Volume 2, Issue 1, No.3 PDF DOWNLOAD
  • Title:
  • Abilities analysis of problem-solving process awareness for elementary school students with different problem-solving performances
  • Author:

    Chia-Hua Hsu

  • Author Affiliation:

    Department of Education, National Chiayi University, Chiayi, Taiwan

  • Received:Apr.21, 2024
  • Accepted:May.15, 2024
  • Published:May.28, 2024
Abstract
Background: Awareness is core ability in problem-solving process, but related performance analysis of problem-solving process awareness for elementary school students is still under study. It is one of the research gaps. This research summarizes problem-solving process awareness dimensions of translation and implementation to study. Former includes recognition and representation, and latter includes strategy and execution, review and check. Objective: According to the results of the literature analysis and research gap, this study aims to explore the problem-solving process awareness ability for elementary school students with different problem-solving performances by utilizing related instruments. Method: This research utilized two instruments of problem-solving process awareness and problem-solving to assess process awareness and problem-solving performances each for elementary school students. There were 389 elementary school students in Chiayi of Taiwan were selected by using stratified and cluster sampling to collect and analyze data. The single-factor multivariate mean test and η 2 effect size value, Roy-Bargman step-down test and simultaneous confidence interval test were carried out. The analysis above which was conducted by SPSS for Windows. Result and conclusion: It is found that there were significant differences in performances of problem-solving process awareness for students with different problem-solving abilities after adequate data analysis. The performances are considerably different in translation and implementation awareness for students with differing word problem solving ability that translation awareness included recognition and representation awareness, and implementation awareness included strategy and execution, review and check awareness. So, conclusion is listed as follows. It is that students with different problem-solving performances have real differences in translation, implementation and overall awareness of problem-solving process corresponding to research problem. 
Keywords

Process awareness in problem-solving, elementary school students, learning.

References

[1] Abdellah, R. (2015). Metacognitive awareness and its relation to academic achievement and teaching performance of pre-service female teachers in Ajman University in UAE. Procedia - Social and Behavioral Sciences, 174, 560-567. http://doi.org/10.1016/j.sbspro.2015.01.707

[2] Adinda, A., Purwanto, P., Parta, I. N., & Chandra, T. D. (2021). Investigation of students’ metacognitive awareness failures about solving absolute value problems in mathematics education. Eurasian Journal of Educational Research, 95(2021), 17-35. https://doi.org/10.14689/ejer.2021.95.2

[3] Bailey, J., & Taylor, M. (2015). Experiencing a mathematical problem-solving teaching approach: Opportunities to identify ambitious teaching practices. Mathematics Teacher Education and Development, 17(2), 111-124. 

[4] Borkowski, J. G. (1992). Metacognitive theory: A framework for teaching literacy, writing, and math skills. Journal of Learning Disabilities, 25(4), 253-257. https://doi.org/10.1177/002221949202500406

[5] Cihanoglu, M. O. (2012). Metacognitive awareness of teacher candidates. Procedia - Social and Behavioral Sciences, 46, 4529-4533. http://doi.org/10.1016/j.sbspro.2012.06.290

[6] Demitra, & Sarjoko. (2018). Effects of handep cooperative learning based on indigenous knowledge on mathematical problem-solving skill. International Journal of Instruction, 11(2), 103-114. https://doi.org/10.12973/iji.2018.1128a 

[7] Fennell, F. M., & Speer, W. R. (2013). Defining mathematics education: Presidential yearbook selections 1926-2012: seventy-fifth yearbook. National Council of Teachers of Mathematics.

[8] Fuson, K. C. (1992). Research on whole number addition and substraction. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 39-48). Macmillan.

[9] Garofalo, J., & Lester, F. K. (1985). Metacogniton, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163-176. https://doi.org/10.2307/748391 

[10] Gul, F., & Shehzad, S. (2012). Relationship between metacognition, goal orientation and academic achievement. Procedia -Social and Behavioral Sciences, 47, 1864-1868. http://doi.org/10.1016/j.sbspro.2012.06.914

[11] Hastuti, I. D., Subanji, T. N., & Susanto, H. (2016). Constructive metacognitive activity shift in mathematical problem solving. Educational Research and Reviews, 11(8), 656-667. https://doi.org/10.5897/ERR2016.2731 

[12] Hsu, W. M., & Tseng, Y. J. (2013). A comparison of algebra content in instructional materials in elementary school mathematic textbooks of Taiwan, Finland and Singapore. Journal of Textbook Research, 6(2), 69-103. 

[13] Hutchinson, N. L. (1992). The challenges of componential analysis: Cognitive and metacognitive instruction in mathematical problem solving. Journal of Learning Disabilities, 25(4), 249-252 & 257. https://doi.org/10.1177/002221949202500405

[14] Jitendra, A. K., Sczesniak, E., Griffin, C. C., & Deatline-Buchman, A. (2007). Mathematical word problem solving in third-grade classrooms. Journal of Educational Research, 100(5), 283-302. https://doi.org/10.3200/JOER.100.5.283-302

[15] Karsli, T. A. (2019). Relation between metacognitive awareness and problem-solving abilities in relation to age and parental educational status. Ekev Academic Review, 23(77), 347-362. 

[16] Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). The role of metacognition in mathematical problem solving: A study of two grade seven classes (Report No. NSF-MDR-85-50346). Bloomington, Indiana University, School of Education, Mathematics Education Development Center. (ERIC Document Reproduction Service No. ED 314 255)

[17] Marcou, A., & Lerman, S. (2006). Towards the development of a self-regulated mathematical problem-solving model. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings 30th conference of the international group for the psychology of mathematics education, 4, 137-144. (ERIC Document Reproduction Service No. ED496934)

[18] Mayer, R. E. (1998). Cognitive, metacognitive and motivational aspects of problem solving. Instructional science, 26(1-2), 49-63. https://doi.org/10.1023/A:1003088013286 

[19] Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of Learning disabilities, 25(4), 230-248. https://doi.org/10.1177/002221949202500404

[20] Montague, M., Warger, C., & Morgan, T. H. (2000). Solve it! strategy instruction to improve mathematical problem solving. Learning Disabilities Research and Practice, 15(2), 110-116. https://doi.org/10.1207/SLDRP1502_7 

[21] Morin, L. L., Watson, S. M. R., Hester, P., & Raver, S. (2017). The use of a bar model drawing to teach word problem solving to students with mathematics difficulties. Learning Disability Quarterly, 40(2), 91-104. https://doi.org/10.1177/0731948717690116 

[22] Mulcahy, C. A., Gagnon, J. C., Atkinson, V. S., & Miller, J. A. (2023). Self-regulated strategy development for algebra problem solving. Teaching Exceptional Children, xx(x), 1-11. https://doi.org/10.1177/00400599231167816

[23] Özcan, Z. Ç. (2016). The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition. International Journal of Mathematical Education in Science and Technology, 47(3), 408-420. https://doi.org/10.1080/0020739X.2015.1080313 

[24] Özcan, Z. Ç., İmamoğlu, Y., & Katmer Bayrakl, V. (2017). Analysis of sixth grade students’think-aloud processes while solving a non-routine mathematical problem. Educational Sciences: Theory & Practice, 17, 129-144. https://doi.org/10.12738/estp.2017.1.2680

[25] Peltier, C., & Vannest, K. J. (2016). Utilizing the STAR strategy to improve the mathematical problem-solving abilities of students with emotional and behavioral disorders. Beyond Behavior, 25(1), 9-15. https://doi.org/10.1177/107429561602500103

[26] Peltier, C., & Vannest, K. J. (2018). The effects of schema-based instruction on the mathematical problem solving of students with emotional and behavioral disorders. Behavioral Disorders, 43 (2), 277-289. https://doi.org/10.1177/0198742917704647

[27] Polya, G. (1957). How to solve it. Princeton University Press.

[28] Powell, S. R. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice (Wiley-Blackwell), 26(2), 94-108. https://doi.org/10.1111%2Fj.1540-5826.2011.00329.x

[29] Sagirli, M. Ö. (2016). A case study on pre-service secondary school mathematics teachers’ cognitive-metacognitive behaviours in mathematical modelling process. Universal Journal of Educational Research, 4(4), 639-663. https://doi.org/10.13189/ujer.2016.040401

[30] Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.). Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 334-370). Macmillan.

[31] Schurter, W. A. (2002). Comprehension monitoring: An aid to mathematical problem solving. Journal of Developmental Education, 26(2), 22-33. 

[32] Singer, F. M., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educ Stud Math, 83, 9–26. https://doi.org/10.1007/S10649-012-9422-X

[33] Verschaffel, L., Greer, B., & DeCorte, E. (2007). Whole number concepts and operations. In F. K. Lester (Eds.), SecondHandbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 557-628). Information Age Publishing Inc.

[34] Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25-48. https://doi.org/10.1007/BF03217394

[35] Yorulmaz, A., Uysal, H., & Çokçaliskan, H. (2021). Pre-service primary school teachers' metacognitive awareness and beliefs about mathematical problem solving. Journal of Research and Advances in Mathematics Education, 6(3), 239-259. https://doi.org/10.23917/jramathedu.v6i3.14349

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