AN INVESTIGATION OF FAILURE SOLVING ILL-STRUCTURED PROBLEMS: A CASE STUDY

Authors

  • Ninik Mutianingsih Universitas PGRI Adi Buana Surabaya
  • Lydia Lia Prayitno
  • Eko Sugandi
  • Sri Rahmawati Fitriatien
  • Agus Prasetyo Kurniawan

DOI:

https://doi.org/10.33477/mp.v8i2.1390

Keywords:

Rectangle, concept, failure

Abstract

63 students were involved in the study and elected Rizka as the subject of research. This is a case study aimed at describing the cause of Rizka's failure in solving ill-structured problems about the rectangle. The results showed that the subject was able to represent the problem with own language. Rizka failed to build a solution that corresponds to the problem due to partial mastery of the rectangular concept. Rizka uses trial and error because it fails to associate a problem with a square concept that is the key to problem-solving success. Rizka success in the justification process because the process is counting without giving meaning. Meanwhile, the monitoring and evaluation process carried out by Rizka has failed. Rizka confusion determines the final solution because the solution is built does not qualify the problem solution. This is where the Rizka fails to provide the final solution. In this case, teachers have a role to teach their students to build relationships between concepts that can be utilized in problem-solving.

References

Abdillah, Nusantara, T., Subanji, Susanto, H., & Abadyo. (2016). The Students Decision Making in Solving Discount Problem. International Education Studies, 9(7), 57–63. https://doi.org/10.5539/ies.v9n7p57

Adanan, H., Adanan, M., & Herawan, T. (2020). M-WebQuest Development : Reading Comprehension of Senior High School Students in Indonesia. International Journal of Emerging Technologies in Learning, 15(3), 74–92. Retrieved from https://doi.org/10.3991/ijet.v15i03.10628

Anwar, R. B., Yuwono, I., As’ari, A. R., Sisworo, & Rahmawati, D. (2016). Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Primeter of Rectangle. Educational Research and Reviewsv, 11(21), 2002–2008. https://doi.org/10.5897/ERR2016.2813

Avdiji, H., Elikan, D., Missonier, S., & Pigneur, Y. (2018). Designing Tools for Collectively Solving Ill-Structured Problems. Proceedings of the 51st Hawaii International Conference on System Sciences, (January). https://doi.org/10.24251/hicss.2018.053

Bal, A. P. (2014). The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems. Educational Sciences: Theory & Practice, 14(6), 2349–2365. https://doi.org/10.12738/estp.2014.6.2189

Boonen, A. J. H., Reed, H. C., Schoonenboom, J., & Jolles, J. (2016). It’s Not a Math Lesson - We’re Learning to Draw ! Teachers’ Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School. Frontline Learning Research, 4(5), 55–82. https://doi.org/http://dx.doi.org/10.14786/flr.v4i5.245

Chi, M. T. H. H., & Glaser, R. (1985). Problem Solving Abilities. Human Abilities: An Information Processing Approach. Washington DC. Retrieved from http://eric.ed.gov/?id=ED257630%5Cnfile:///Users/jessicabartley/Downloads/ADA134717.pdf%5Cnhttp://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA134717

Debrenti, E. (2015). Visual Representations in Mathematics Teaching: An Experiment with Students. Acta Didactica Napocensia, 8(1), 19–26. Retrieved from eric.ed.gov

Ge, X., & Land, S. (2003). Scaffolding students’ problem solving processes in an ill-structured task using question prompts and peer interactions. Educational Technology Research and Development, 51(1), 21–38. Retrieved from http://dx.doi.org/10.1007/BF02504515

Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137–165. https://doi.org/10.1016/S0364-0213(99)80056-1

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of Arithmetic Word Problems : A Comparison of Successful and Unsuccessful Problem Solvers inconsistent problems with those of problem solvers who do. Journal of Educational Psychology, 87(1), 18–32.

Hong, J., & Kim, M. (2016). Mathematical abstraction in the solving of ill-structured problems by elementary school students in Korea. Eurasia Journal of Mathematics, Science and Technology Education, 12(2), 267–281. https://doi.org/10.12973/eurasia.2016.1204a

Hong, N. S. (1998). The Relationship Between Well-Structured and Ill-Structured Problem Solving in Multimedia Simulation. The Pennsylvania State University.

Hoogland, K., de Koning, J., Bakker, A., Pepin, B. E. U., & Gravemeijer, K. (2018). Changing representation in contextual mathematical problems from descriptive to depictive: The effect on students’ performance. Studies in Educational Evaluation, 58(November 2017), 122–131. https://doi.org/10.1016/j.stueduc.2018.06.004

Hoogland, K., & Pepin, B. (2016). The Intricacies of Assessing Numeracy : Investigating Alternatives to Word Problems Kees Hoogland. Adults Learning Mathematics: An International Journal, 11(2), 14–26. Retrieved from http://www/researchgate.net/publication/3132332761_The_Intricacies_of_Assessing_Numeracy_Incestigating_Alternatives_to_Word_Problems

Ijirana, & Nadjamuddin, L. (2019). Time series study of problem solving ability of Tadulako University students using metacognitive skill based learning model. International Journal of Emerging Technologies in Learning, 14(21), 227–234. https://doi.org/10.3991/ijet.v14i21.11684

Jonassen, D. (2003). Using Cognitive Tools to Represent Problems. Journal of Research on Technology in Education, 35(October2003), 37–41. https://doi.org/10.1080/15391523.2003.10782391

Jonassen, D. H. (1997). Instructional Design Models for Well-Structured and Ill-Structured Problem-Solving Learning Outcomes. Educational Technology Research and Development, 45(1), 65–94. Retrieved from http://www.jstor.org/stable/30220169

Liang, C., Tsai, S., Chang, T., Lin, Y., & Su, K. (2016). A Meaning-based English Math Word Problem Solver with Understanding , Reasoning and Explanation. In COLING 2016, the 26th International Conference on Computational Linguistic: System Demonstrations (pp. 151–155).

Lim, C. L., Jaya, S., Jalil, H. A., & Saad, W. Z. (2020). Peer Learning, Self-Regulated Learning and Academic Achievement in Blended Learning Courses : A Structural Equation Modeling Approach. International Journal of Emerging Technologies in Learning (IJET), 15(3), 110–125.

Lizunkov, V., Politsinskaya, E., Gazin, K., & Oblast, K. (2020). The Architecture of Project-Based Learning in the Supplementary Vocational Education System in a Higher Education. International Journal of Emerging Technologies in Learning (IJET), 15(4), 227–234. Retrieved from https://doi.org/10.3991/ijet.v15i04.11694

Mairing, J. P. (2017). Thinking Process of Naive Problem Solvers to Solve Mathematical Problems. International Education Studies, 10(1), 1–11. https://doi.org/10.5539/ies.v10n1p1

Merriam, S. (2009). Qualitative Research and Case Study Aplication in Education. San Fransisco: Jossey-Bass.

Miles, M. B., & Huberman, M. A. (1994). Qualitative Data Analysis: A Sourcebook of New Methods. Baverly Hills: SAGE Publications, Inc.

NCTM. (2000). Principles and Standards for School Mathematics. United States of America: The National Council of Teachers of Mathematics Inc. Retrieved from www.nctm.org

Palupi, B. S., Subiyantoro, S., Triyanto, T., & Rukayah, R. (2020). Creative-Thinking Skills in Explanatory Writing Skills Viewed from Learning Behaviour: A Mixed Method Case Study. International Journal of Emerging Technologies in Learning (IJET), 15(01), 200–212. https://doi.org/10.3991/ijet.v15i01.11487

Pape, S. J. (2004). Middle School Children’s Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 35(3), 187–219.

Prayitno, L. L., Purwanto, P., Subanji, S., & Susiswo, S. (2018). Identification Errors of Problem Posed by Prospective Teachers About Fraction Based Meaning Structure. International Journal of Insights for Mathematics Teaching, 01(1), 76–84. Retrieved from http://journal2.um.ac.id/index.php/ijoimt/article/viewFile/3018/1828

Role, T., Skill, F. M., Fuchs, L. S., Gilbert, J. K., Powell, S. R., Cirino, P. T., … Tolar, T. D. (2016). The Role of Cognitive Processand Calculation Accuracy and Fluency in Word-Problem The Role of Cognitive Processes , Foundational Math Skill , and Calculation Accuracy and Fluency in Word-Problem Solving Versus Prealgebraic Knowledge.

Shin, N., Jonassen, D. H., & McGee, S. (2003). Predictors of well-structured and ill-structured problem solving in an astronomy simulation. Journal of Research in Science Teaching, 40(1), 6–33. https://doi.org/10.1002/tea.10058

Stylianou, D. A., & Silver, E. A. (2004). The Role of Visual Representations in Advanced Mathematical Problem Solving : An Examination of Expert- Novice Similarities and Differences. Mathematical Thinking and Learning, 6(4), 353–387. Retrieved from http://sci-hub.tw/10.1207/s15327833mtl0604_1#

Subanji, S., & Nusantara, T. (2016). Thinking Process of Pseudo Construction in Mathematics Concepts. International Education Studies, 9(2), 17. https://doi.org/10.5539/ies.v9n2p17

Sukoriyanto, J., Nusantara, T., Subanji, S., & Chandra, T. D. (2016). Students ’ thinking process in solving combination problems considered from assimilation and accommodation framework. Educational Research and Reviews, 11(16), 1494–1499. https://doi.org/10.5897/ERR2016.2811

Swastika, G. T., Nusantara, T., Subanji, & Irawati, S. (2020). Alteration representation in the Process of Translation Graphic to Graphic. Humanities & Social Sciences Reviews, 8(1), 334–343. https://doi.org/http://doi.org/10/18510/hsr.2020.8144

Xin, Y. P., Jitendra, A. K., & Buchman, A. D. (2005). Effects of Mathematical Word Problem – Solving Instruction on Middle School Students with Learning Problems. The Journal of Special Education, 39(3), 181–192.

Downloads

Published

2020-12-31