Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models

Yılmaz Aksoy; İbrahim Bayazit; S. Merve Kırnap Dönmez

doi:10.12973/eurasia.2015.1442a

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Yılmaz Aksoy ¹ ^* , İbrahim Bayazit ¹, S. Merve Kırnap Dönmez ¹

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¹ Erciyes University, TURKEY^* Corresponding Author

Abstract

This study investigates approaches, strategies and models used by prospective primary school teachers in responding to real-world problems. The research was carried out with 82 participants. Data were collected through written-exam and semi-structured interviews; and they were analysed using content and discourse analysis methods. Most of the prospective teachers did not pay attention to the realities of the contexts in which the problems are situated. Most of them displayed non-realistic approaches excluding their real world knowledge and experiences from their solutions. Many participants tended to use rules and procedures in a straightforward way leading to failures at interpreting salient aspects of the problem situations. Majority of the participants lacked the ability to use appropriate strategies that could scaffold their realistic considerations. Some constructed models of the situations; nevertheless, many of them lacked the ability to use these instruments as a conceptual tool to identify key aspects of the problem contexts.

Keywords

models
primary education
problem solving strategies
prospective teachers
real-world problems
realistic and non-realistic approaches

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2015, Volume 11, Issue 4, 827-839

https://doi.org/10.12973/eurasia.2015.1442a

Publication date: 16 Nov 2015

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Article Downloads: 895

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References

Arslan, Ç., & Altun, M. (2007). Learning to solve non-routine problems. Elementary Education Online, 6(1), 50-61.
Barnet, J. C., Sowder, L., & Vos, K. E. (1980). Textbook problems: Supplementing and understanding them. In S. Krulik, & R. E. Reys (Eds.), Problem solving in school mathematics: 1980 yearbook (pp. 334-371). Reston, VA: National Council of Teachers of Mathematics.
Blum, W. (1993). Mathematical modelling in mathematics education and instruction. In T. Breiteig, I. Huntley, & G. Kaiser-Messmer (Eds.), Teaching and learning mathematics in context (pp. 3-14). Chichester, UK: Ellis Horwood.
Blum, W., & Ferri, B. (2009). Mathematical modelling: Can it be taught and learned? Journal of Mathematical Modelling and Application, 1(1), 45-58.
Brousseau, G. (1984). The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics. In H. G. Steiner (Ed.), Theory of mathematics education (pp. 110-119). Germany, Bielefeld: IDM.
Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.
Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45-75.
Carpenter, T. P., Lindquist, M. M., Mathews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652-659.
Chacko, I. (2004). Solution of real-world and standard problems by primary and secondary school students: A Zimbabwean example. African Journal of Research in SMT Education, 8(2), 91-103
Cockroft, W. H. (1982). Mathematics count. London, UK: Her Majesty’s Stationary Office.
De Corte, E. (2000). New perspectives for research and practice in mathematics education. Pythagoras, 52, 33-46.
Demetriou, A. (2004). Mind intelligence and development: A cognitive, differential, and developmental theory of intelligence. In A. Demetriou, & A. Raftopoulos (Eds.), Developmental change: Theories, models and measurement (pp. 21-73). Cambridge, UK: Cambridge University Press.
Elia, I., Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in nonroutine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605-618
Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Gingsburg, H. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 57-64.
Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. Utrecht, The Netherlands: CD-B Press/ Freudenthal Institute.
Greca, I. M., & Moreira, M. A. (2002). Mental, physical, and mathematical models in the teaching and learning of physics. Science Education, 1, 106-121.
Greer, B. (1993). The mathematical modelling perspective on world problems. Journal of Mathematical Behaviour, 12, 239-250.
Hartman, H. J. (1998). Metacognition in teaching and learning: An introduction. Instructional Science, 26, 1-3.
Inoue, N. (2005). The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving. Learning and Instruction, 15, 69-83.
Jonassen, J. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63–85.
Krulick, S., & Rudnick, J. A. (1985). Developing problem solving skills. Mathematics Teacher, 79(9), 685-692.
Lesh, R., & Harel, G. (2003). Problem solving, modelling and conceptual development. Mathematical Thinking and Learning, 5(2), 157-189.
Mahlios, J. (1988). Word problems: Do I add or subtract. Arithmetic Teacher, 36(3), 48-52.
Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematical problems. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 29-53). Mahwah, NJ: Lawrence Erlbaum.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. London, UK: Sage Publications.
Nancarrow, M. (2004). Exploration of metacognition and non-routine problem based mathematics instruction on undergraduate student problem solving success (Unpublished Doctoral Thesis). The Florida State University, Florida.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Phillips, N., & Hardy, C. (2002). Discourse analysis: Investigating processes of social construction. London, UK: Sage Publications.
Polya, G. (1962). Mathematical discovery. New York, NY: Wiley.
Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton, NJ: Princeton University Press.
Posamentier, A. S., & Krulik, S. (1998). Problem solving strategies for efficient and elegant solutions – A resource for the mathematics teacher (2nd ed.). Thousand Oaks, California: Corwin Press.
Reusser, K., & Stebler, R. (1997). Every word problem has a solution: The social rationality of mathematical modelling in schools. Learning and Instruction, 7(4), 309- 327.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouvs (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York, NY: MacMillan.
Suydam, M. N. (1980). Untangling clues from research on problem solving. In S. Krulik, & R. E. Reys (Eds.), Problem solving in school mathematics: 1980 yearbook (pp. 34- 50). Reston, VA: National Council of Teachers of Mathematics.
Talim ve Terbiye Kurulu Başkanlığı (2009). İlköğretim matematik dersi 1–5. sınıflar öğretim programı ve kılavuzu [Curriculum guidebook for elementary school mathematics course: Grades 1 to 5]. Ankara: Ministry of Education.
Verchaffel, L., De Corte, E., & Borghart, I. (1997). Preservice teachers’ conceptions and beliefs about the realworld knowledge in mathematical modelling of school word problems. Learning and Instruction, 7, 339-359.
Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modelling in the elementary school: A teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28, 577-601.
Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction, 4, 273-294.
Verschaffel, L., De Corte, E., & Vierstraete, H. (1999). Upper elementary school pupils’ difficulties in modelling and solving nonstandard additive word problems involving ordinal numbers. Journal for Research in Mathematics Education, 30(3), 265-285.
Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 3, 335-359.
Yıldırım, S., & Ersozlu Z. N. (2013). The relationship between students’ metacognitive awareness and their solutions to similar types of mathematical problems. Eurasia Journal of Mathematics, Science & Technology Education,9(4), 411-415.
Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). London, UK: Sage Publications.
Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning and Instruction, 7, 329-338.
Zbiek, R. M. (1998). Prospective teaches’ use of computing tools to develop and validate functions as mathematical models. Journal for Research in Mathematics Education, 29(2), 184-201.

How to cite this article

APA

Aksoy, Y., Bayazit, İ., & Dönmez, S. M. K. (2015). Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), 827-839. https://doi.org/10.12973/eurasia.2015.1442a

Vancouver

Aksoy Y, Bayazit İ, Dönmez SMK. Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models. EURASIA J Math Sci Tech Ed. 2015;11(4):827-39. https://doi.org/10.12973/eurasia.2015.1442a

AMA

Aksoy Y, Bayazit İ, Dönmez SMK. Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models. EURASIA J Math Sci Tech Ed. 2015;11(4), 827-839. https://doi.org/10.12973/eurasia.2015.1442a

Chicago

Aksoy, Yılmaz, İbrahim Bayazit, and S. Merve Kırnap Dönmez. "Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models". Eurasia Journal of Mathematics, Science and Technology Education 2015 11 no. 4 (2015): 827-839. https://doi.org/10.12973/eurasia.2015.1442a

Harvard

Aksoy, Y., Bayazit, İ., and Dönmez, S. M. K. (2015). Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), pp. 827-839. https://doi.org/10.12973/eurasia.2015.1442a

MLA

Aksoy, Yılmaz et al. "Prospective Primary School Teachers’ Proficiencies in Solving Real-World Problems: Approaches, Strategies and Models". Eurasia Journal of Mathematics, Science and Technology Education, vol. 11, no. 4, 2015, pp. 827-839. https://doi.org/10.12973/eurasia.2015.1442a