Дијана Р. Обрадовић, др Маријана Ж. Зељић, Универзитет у Београду, Учитељски факултет,
имејл: marijana.zeljic@uf.bg.ac.rs

Иновације у настави, XXVIII, 2015/1, стр. 69–81

doi:10.5937/inovacije1501069O

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Резиме: Способност решавања текстуалних проблема ефикасан је показатељ математичких знања и способности ученика. Истраживања процеса визуелизације и улоге менталних слика у математичком резоновању показују важност изабране репрезентације у процесу решавања проблема. Начин моделовања при решавању текстуалних задатака може да допринесе (или спречи) развијању релационог разумевања поступака њиховог решавања. Циљ овог истраживања је анализа метода и стратегија које ученици користе на крају првог циклуса школовања при решавању текстуалних проблема. Посебан акценат је на истраживању начина представљања информација које ученици користе у процесу решавања задатака. У истраживању су коришћене дескриптивна метода и техника тестирања. Резултати истраживања показују да ученици при решавању текстуалних задатака користе искључиво симболичке репрезентације проблема, што доводи до тога да задатке који се не могу решити директним методама ученици не могу решити. Иако бројна истраживања показују значај коришћења различитих модела при решавању задатака, наши резултати показују да ученици, уместо да проблем преведу на мање апстрактан ниво, преводе га у апстрактну форму, која је изнад њихове могућности разумевања. Једно од решења за превазилажење наведеног проблема јесте дефинисање оперативних задатака и садржаја који се односе на моделовање и различите стратегије решавања текстуалних задатака у Наставном програму за почетну наставу.

Кључне речи: текстуални задаци, моделовање, методе, стратегије решавања задатака.

Summary: Ability for solving story problems is an efficient determinant of mathematical knowledge and students’ abilities. Research of the process of visualization and the role of mental images in mathematical reasoning show the significance of the chosen representation in the process of solving problems. The way of modelling during solving story problems tasks can contribute to (or prevent) development of relating understanding of the procedures of their solving. The aim of this research is the analysis of methods and strategies, which students use in the end of the first cycle of education when solving story problems. Research of the ways in which students present information in the process of task solving is particularly stressed. Results of the research show that students, in the process of solving story problems use exclusively symbolic representations of problems and this leads to conclusion that tasks which cannot be solved by direct methods, cannot be solved by students at all. Even though numerous kinds of research point at the significance of using different models when solving story problems, our results show that students, instead of transmitting problems to the less abstract level, they transmit them to the abstract form and this is above their perceptive ability. One of the solutions for overcoming the stated problem is defining operational tasks and contents referring to modelling and different strategies of solving story problems in the curriculum for initial teaching.

Key words: story problems, modelling, methods, strategies of solving tasks.

Литература:

• Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Exploring the impact of early algebra learning and teachers’ beliefs. Journal of Mathematical Behavior, 23, 135–167. Dejić, M. i Egerić, M. (2007). Metodika nastave matematike. Beograd: Učiteljski fakultet.
• Di Sessa, A. A. (2002). Students’ criteria for representational adequacy. In: Gravemeijer, K., Lehrer, R., Van Oers, B. and Verschaffel, L. (Eds.). Symbolizing, modelling and tool use in mathematics education (105–130). Dordrecht, The Netherlands: Kluwer Academic Publishers.
• Dufour-Janvier, B., Bednarz, N. and Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In: Janvier, C. (Ed.). Problems of representation in the teaching and learning of mathematics (109–122). Hillsdale, NJ: Lawrence Erlbaum Associates Publishers.
• Еnglish, L. (2009). Promoting interdisciplinarity through mathematical modelling. The International Journal
  on Mathematics Education, 41, (1–2), 161–181. Gagatsis, A. and Elia, I. (2004). The effects of different modes of representations on mathematical problem solving. In: Johnsen-Hoines, M. and Berit-Fuglestad, A. (Eds.). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (447–454). Bergen, Norway: Bergen
  University College.
• Gilbert, J. K., Boulter, C. J. and Elmer, R. (2000). Positioning models in science education and in design and technology education. In: Gilbert, J. K. and Boulter, C. J. (Eds.). Developing models in science education (3–18). Dordrecht: Kluwer Academic Publishers.
• Gortcheva, I. G. (2014). Mathematical and cultural messages from the period between the two world wars: Elin Pelin’s story problems. In: Lawrence, S. & Djokic, O. (Eds.). Special Issue of Journal Teaching Innovations „History of Mathematics in Education and History of Mathematics Education – Mathematical Education Cul tures“, Vol. 27, No. 3, 94–104. Retrived from the World Wide Web March 21st 2015: http://www.uf.bg.ac.rs/wp-content/uploads/2015/01/INOVACIJE-3_14.pdf .
• Gravemeijer, K., Lehrer, R., Van Oers, B. аnd Verschaffel, L. (Eds.) (2003). Symbolizing, modelling and tool use in mathematics education (105–130). Dordrecht, The Netherlands: Kluwer Academic Publishers.
• Kaminski, J. A., Sloutsky, V. M. and Heckler, A. F. (2008). The advantage of abstract examples in learning math. Science, 320, 454–455.
• Kieran, C. (1992). The learning and teaching of school algebra. In: Grouws, D. A. (Ed.). Handbook of research on mathematics teaching and learning (390–419). New York: Macmillan.
• Kieran, C. (2006). Research on the learning and teaching of algebra. In: Gutiérrez, A. and Boero, P. (Eds.). Handbook of research on the psychology of mathematics education (11–50). Rotterdam: Sense.
• Koedinger, K. R., Alibali, M. W. and Nathan, M. J. (2008). Trade-offs between grounded and abstracter presentations: Evidence from algebra problem solving. Cognitive Science, 32, 366–397.
• Lesh, R., Post, T. and Behr, M. (1987). Dienes revisited: Multiple embodiments in computer environments. In: Wirszup, I. and Streit, R. (Eds.). Developments in school mathematics education aroun dthe world (647–680). Reston, VA: National Council of Teachers of Mathematics.
• Mason. J. (1996). Expressing Generality and Roots of Algebra. In: Bednarz, N., Kieran, C. and Lee, L. (Eds.). Approach esto Algebra (65–111). Dordrecht/Boston/London: Kluwer academic Publishers.
• Novotná, J. (1997). Phenomena Discovered in the Process of Solving Word Problems. In: Hejny, M. and Novotná, J. (Eds.). Proceedings ERCME 97 (105–109). Praha: Prometheus.
• Novotná, J. and Rogers, L. (2003). Word Problems: A Framework for Understanding. In: Rogers, L. and Novotná, J. (Eds.). Analysis and Teaching. Classroom Contexts. Effective Learning and Teaching of Mathematics from Primary to Secondary School (79–96). Bologna: Pitagora Editrice.
• Novotná, J. and Sarrazy, B. (2005). Model of a professor’s didactical action in mathematics education: professor’s variability and students’ algorithmic flexibility in solving arithmetical problems. In: Drouhard, J. P (Ed.). The Fourth Congress of the European Society in Mathematics Education (696–705). Retrieved May 25, 2014. from: http: //www. cerme 4.crm.es.
• Polya, G. (1966). Kako ću riješiti matematički zadatak. Zagreb: Školska knjiga.
• Presmeg, N. C. (1992). Prototypes, Metaphors, Metonymies and Imaginative Rationality in High School Mathematics. Educational Studies in Mathematics, 23, 595–610.
• Reusser, K. (1989). Textual and situational factors in solving mathematical word problems. Bern: Universität Bern.
• Terwel, J., Van Oersa, B., Van Dijka, I. and Vanden Eeden, P. (2009). Are representations to be provided or generated in primary mathematics education? Effects on transfer. Educational Research and Evaluation, 15 (1), 25–44.
• Verschaffel, L., Greer, B. and De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.
• Zeljić, M. (2014). Metodički aspekti rane algebre. Beograd: Učiteljski fakultet.
• Zeljić, M. i Dabić, M. (2014). Iconic Represention as Student’s Success Factor in Algebraic Generalisation. Journal Plus Education, 1, 173–184.