Маријана Ж. Зељић, Универзитет у Београду, Учитељски факултет, Београд, Србија, имејл: marijana.zeljic@uf.bg.ac.rs
Милана M. Дабић Боричић, Универзитет у Београду, Учитељски факултет, Београд, Србија
Светлана М. Илић, Универзитет у Београду, Учитељски факултет, Београд, Србија
Иновације у настави, XXXVI, 2023/1, стр. 117–132

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DOI: 10.5937/inovacije2301117Z

Резиме: У раду се испитује разумевање релационе терминологије и постигнућа ученика при решавању задатака поређења, а који су у постојећој литератури идентификовани као најтежи међу задацима са једном рачунском операцијом. Претходна истраживања проширујемо, бавећи се испитивањем постигнућа на сложенијим задацима, у којима су проблеми поређења потпроблеми у оквиру проблема комбиновања; испитивањем постигнућа на задацима са два поређења и испитивањем ефекта конзистентности на задацима различите семантичке структуре. Резултати истраживања показују да је ефекат конзи-стентности, који се огледа у коришћењу погрешне операције услед неразумевања релационе терминологије, био доминантан проблем ученицима при решавању задатака поређења. Број поређења у задатку и семантичка структура проблема нису се показали као значајни фактори који утичу на успешност ученика. Даље, постојање умерене повезаности између конзистентних и неконзистентних формулација постоји само на задацима сложеније структуре. Ови резултати упућују да се тек на задацима сложеније структуре може испитивати да ли ученици испољавају дубље разумевање задатака поређења. Концептуално разумевање проблема поређења изграђује се кроз разумевање релација веће – мање и коришћење задатака различитих семантичких структура и сложености.

Кључне речи: текстуални задаци, задаци поређења, релације поређења, конзистентност језика

Summary: The paper examines students’ understanding of relational terminology and their achievement in solving comparison tasks identified in the existing literature as the most difficult among the tasks with a single calculation operation. We expand previous research by examining achievement on more complex tasks in which comparison problems are subproblems within the combining problem;
by examining students’ achievement on tasks with two comparisons, and examining the effect of consistency on the tasks of different semantic structure. The research results indicate that the consistency effect, which is reflected in the use of the wrong operation due to the misunderstanding of the relational terminology, was the dominant problem for students when solving comparison tasks. The number of comparisons in the task, as well as the semantic structure of the problem, did not prove to be significant factors affecting students’ success. In addition, the existence of a moderate connection between consistent and inconsistent formulations exists only on tasks with a more complex structure. The results indicate that it is possible only on the tasks with a more complex structure to determine whether students demonstrate a deeper understanding of the comparison tasks. Conceptual understanding of comparison problems is built through understanding more/less relations and the use of the tasks of different semantic structures and complexity.

Keywords: textual tasks, comparison tasks, comparison relations, language consistency

Литература

• Boesen, J., Helenius, O., Lithner, J., Bergqvist, E., Bergqvist, T., Palm, T. & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. Journal of Mathematical Behavior. 33 (1), 72–87.
• Boonen, A. J. H. & Jolles, J. (2015). Second Grade Elementary School Students’ Differing Performance on Combine, Change and Compare Word Problems. International Journal School and Cognitive Psychology. 2 (122), Article 2.
• Boonen, A. J. H., de Koning, B. B., Jolles, J. and Van der Schoot, M. (2016). Word problem solving in contemporary math education: A plea for reading comprehension skills training. Frontiers in Psychology. 7, Article 191.
• Briars, D. J. & Larkin, J. H. (1984). An integrated model of skill in solving elementary word problems. Cognition and Instruction. 1 (3), 245–296.
• Carpenter, T. P & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grade one through three. Journal of Research in Mathematics Education. 15 (3), 179–202.
• Carpenter, T. P., Hiebert, J. & Moser, J. M. (1983). The effect of instruction on children’s solutions of addition and subtraction word problems. Educational Studies in Mathematics. 14 (1), 55–72.
• Cummins, D. (1991). Children’s interpretation of arithmetic word problems. Cognition and Instruction. 8 (3), 261–289.
• Cummins, D., Kintsch, W., Reusser, K. & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology. 20 (4), 405–438.
• De Corte, E., Verschaffel, L. & Pauwels, A. (1990). Influence of the semantic structure of word problems on second graders’ eye movements. Journal of Educational Psychology. 82 (2), 359–365.
• De Koning, B. B., Boonen, A. J. H. & Van der Schoot, M. (2017). The consistency effect in word problem solving is effectively reduced through verbal instruction. Contemporary Educational Psychology. 49, 121–129.
• Daroczy, G., Wolska, M., Meurers, W. D. & Nuerk, H. C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, Article 348.
• Hegarty, M., Mayer, R. E. & Green, C. E. (1992). Comprehension of arithmetic word problems: Evidence from students’ eye fixations. Journal of Educational Psychology. 84 (1), 76–84.
• Hegarty, M., Mayer, R. E. & Monk, C. A (1995). Comprehension of Arithmetic Word Problems: A Comparison of Successful and Unsuccessful Problem Solvers. Journal of Educational Psychology. 87 (1), 18–32.
• Koedinger, K. R. & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. Journal of the Learning Sciences. 13 (2), 129–164.
• Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology. 81 (4), 521–531.
• Lewis, A. and Mayer, R. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology. 79 (4), 199–216.
• Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics. 67 (3), 255–276.
• Littlefield, J. & Rieser, J. J. (1993). Semantic features of similarity and children’s strategies for identification of relevant information in mathematical story problems. Cognition and Instruction. 11 (2), 133–188.
• Morales, R. V., Shute, V. J. & Pellegrino, J. M. (1985). Developmental differences in understanding and solving simple word problems. Cognition and Instruction. 2 (1), 41–57.
• Mwangi, W. & Sweller, J. (1998). Learning to solve compare word problems: The effect of example format and generating self-explanations. Cognition and Instruction. 16 (2), 173–199.
• Nesher, P., Greeno, J. G. & Riley, M. S. (1982). The Development of Semantic Categories for Addition and Subtraction. Educational Studies in Mathematics. 13 (4), 373–394.
• Obradović, D., Zeljić, M. (2015). Metode i strategije rešavanja tekstualnih zadataka u nastavi matematike. Inovacije u nastavi. 28 (1), 69–81.
• Okamoto, Y. (1996). Modelling children’s understanding of quantitative relations in texts: A developmental perspectives. Cognition and Instruction. 14 (4), 409–440.
• Okamoto, Y., & Case, R. (1996). Exploring the microstructure of children’s central conceptual structures in the domain of number. Monographs of the Society for research in Child Development. 61 (1–2), 27–58.
• Pape, S. J. (2003). Compare word problems: Consistency hypothesis revisited. Contemporary Educational Psychology. 28 (3), 396–421.
• Resnick, L. B. (1983). A developmental theory of number understanding. In: Ginsburg, H. P. (Ed.). The development of mathematical thinking (109–151). New York: Academic.
• Riley, M. S. & Greeno, J. G. (1988). Developmental analysis of language about quantities and of solving problems. Cognition and Instruction. 5 (1), 49–101.
• Riley, M. S., Greeno, J. G. & Heller, J. H. (1983). Development of children’s problem solving ability in arithmetic. In: Ginsburg, H. P. (Ed.). The development of mathematical thinking (109–151). New York: Academic Press.
• Schumacher, R. F. & Fuchs, L. S. (2012). Does understanding relational terminology mediate effects of intervention on compare word problem? Journal of Experimental Child Psychology. 111 (4), 607–628.
• Stern, E. (1993). What makes certain arithmetic word problems involving the comparison of sets so difficult for children. Journal of Educational Psychology. 85 (1), 7–23.
• Stigler, J. W., Lee, S–Y. & Stevenson, H. W. (1990). Mathematical knowledge of Japanese, Chinese, and American elementary school children. Reston, VA: National Council of Teachers of Mathematics.
• Van der Schoot, M., Bakker Arkema, A. H., Horsley, T. M. & Van Lieshout, E. D. C. M. (2009). The consistency effect depends on markedness in less successful but not successful problem solvers: An eye movement study in primary school children. Contemporary Educational Psychology. 34 (1), 58–66.
• Verschaffel, L. (1994). Using retelling data to study elementary school children’s representations and solutions of compare problems. Journal of Research in Mathematics Education. 25 (2), 141–165.
• Verschaffel, L., De Corte, E. & Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer’s consistency hypothesis. Journal of Educational Psychology. 84 (1), 85–94.
• Vicente, S., Orrantia, J. & Verschaffel, L. (2007) Influence of situational and conceptual rewording on word problem solving. British Journal of Educational Psychology. 77 (4), 829–848.
• Willis, G. B. & Fuson, K. C. (1988). Teaching children to use schematic drawings to solve addition and subtraction word problems. Journal of Educational Psychology, 80 (2), 192–201.