Strategies of Math Teachers for Converting Standard Word Problems into Interpretive Word Problems

Document Type : Research Paper

Authors

1 Associate Professor, Department of Mathematics Education, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. & Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, Iran

2 PhD student, Department of Mathematics Education, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. & Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

Solving applied mathematical problems is one of the educational goals of many countries. In the Iranian national curriculum document, in the section related to mathematics, "the ability to solve every day and abstract problems" and "mathematical modeling" are stated as among the basic goals of the mathematics education program. In this regard, interpretive word problems consider as an good exercise for mathematical modeling. In the present study, after reviewing the research literature on modeling and interpretive word problems, the results of the analysis of 75 mathematics teachers who participated in two webinars will be presented. These webinars were planned in the form of workshops, and the participants in the meetings collaborated in groups on their ideas. The results of the study on the problems rewritten by the participants showed that half of the groups give information that were unrelated to the problem and proposed problems without answers. 26.6% of the problems were designed in such a way that the mathematical answer was different according to realistic considerations, and 26.6% of the problems were solvable and had a numerical answer. This analysis showed that the most added elements (55.3%) are related to the descriptive information of the problem situation.

Keywords

References

Dewolf, T., Van Dooren, W., & Verschaffel, L. (2016). Can visual aids in representational illustrations help pupils to solve mathematical word problems more realistically? European Journal of Psychology of Education, 32, 335-351. https://doi.org/10.1007/s10212-016-0308-7
Dewolf, T., Van Dooren, W., Ev Cimen, E., & Verschaffel, L. (2014). The impact of illustrations and warnings on solving mathematical word problems realistically. Journal of Experimental Education, 82, 103–120. https://doi.org/10.1080/00220973.2012.745468
Dewolf, T., Van Dooren, W., Hermens, F., & Verschaffel, L. (2015). Do students attend to representational illustrations of nonstandard mathematical word problems, and, if so, how helpful are they? Instructional Science, 43, 147–3171. https://doi.org/10.1007/s11251-014-9332-7
Dorri, M. & Rafipour, A. (2015). Ignoring common sense in solving mathematical verbal problems: The role of originality, Proceedings of the National Conference on Elementary Education and Honoring Professor Gholamhossein Shokoohi, 575-586. Birjand. Iran [In Persian].
Faramarzpour Darzini, N., & Rafipour, A. (2013). What do the unwritten rules say about the age of the captain? Mathematics Education Development, 30, 4-9 [In Persian].
Flick, U. (2008). An Introduction to Qualitative Research (translated by Hadi Jalili). Tehran, Ni. (Original publication date: 1956) [In Persian].
Gooya, Z. (2011). The evolution and formation of Iranian school mathematics curricula. Mathematics Education Development, 28(4), 4-12. [In Persian].
Greer, B., Verschaffel, L., & De Corte, E. (2003). The answer is really 4.5: Beliefs about word problems. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 271–292). Dordrecht: Kluwer Academic Publishers.
Greer, B., Verschaffel, L., Mukhopadhyay, S. (2007). Modelling for Life: Mathematics and Children’s Experience. In: Blum, W., Galbraith, P.L., Henn, HW., Niss, M. (Eds.) Modelling and Applications in Mathematics Education. New ICMI Study Series, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-29822-1_7
Inoue, N. (2005). The realistic reasons behind unrealistic solutions: the role of interpretive activity in word problem solving. Learning and Instruction, 15, 69–83. https://doi.org/10.1016/j.learninstruc.2004.12.004
Karimianzadeh, A. & Rafipour, A. (2012). Ignoring common sense in solving real-world problems. Mathematics Education Development, 29, 37-44. [In Persian]
Khazaei, Z. & Rafipour, A. (2017). Students' involvement in playing mathematical word problems; ignoring common sense, 9th National Mathematics Conference of Payam Noor University of Kerman.  [In Persian]
Koç, D., & Elçi, A. N. (2022). The effect of mathematical modeling instruction on pre-service primary school teachers’ problem solving skills and attitudes towards mathematics. Journal of Pedagogical Research, 6(4), 111–129. https://doi.org/10.33902/JPR.202217783
Mellone M., Verschaffel, L., & Van Dooren, V. (2017) The effect of rewording and dyadic interaction on realistic reasoning in solving word problems. Journal of Mathematical Behavior, 46,1-12. https://doi.org/10.1016/j.jmathb.2017.02.002
Supreme Council of Education (2012). National Curriculum of the Islamic Republic of Iran. Tehran: Secretariat of the Supreme Council of Education.
Van Dooren, W., Lem, S., De Wortelaer, H., & Verschaffel, L. (2019). Improving realistic word problem solving by using humor. The Journal of Mathematical Behavior, 53, 96-104. https://doi.org/10.1016/j.jmathb.2018.10.004
Verschaffel, L., De Corte, B., & Greer, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.
Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real world knowledge in mathematical modelling of school word problems. Learning and Instruction, 4, 339–359. https://doi.org/10.1016/S0959-4752(97)00008-X
Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction, 4, 273–294. https://doi.org/10.1016/0959-4752(94)90002-7
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52, 1-16. https://doi.org/10.1007/s11858-020-02203-x
Verschaffel, L., Van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling. Journal für Mathematik-Didaktik, 31(1), 9-29. https://doi.org/10.1007/s13138-010-0001-2
Vicente, S., Orrantia, J., & Verschaffel, L. (2007). Influence of situational and conceptual rewording on word problem solving. British Journal of Educational Psychology, 77, 829–848. https://doi.org/10.1348/000709907X178200
Vos, P. (2011). What Is ‘Authentic’ in the Teaching and Learning of Mathematical Modelling? Trends in Teaching and Learning of Mathematical Modelling, International Perspectives on the Teaching and Learning of Mathematical Modelling, ICTMA14, 713-722. https://doi.org/10.1007/978-94-007-0910-2_68
Wisenöcker, A. S., Binder, S., Holzer, M., Valentic, A., Wally, C., & Große, C. S. (2024). Mathematical problems in and out of school: The impact of considering mathematical operations and reality on real-life solutions. European Journal of Psychology of Education, 39(2), 767-783. https://doi.org/10.1007/s10212-023-00734-2
Xin, Z., Lin, C., Zhang, L., & Yan, R. (2007). The performance of Chinese primary school students on realistic arithmetic word problems. Educational Psychology in Practice, 23, 145–159.https://doi.org/10.1080/02667360701320853
Yaftian, N., & Ebrahimi Aloveicheh, M. (2019). The Trend of Changes in School Curriculum and Mathematics Textbooks in Iran with Emphasis on Secondary Courses. Mathematical Culture and Thought, 39(67), 60-41 [In Persian].
https://dorl.net/dor/20.1001.1.10226443.1399.39.67.4.9

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