# The Students’ Representative Processes in Solving Mathematical Word Problems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Abdullah, N.; Zakaria, E.; Halim, L. The effect of a thinking strategy approach through visual representation on achievement and conceptual understanding in solving mathematical word-problems. Asian Soc. Sci.
**2012**, 8, 30–37. [Google Scholar] [CrossRef][Green Version] - Cankoy, O.; Özder, H. The influence of visual representations and context on mathematical word problem solving. Pamukkale Univ. J. Educ.
**2011**, 30, 91–100. Available online: http://pauegitimdergi.pau.edu.tr/Makaleler/745832325_91-100.pdf (accessed on 15 July 2022). - Chang, B.L.; Cromley, J.G.; Tran, N. Coordinating multiple representations in a reform calculus textbook. Int. J. Sci. Math. Educ.
**2016**, 14, 1475–1497. [Google Scholar] [CrossRef] - Sajadi, M.; Amiripour, P.; Rostamy-Malkhalifeh, M. The examining mathematical word-problems solving ability under efficient representation aspect. Math. Educ. Trends Res.
**2013**, 2013, 1–11. [Google Scholar] [CrossRef] - Hwang, W.Y.; Chen, N.S.; Dung, J.J.; Yang, Y.L. Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. J. Educ. Technol. Soc.
**2007**, 10, 191–212. Available online: https://www.jstor.org/stable/10.2307/jeductechsoci.10.2.191 (accessed on 15 July 2022). - NCTM. Principles and Standards for School Mathematics; NCTM: Reston, VA, USA, 2000. [Google Scholar]
- Filloy, E.; Rojano, T.; Solares, A. Arithmetic/Algebraic problem-solving and the representation of two unknown quantities. In Proceedings of the International Group for the Psychology of Mathematics Education, 28th, Bergen, Norway, 14–18 July 2004; Volume 2, pp. 391–398. [Google Scholar]
- Stylianou, D.A. Teachers’ conceptions of representation in middle school mathematics. J. Math. Teach. Educ.
**2010**, 13, 325–343. [Google Scholar] [CrossRef] - Crespo, S.M.; Kyriakides, A.O. To draw or not to draw: Exploring children’s drawings for solving mathematics problems. Teach. Child. Math.
**2007**, 14, 118–125. [Google Scholar] [CrossRef] - Boonen, A.J.H.; van der Schoot, M.; van Wesel, F.; de Vries, M.H.; Jolles, J. What underlies successful word problems solving? A path analysis in sixth grade students. Contemp. Educ. Psychol.
**2013**, 38, 271–279. [Google Scholar] [CrossRef] - Özsoy, G. Pre-service teachers’ use of visual representations. Int. Electron. J. Elem. Educ.
**2018**, 11, 49–54. [Google Scholar] [CrossRef][Green Version] - Poch, A.L.; van Garderen, D.; Scheuermann, A.M. Students’ understanding of diagrams for solving word-problems: A framework for assessing diagram proficiency. Teach. Except. Child.
**2015**, 47, 153–162. [Google Scholar] [CrossRef] - Boonen, A.J.H.; Van Wesel, F.; Jolles, J.; Van der Schoot, M. The role of visual representation type, spatial ability, and reading comprehension in word-problems solving: An item-level analysis in elementary school children. Int. J. Educ. Res.
**2014**, 68, 15–26. [Google Scholar] [CrossRef] - Rahmah, F.; Irawati, S. Mathematical representation analysis of students in solving mathematics problems. J. Phys. Conf. Ser.
**2019**, 1200, 012011. [Google Scholar] [CrossRef] - Cromley, J.G.; Booth, J.L.; Wills, T.W.; Chang, B.L.; Tran, N.; Madeja, M.; Zahner, W. Relation of spatial skills to calculus proficiency: A brief report. Math. Think. Learn.
**2017**, 19, 55–68. [Google Scholar] [CrossRef] - Hackenberg, A.J. Students’ reasoning with reversible multiplicative relationships. Cogn. Instr.
**2010**, 28, 383–432. [Google Scholar] [CrossRef] - Ramful, A. Reversible reasoning in fractional situations: Theorems-in-action and constraints. J. Math. Behav.
**2014**, 33, 119–130. [Google Scholar] [CrossRef] - Beckmann, S.; Izsák, A. Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. J. Res. Math. Educ.
**2015**, 46, 17–38. [Google Scholar] [CrossRef] - As’ ari, A.R.; Kurniati, D. Teachers expectation of students’ thinking processes in written works: A survey of teachers’ readiness in making thinking visible. J. Math. Educ.
**2019**, 10, 409–424. [Google Scholar] [CrossRef][Green Version] - Sari, F.; Sa’dijah, C.; Nengah, P.; Rahardjo, S. Looking without seeing: The role of meta-cognitive blindness of student with high math anxiety. Int. J. Cogn. Res. Sci. Eng. Educ.
**2019**, 7, 53–65. [Google Scholar] [CrossRef][Green Version] - Gagne, E.D. The Cognitive Psychology of School Learning; Little, Brown and Company: Boston, UK, 1985. [Google Scholar]
- Mayer, R.E. Thinking, Problem Solving, Cognition; W. H. Freeman and Company: New York, NY, USA, 1992. [Google Scholar]
- Kaur, B.; Ban-har, Y.; Kapur, M. Mathematical Problem Solving: Yearbook 2009, Association of Mathematics Educators; World Scientific Publishing: Singapore, 2009. [Google Scholar]
- Yeap, B.H. Mathematical Problem Posing in Singapore Primary Schools, Yearbook 2009, Association of Mathematics Educators; World Scientific Publishing: Singapore, 2009. [Google Scholar]
- Creswell, J.W.; Creswell, J.D. Research Design: Qualitative, Quantitative, and Mixed Methods Approaches; Sage Publications: London, UK, 2017. [Google Scholar]
- Hegarty, M.; Mayer, R.E.; Monk, C.A. Comprehension of arithmetic word-problems: A comparison of successful and unsuccessful problem solvers. J. Educ. Psychol.
**1995**, 87, 18–32. [Google Scholar] [CrossRef] - Nunes, T.; Bryant, P.; Watson, A. Key Understandings in Mathematics Learning: A Report to the Nuffield Foundation; Nuffield Foundation: London, UK, 2009. [Google Scholar]
- Hegarty, M.; Mayer, R.E.; Green, C.E. Comprehension of arithmetic word problems: Evidence from students’ eye fixations. J. Educ. Psychol.
**1992**, 84, 76–84. [Google Scholar] [CrossRef] - Barrios, F.M.G.; Martínez, E.C. Diagrams produced by secondary students in multiplicative comparison word problems. J. Math. Syst. Sci.
**2014**, 4, 83–92. Available online: https://www.davidpublisher.com/Public/uploads/file/20150318/20150318111621_73932.pdf#page=18 (accessed on 15 July 2022). - Swartz, R.J.; Perkins, D.N. Teaching Thinking: Issues Approaches; Routledge: London, UK, 1990. [Google Scholar] [CrossRef]
- Dindyal, J.; Tay, E.G.; Toh, T.L.; Leong, Y.H.; Quek, K.S. Mathematical problem solving for everyone: A new beginning. Math. Educ.
**2012**, 13, 1–20. Available online: http://math.nie.edu.sg/ame/matheduc/tme/tmeV13_2/1.pdf (accessed on 15 July 2022). - Kirkwood, M.J. Learning to Think, Thinking to Learn: An Introduction to Thinking Skills from Nursery to Secondary. Continuing Professional Development in Education; Hodder Gibson: Paisley, UK, 2005. [Google Scholar]
- Bednarz, N.; Dufour-Janvier, B. The emergence and development of algebra in a problem-solving context: A problem analysis. In Proceedings of the 18th Conference of the International group for the psychology of Mathematics Education, Lisbon, Portugal, 29 July–3 August 1994; Volume 2, pp. 64–71. [Google Scholar]
- Duval, R.A. Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educ. Stud. Math.
**2006**, 61, 103–131. [Google Scholar] [CrossRef] - Smith, F.; Hardman, F.; Higgins, S. The impact of IWBs on teacher–pupil interaction in the National Literacy and Numeracy Strategies. Br. Educ. Res. J.
**2006**, 32, 443–457. [Google Scholar] [CrossRef] - Smith, F.; Hardman, F.; Wall, K.; Mroz, M. Interactive whole class teaching in the National Literacy and Numeracy Strategies. Br. Educ. Res. J.
**2004**, 30, 395–411. [Google Scholar] [CrossRef] - Beard, R. Research and the national literacy strategy. Oxf. Rev. Educ.
**2000**, 26, 421–436. [Google Scholar] [CrossRef]

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nasrun; Prahmana, R.C.I.; Akib, I.
The Students’ Representative Processes in Solving Mathematical Word Problems. *Knowledge* **2023**, *3*, 70-79.
https://doi.org/10.3390/knowledge3010006

**AMA Style**

Nasrun, Prahmana RCI, Akib I.
The Students’ Representative Processes in Solving Mathematical Word Problems. *Knowledge*. 2023; 3(1):70-79.
https://doi.org/10.3390/knowledge3010006

**Chicago/Turabian Style**

Nasrun, Rully Charitas Indra Prahmana, and Irwan Akib.
2023. "The Students’ Representative Processes in Solving Mathematical Word Problems" *Knowledge* 3, no. 1: 70-79.
https://doi.org/10.3390/knowledge3010006