Main Article Content

Abstract

This study investigated Grade 10 Namibian learners' problem-solving skills in algebraic word problems. A sample of 351 Grade 10 learners from ten secondary schools in the Ohangwena Region in Namibia participated in this study. The study followed a qualitative approach and adopted Polya's Problem-Solving Model as the framework. The data were collected using the Algebra Word Problem-solving Test and Interview. The findings showed that the learners needed better problem-solving skills in algebraic word problems. Only 6% and 7% of the learners showed an ability to understand the problems and devise a plan, respectively, while only 5% could carry out the plans. Based on the findings, it is recommended that teachers introduce learners to Polya's steps of problem-solving and incorporate word problems into mathematics teaching.

Keywords

Algebraic word problem Polya problem-solving steps Problem-solving Problem-solving skills

Article Details

Author Biographies

Hesekiel K. Iilonga, University of Pretoria

Department of Science, Mathematics & Technology Education

Ugorji I. Ogbonnaya, University of Pretoria

Department of Science, Mathematics & Technology Education

References

  1. Abazov, R. (2016). How to improve your problem-solving skills. QS Top Universities, 1(1), 1-3.

  2. Akyüz, G. (2020). Non-routine problem solving performances of mathematics teacher candidates. Educational Research and Reviews, 15(5), 214-224. https://doi.org/10.5897/ERR2020.3907

  3. Albin, S., & von Watzdorf, A. (2019). A comparative analysis of word problems in six junior primary Mathematics textbooks in Namibia. Journal of Engineering Research and Application, 9(6), 47-55.

  4. Aljaberi, N. M. (2015). University students' learning styles and their ability to solve mathematical problems. International Journal of Business and Social Science, 6(4), 152-165.

  5. Al-Mutawah, M. A., Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual understanding, procedural knowledge and problem-solving skills in mathematics: High school graduates work analysis and standpoints. International journal of education and practice, 7(3), 258-273. https://doi.org/10.18488/journal.61.2019.73.258.273

  6. Berlinghoff, W. P., & Gouvêa, F. Q. (2021). Math through the ages: A gentle history for teachers and others expanded second edition (Vol. 32). American Mathematical Soc.

  7. Brijlall, D. (2015). Exploring the stages of Polya’s problem-solving model during collaborative learning: A case of fractions. International Journal of Educational Sciences, 11(3), 291-299. https://doi.org/10.1080/09751122.2015.11890401

  8. Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. The Journal of Mathematical Behavior, 32(3), 613-632. https://doi.org/10.1016/j.jmathb.2013.07.002

  9. Capraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27(2-3), 147-164. https://doi.org/10.1080/02702710600642467

  10. Chang, B. (2019). Reflection in learning. Online Learning, 23(1), 95-110. https://doi.org/10.24059/olj.v23i1.1447

  11. Charles, R., Lester, F., & O’Daffer, P. (1987). How to evaluate progress in problem solving. National Council of Teachers of Mathematics.

  12. Daulay, K. R., & Ruhaimah, I. (2019). Polya theory to improve problem-solving skills. Journal of Physics: Conference Series, 1188(1), 012070. https://doi.org/10.1088/1742-6596/1188/1/012070

  13. Directorate of National Examinations and Assessment. (2014). Examiners’ reports. DNEA Printers.

  14. Directorate of National Examinations and Assessment. (2015). Examiners’ reports. DNEA Printers.

  15. Directorate of National Examinations and Assessment. (2016). Examiners’ reports. DNEA Printers.

  16. Directorate of National Examinations and Assessment. (2017). Examiners’ reports. DNEA Printers.

  17. Directorate of National Examinations and Assessment. (2018). Examiners’ reports. DNEA Printers.

  18. Ersoy, E. (2016). Problem solving and its teaching in mathematics. The Online Journal of New Horizons in Education, 6(2), 79-87.

  19. Franestian, I. D., Suyanta, S., & Wiyono, A. (2020). Analysis problem solving skills of student in Junior High School. Journal of Physics: Conference Series, 1440(1), 012089. https://doi.org/10.1088/1742-6596/1440/1/012089

  20. Gray, C. A. (2018). The impact of applying the first two steps of Polya’s four problem-solving steps in an advanced mathematics classroom. Doctoral dissertation. University of South Carolina - Columbia. Retrieved from https://scholarcommons.sc.edu/etd/5037

  21. Greer, B., Verschaffel, L., & De Corte, E. (2002). “The Answer is Really 4.5”: Beliefs About Word Problems. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp. 271-292). Springer Netherlands. https://doi.org/10.1007/0-306-47958-3_16

  22. Gunawan, G., Harjono, A., Nisyah, M. a., Kusdiastuti, M., & Herayanti, L. (2020). Improving students' problem-solving skills using inquiry learning model combined with advance organizer. International Journal of Instruction, 13(4), 427-442. https://doi.org/10.29333/iji.2020.13427a

  23. Hendriana, H., Purwasih, R., Triawan, E., Prasetio, Y., & Satria, T. (2018). Analysis of student problem solving skill and activity concentration on a senior high school. Al-Jabar: Jurnal Pendidikan Matematika, 9(1), 1-8. https://doi.org/10.24042/ajpm.v9i1.2068

  24. Hijada Jr, M. V., & Cruz, M. L. D. (2022). The gap between comprehension level and problem-solving skills in learning mathematics. Universal Journal of Educational Research, 1(1), 35-43.

  25. Hooshyar, D., Pedaste, M., Yang, Y., Malva, L., Hwang, G.-J., Wang, M., Lim, H., & Delev, D. (2021). From gaming to computational thinking: An adaptive educational computer game-based learning approach. Journal of Educational Computing Research, 59(3), 383-409. https://doi.org/10.1177/0735633120965919

  26. In'am, A. (2014). The implementation of the Polya method in solving euclidean geometry problems. International Education Studies, 7(7), 149-158. https://doi.org/10.5539/ies.v7n7p149

  27. İncebacak, B. B., & Ersoy, E. (2016). Problem solving skills of secondary school students. China-USA Business Review, 15(6), 275-285. https://doi.org/10.17265/1537-1514/2016.06.002

  28. Jupri, A., & Drijvers, P. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a

  29. Khabibah, S., Manuharawati, M., & Agung, L. (2018). Problem solving ability: A case study in postgraduate mathematics student. In Proceedings of the Mathematics, Informatics, Science, and Education International Conference. https://doi.org/10.2991/miseic-18.2018.54

  30. Kivunja, C. (2015). Exploring the pedagogical meaning and implications of the 4Cs" super skills" for the 21st century through Bruner's 5E lenses of knowledge construction to improve pedagogies of the new learning paradigm. Creative Education. https://doi.org/10.4236/ce.2015.62021

  31. Krawitz, J., Schukajlow, S., & Van Dooren, W. (2018). Unrealistic responses to realistic problems with missing information: what are important barriers? Educational Psychology, 38(10), 1221-1238. https://doi.org/10.1080/01443410.2018.1502413

  32. Kusumadewi, C. A., & Retnawati, H. (2020). Identification of elementary school students’ difficulties in mathematical problem-solving. Journal of Physics: Conference Series, 1511(1), 012031. https://doi.org/10.1088/1742-6596/1511/1/012031

  33. Lee, C. I. (2016). An appropriate prompts system based on the Polya method for mathematical problem-solving. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 893-910. https://doi.org/10.12973/eurasia.2017.00649a

  34. Lubis, J. N., Panjaitan, A., Surya, E., & Syahputra, E. (2017). Analysis mathematical problem solving skills of student of the grade VIII-2 junior high school Bilah Hulu Labuhan Batu. International Journal of Novel Research in Education and Learning, 4(2), 131-137.

  35. Lupahla, N. (2014). Assessing the algebraic problem solving skills of Grade 12 learners in Oshana Region, Namibia. Master’s dissertation. UNISA Institutional Repository. Retrieved from http://hdl.handle.net/10500/19225

  36. Maulyda, M. A., Hidayati, V. R., Rosyidah, A. N. K., & Nurmawanti, I. (2019). Problem-solving ability of primary school teachers based on Polya’s method in Mataram City. Pythagoras, 14(2), 139-149. https://doi.org/10.21831/pg.v14i2.28686

  37. Meutia, C. I., Ikhsan, M., & Saminan, S. (2020). Mathematical problem-solving skills of junior high school students. Journal of Physics: Conference Series, 1460(1), 012010. https://doi.org/10.1088/1742-6596/1460/1/012010

  38. National Institute for Educational Development. (2016). Namibia junior secondary certificate mathematics guide. NIED.

  39. Nikmah, I. L., Juandi, D., & Prabawanto, S. (2019). Students’ difficulties on solving mathematical problem based on ESD objectives. Journal of Physics: Conference Series, 1157(3), 032116. https://doi.org/10.1088/1742-6596/1157/3/032116

  40. Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9-28. https://doi.org/10.1007/s10649-019-09903-9

  41. Nurkaeti, N. (2018). Polya’s strategy: an analysis of mathematical problem solving difficulty in 5th grade elementary school. EduHumaniora: Jurnal Pendidikan Dasar, 10(2), 140-147. https://doi.org/10.17509/eh.v10i2.10868

  42. Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the learning of Mathematics, 26(1), 42-47.

  43. Pentang, J., Ibañez, E. D., Subia, G., Domingo, J. G., Gamit, A. M., & Pascual, L. E. (2021). Problem-solving performance and skills of prospective elementary teachers in Northern Philippines. Hunan Daxue Xuebao, 48(1), 122-132.

  44. Peterson, R. L., Boada, R., McGrath, L. M., Willcutt, E. G., Olson, R. K., & Pennington, B. F. (2017). Cognitive prediction of reading, math, and attention: Shared and unique influences. Journal of Learning Disabilities, 50(4), 408-421. https://doi.org/10.1177/0022219415618500

  45. Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton university press.

  46. Polya, G. (1957). How to solve it: A new aspect of mathematical method. Prentice university press.

  47. Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton university press.

  48. Polya, G. (1981). Mathematical discovery on understanding learning and teaching problem solving. John Wiley and Sons.

  49. Rahman, M. M. (2019). 21st century skill "problem solving": Defining the concept. Asian Journal of Interdisciplinary Research, 2(1), 64-74. https://doi.org/10.34256/ajir1917

  50. Riyadi, R., Syarifah, T. J., & Nikmaturrohmah, P. (2021). Profile of students’ problem-solving skills viewed from Polya's four-steps approach and elementary school students. European Journal of Educational Research, 10(4), 1625-1638. https://doi.org/10.12973/eu-jer.10.4.1625

  51. Schoenfeld, A. H. (2014). Mathematical problem solving. Elsevier.

  52. Sikukumwa, E. (2017). Types of strategies used to solve algebraic word problems by grade 12 ordinary level Mathematics learners of Kavango East region of Namibia. Doctoral dissertation. University of Namibia. Retrieved from http://hdl.handle.net/11070/2023

  53. Sipayung, T. N., & Anzelina, D. (2019). An analysis of students problem solving skills using a realistic mathematics approach on integers materials. Journal of Physics: Conference Series, 1211(1), 012083. https://doi.org/10.1088/1742-6596/1211/1/012083

  54. Steinbrink, G. (2009). Reading mathematic. Math in the Middle Institute Partnership, Action Research Project Report. Master’s dissertation. University of Nebraska-Lincoln.

  55. Sumaryanta, D. (2015). Pedoman Penskoran [Scoring rubric]. Idealmathedu: Indonesian Digital Journal of Mathematics and Education, 2(3), 181-190.

  56. Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia - Social and Behavioral Sciences, 8, 142-151. https://doi.org/10.1016/j.sbspro.2010.12.020

  57. Van Amerom, B. A. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54(1), 63-75. https://doi.org/10.1023/B:EDUC.0000005237.72281.bf

  58. 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.2018.06.008

  59. Wickramasinghe, I., & Valles, J. (2015). Can we use Polya’s method to improve students’ performance in the statistics classes? Numeracy, 8(1), 12. https://doi.org/10.5038/1936-4660.8.1.12

  60. Yayuk, E., & Husamah, H. (2020). The difficulties of prospective elementary school teachers in item problem solving for mathematics: Polya’s steps. Journal for the Education of Gifted Young Scientists, 8(1), 361-378. https://doi.org/10.17478/jegys.665833

  61. Yeh, C. Y. C., Cheng, H. N. H., Chen, Z.-H., Liao, C. C. Y., & Chan, T.-W. (2019). Enhancing achievement and interest in mathematics learning through Math-Island. Research and Practice in Technology Enhanced Learning, 14(1), 1-19. https://doi.org/10.1186/s41039-019-0100-9

  62. Yöyen, E. G., Azakli, A., Üney, R., Demirci, O. O., & Merdan, E. (2017). Ergenlerin kişilik özelliklerinin problem çözme becerisi üzerine etkisi. Doğu Anadolu Sosyal Bilimlerde Eğilimler Dergisi, 1(1), 75-93.