan.
• Schoenfeld, A. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. Voss, D. Perkins & J. Segal (Eds.), Informal reasoning and education (pp. 311-343). Hillsdale, NJ: Lawrence Erlbaum Associates.
• Shah, P., & Mijake, A. (1996). The separability of working memory resources for spatial thinking and language processing: An individual differences approach. Journal of Experimental Psychology: General, 125, 4-27.
• Silver, E., Shapiro, L., & Deutsch, A. (1993). Sense making and the solution of division problems involving remainders: An examination of middle school students' solution processes and their interpretations of solutions. Journal for Research in Mathematics Education, 24(2), 117-135.
• Stein, N. L., & Glenn, C. C. (1979). An analysis of story comprehension in elementary school children. In R. O. Freedle (Ed.), New directions in discourse processing: Advances in discourse processing (pp. 53-120). Norwood, NJ: Ablex.
• Sunberg, S., & Goodman, T. (2005). Incorporating spatial ability instruction in teacher preparation. Mathematics Teaching in the Middle School, 11(1), 28–34.
• Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4, 295-312.
• Thevenot, C., Devidal, M., Barrouillet, P., & Fayol, M. (2007). Why does placing the question before an arithmetic word problem improve performance? A situation model account. The Quarterly Journal of Experimental Psychology, 60(1), 43- 56.
• Trabasso, T., & Magliano, J. P. (1996). Conscious understanding during comprehension. Discourse Processes, 21, 255-287.
• van den Broek, P., Lorch, E. P., & Thurlow, R. (1996). Children's and adults' memory for television stories: The role of causal factors, story-grammar categories, and hierarchical level. Child Development, 67, 3010-3028.
• van Dijk, T.A., & Kintsch, W. (1983). Strategies of discourse comprehension. New York: Academic Press.
• van Garderen, D., & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246-254.
• Verschaffel, L., De Corte, E., & Vierstraete, H. (1999). Upper elementary school pupils’ difficulties in modeling and solving nonstandard additive word problems involving ordinal numbers. Journal for Research in Mathematics Education, 30(3), 265-285.
• Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets and Zietlinger.
• Wheatley, G. W. (1998). Imagery and mathematics learning. Focus on Learning Problems in Mathematics, 20(2-3), 65-77.
• Wilson, S. G., Rinck, M., McNamara, T. P., Bower, G. H., & Morrow, D. G. (1993). Mental models and narrative comprehension: Some qualifications. Journal of Memory and Language, 32, 141-154.
• Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning – A study of children’s mastery of reference and meaning in textual realities. Learning and Instruction, 7(4), 361-382.
• Zwaan, R. A. (1996). Processing narrative time shifts. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(5), 1196-1207.
• Zwaan, R. A., Langston, M. C., & Graesser, A. C. (1995). The construction of situation models in narrative comprehension: An event-indexing approach. Psychological Science, 6, 292-297.
• Zwaan, R. A., Radvansky, G. A., Hilliard, A. E., & Curiel, J. M. (1998). Constructing multidimensional situation models during reading. Scientific Studies of Reading, 2, 199-220.
• Zwaan, R. A., & van Oostendorp, H. (1993). Do readers construct spatial representations in naturalistic story comprehension? Discourse Processes, 16(1-2), 125-143.