International Association of Educators   |  ISSN: 1949-4270   |  e-ISSN: 1949-4289

Original article | Educational Policy Analysis and Strategic Research 2022, Vol. 17(4) 142-163

Problem-Solving and Students’ Use of Metacognitive Skills

Ayten Pinar Bal & Ahmet Doğanay

pp. 142 - 163   |  DOI: https://doi.org/10.29329/epasr.2022.478.7   |  Manu. Number: MANU-2205-27-0004.R1

Published online: December 05, 2022  |   Number of Views: 104  |  Number of Download: 224


Abstract

We examined how high school students use their cognitive and metacognitive skills in the geometry problem-solving process. This research employed a mixed-methods descriptive sequential design. Data were collected in the 2019–2020 academic year at secondary education institutions in the central districts of Adana, Türkiye. Using stratified sampling, 313 students participated in the quantitative component, of 313 students 149 are girls and 164 were boys and they were all 15 years olds. Then, using extreme case sampling, 18 students were selected as participant of the qualitative component. Fourteen of them were boys and four were girls. Measures included the metacognitive skills scale, geometry problem test, thinking-aloud protocol, and an observation form. Descriptive statistics and content analysis were applied for data analysis. Results showed that students with high metacognitive skills used metacognitive skills more when solving geometry problems than students with low metacognitive skills. As the implication of the result it is suggested that attention should be paid to the development of students' metacognitive skills in schools. In this context, it would be beneficial to train teachers to develop metacognitive skills. In addition, there is a need to investigate the effect of metacognitive skills on learning in different learning areas.

Keywords: Metacognitive Skills; Problem-Solving; Geometry Problem; Secondary Education


How to Cite this Article?

APA 6th edition
Bal, A.P. & Doganay, A. (2022). Problem-Solving and Students’ Use of Metacognitive Skills . Educational Policy Analysis and Strategic Research, 17(4), 142-163. doi: 10.29329/epasr.2022.478.7

Harvard
Bal, A. and Doganay, A. (2022). Problem-Solving and Students’ Use of Metacognitive Skills . Educational Policy Analysis and Strategic Research, 17(4), pp. 142-163.

Chicago 16th edition
Bal, Ayten Pinar and Ahmet Doganay (2022). "Problem-Solving and Students’ Use of Metacognitive Skills ". Educational Policy Analysis and Strategic Research 17 (4):142-163. doi:10.29329/epasr.2022.478.7.

References
  1. Ader, E. 2019. “What Would You Demand Beyond Mathematics? Teachers’ Promotion of Students’ Self-Regulated Learning and Metacognition.” ZDM Mathematics Education 51 (4): 613–624. doi:10.1007/s11858-019-01054-8. [Google Scholar] [Crossref] 
  2. Aljaberi, N. M., and E. Gheith. 2015. “University Students’ Level of Metacognitive Thinking and Their Ability to Solve Problems.” American International Journal of Contemporary Research 5 (3): 121-134. http://www.aijcrnet.com/ [Google Scholar]
  3. Artzt, A. F., and E. Armour Thomas. 1992. “Development of a Cognitive-Metacognitive Framework for Protocol Analysis Of Mathematical Problem Solving in Small Groups.” Cognition and Instruction 9 (2): 137–175. doi:10.1207/s1532690xci0902_3 [Google Scholar] [Crossref] 
  4. Aydemir, H., and Y. Kubanc 2014. “Investigation of the Cognitive Behavioral Problem Solving Process.” Turkish Studies 9 (2): 203-219. doi:10.7827/TurkishStudies.6555 [Google Scholar] [Crossref] 
  5. Aydın, U., and B. Ubuz 2010. “Turkish Version of The Junior Metacognitive Awareness Inventory: the Validation Study.” Education and Science 35: 30–42.  [Google Scholar]
  6. Bani, B. S., E. Ekawati, and E. B. Rahaju 2019. “Metacognition Behavior of Junior High School Students in Solving Algebra Problems in Terms of Mathematical Abilities.” International Journal of Scientific and Research Publications 9(9): doi:10.29322/IJSRP.9.09.2019.p9310 [Google Scholar] [Crossref] 
  7. Blum, W., M. Niss,1991. “Applied mathematical problem solving, modelling, applications, and links to other subjects – state, trends and issues in mathematics instruction.” Educational Studies in Mathematics 22 (1): 37-68. doi:10.1007/BF00302716.pdf [Google Scholar] [Crossref] 
  8. Brown, A. 1987. “Metacognition, Executive Control, Self-Regulation and Other More Mysterious Mechanisms.” In Metacognition, motivation and understanding, edited by F. E. Weinert and R. H. Kluwe, 65–116. Hillsdale, NJ: Lawrence Erlbaum Associates. [Google Scholar]
  9. Costa, L.A., and B. Kallick. 2000. “Getting into the Habit of Reflection.” Educational Leadership, 57 (7): 60-62. [Google Scholar]
  10. Cozza, B., and M. Oreshkina 2013. “Cross-cultural Study of Cognitive and Metacognitive Processes During Math Problem Solving. School Science and Mathematics, 113(3), 275-284. [Google Scholar]
  11. Creswell, J. W. 2013. Qualitative Inquiry and Research Design. London, UK: Sage. [Google Scholar]
  12. Creswell, J. W., and C. N. Poth, C. N. 2017. Qualitative Inquiry and Research Design: Choosing Among Five Approaches. London, UK: SAGE Publications, Inc. [Google Scholar]
  13. Depaepe, F., E. De Corte, and L. Verschaffel. 2010. “Teachers’ Metacognitive and Heuristic Approaches to Word Problem Solving: Analysis and Impact on Students’ Beliefs and Performance.” ZDM Mathematics Education 42: 205-218. doi:10.1007/s11858-009-0221-5. [Google Scholar] [Crossref] 
  14. Desoete, A., and B. De Craene. 2019. “Metacognition and Mathematics Education: An Overview.” ZDM 51: 565–575. https://doi.org/10.1007/s11858-019-01060-w  [Google Scholar] [Crossref] 
  15. Desoete, A., H. Roeyers, and A. Buysse. 2001. “Metacognition and Mathematical Problem Solving in Grade 3.” Journal of Learning Disabilities, 34 (5): 435-449. [Google Scholar]
  16. Donaldson, S. E. 2011. “Teaching through problem solving: practices of four high school mathematics teachers.” PhD diss., University of Georgia. [Google Scholar]
  17. Erbas, A. K., and S. Okur. 2012. “Researching Students’ Strategies, Episodes, And Metacognitions in Mathematical Problem Solving.” Qual Quant, 46: 89–102. doi:10.1007/s11135-010-9329-5 [Google Scholar] [Crossref] 
  18. Evans, N. 2012. “Destroying Collaboration and Knowledge Sharing in The Workplace: A Reverse Brainstorming Approach.” Knowledge Management Research and Practice, 10: 175–187. doi:10.1057/kmrp.2011.43 [Google Scholar] [Crossref] 
  19. Flavell, J. H. 1979. “Metacognitive and Cognitive Monitoring.” American Psychologist, 34: 906- 911. doi:10.1037/0003-066X.34.10.906 [Google Scholar] [Crossref] 
  20. Fraenkel, J. R., N. E. Wallen, and H. H. Hyun. 2012. How to Design and Evaluate Research in Education. New York: McGram-Hill Companies. [Google Scholar]
  21. Garofalo, J., and F. K. Lester. 1985. “Metacognition, cognitive monitoring, and mathematical performance.” Journal for Research in Mathematics Education, 16: 163-176. doi:10.5951/jresematheduc.16.3.0163. [Google Scholar] [Crossref] 
  22. Hacker, D. J. 1998. “Definitions and Emprical Foundations.” In D. The Educational Psychology Series. Metacognition İn Educational Theory And Practice, edited by J. Hacker, J. Dunlosky, and A. C. Graesser, 1-25. New York: Routledge. [Google Scholar]
  23. Hennessey, B. A. 2003. “The Social Psychology of Creativity.” Scandinavian Journal of Educational Research, 47 (3): 253-271. doi:10.1080/00313830308601 [Google Scholar] [Crossref] 
  24. Jacobs, J., and S. Paris. 1987. “Children’s Metacognition about Reading. Issues in Definition, Measurement and Instruction.” Educational Psychologist, 22: 255-278. doi:10.1207/s15326985ep2203&4_4 [Google Scholar] [Crossref] 
  25. Jacobse, A. E., and E. G. Harskamp 2012. “Towards efficient measurement of metacognition in mathematical problem solving.” Metacognition and Learning 7 (2): 133-149. doi:10.1007/s11409-012-9088-x [Google Scholar] [Crossref] 
  26. Jonassen, D. H. 2000. “Toward a Design Theory of Problem Solving.” Educational Technology Research and Development 48: 63–85. [Google Scholar]
  27. Jöreskog, K. G., and D. Sörbom. 1993. Lisrel 8: Structural equation modelling with the SIMPLES common language. Chicago: Scientific Software International. [Google Scholar]
  28. Kramarski B., Z. R. Mevarech, and M Arami 2002. “The Effects of Metacognitive Training on Solving Mathematical Authentic Tasks.” Educational Studies in Mathematics 49, 225-250. doi:10.1023/A:1016282811724 [Google Scholar] [Crossref] 
  29. Krulik, S., and J. A. Rudnick. 1989. Problem solving: A handbook for senior high school teachers. Needham Heights, MA: Allyn & Bacon. [Google Scholar]
  30. Kuzle, A. 2017. “Delving into the Nature of Problem Solving Processes in a Dynamic Geometry Environment: Different Technological Effects on Cognitive Processing.” Technology, Knowledge and Learning 22 (1): 37–64. doi:10.1007/s10758-016-9284-x [Google Scholar] [Crossref] 
  31. Kuzle, A. 2018. “Assessing Metacognition of Grade 2 and Grade 4 Students Using an Adaptation of Multi-Method Interview Approach During Problem Solving.” Mathematics Education Research Journal 30 (2): 185–207. doi:10.1007/s13394-017-0227-1 [Google Scholar] [Crossref] 
  32. Kuzle, A. 2019. “Second Graders’ Metacognitive Actions in Problem Solving Revealed Through Action Cards.” The Mathematics Educator 28 (1): 27–60. https://eric.ed.gov/?id=EJ1225418 [Google Scholar]
  33. Lester, F. K. 1994. “Musing about Mathematical Problem Solving Research: 1970-1994.”, Journal for Research in Mathematics Education 25 (6): 660-675. doi: 10.2307/749578 [Google Scholar] [Crossref] 
  34. Livingston, J. A. 2003. “Metacognition: An Overview.” ERIC Document Reproduction Service No. ED474273.https://files.eric.ed.gov/fulltext/ED474273.pdf. [Google Scholar]
  35. Lucangeli, D., and C. Cornoldi. 1997. “Mathematics and Metacognition: What is the Nature of the Relationship?” Mathematical Cognition 3: 121–139. doi: 10.1080/135467997387443 [Google Scholar] [Crossref] 
  36. Lucangeli, D., M. C. Fastame, M. Pedron, A. Porru, V. Duca, P. K. Hitchcott, and M. P. Penna. 2019. “Metacognition and Errors: The Impact of Self-regulatory Trainings in Children with Specific Learning Disabilities.” ZDM 51 (4): 577–585 doi: 10.1007/s11858-019-01044-w. [Google Scholar] [Crossref] 
  37. Merriam, S. B., and E. J. Tisdell. 2013. Qualitative Research: A Guide to Design and Implementation, San Francisco, CA: John Wiley & Sons. [Google Scholar]
  38. Mevarech, Z. R., and B. Kramarski. 1997. “Improve: A Multidimensional Method for Teaching Mathematics in Heterogeneous Classrooms.” American Educational Research Journal  34 (2): 365- 394. https://doi.org/10.3102/00028312034002365 [Google Scholar] [Crossref] 
  39. Miles, M, B., A. M. Huberman, and J. Saldana. 2014. Qualitative Data Analysis: A Methods Sourcebook. London: Sage. [Google Scholar]
  40. Mills, G. E. and L. R. Gay. 2019. Competencies for Analysis and Applications. NY: Pearson Education. [Google Scholar]
  41. 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 [Google Scholar] [Crossref] 
  42. Montague, M., and B. Applegate. 1993. “Middle School Students’ Mathematical Problem Solving: An Analysis of Think-Aloud Protocols.” Learning Disabilities Quarterly 16: 19- 32. https://www.jstor.org/stable/1511157  [Google Scholar]
  43. Ohtani, K., and T. Hisasaka. 2018. “Beyond Intelligence: A Metaanalytic Review of the Relationship Among Metacognition, Intelligence, and Academic Performance.” Metacognition Learning, 13: 179–212. https://doi.org/10.1007/s11409-018-9183-8. [Google Scholar] [Crossref] 
  44. Özkubat, U., and E. R. Özmen. 2021. “Identifying the Cognitive and Metacognitive Strategies Used by Students with Learning Disabilities and Low and Average Achieving Students During Mathematical Problem Solving.” Ankara University Faculty of Educational Sciences Journal of Special Education 58 (1): 1-38. doi:10.21565/ozelegitimdergisi.736761 [Google Scholar] [Crossref] 
  45. Patton, M. Q. 2015. Qualitative Research & Evaluation Methods. Thousand Oaks, CA: Sage. [Google Scholar]
  46. Posamentier, A. S., and S. Krulik. 2008. Problem Solving Strategies for Efficient and Elegant Solutions: A Resource for The Mathematics Teacher. Thousand Oaks: Corwin Press [Google Scholar]
  47. Purnomo, D., T. Nusantara, S. Rahardjo, and S. Subanji. 2016. “Metacognition Process Characteristics of The Students in Solving Mathematics Problems.” IOSR Journal of Research & Method in Education 6 (5): 26-35. doi: 10.9790/7388-0605032635  [Google Scholar] [Crossref] 
  48. Rickey, D., and A. M. Stacy. 2000. “The Role Metacognition in Learning Chemistry.” Journal of Chemical Education 77: 915-920. doi:10.1021/ed077p915 [Google Scholar] [Crossref] 
  49. Rofii, A., S. Sunardi, and M. 2018. “Characteristics of students’ metacognition process at informal deduction thinking level in geometry problems.” International Journal on Emerging Mathematics Education 2 (1): 89-104. doi:10.12928/ijeme.v2i1.7684 [Google Scholar] [Crossref] 
  50. Rosenzweig, C., J. Krawec, and M. Montague. 2011. “Metacognitive Strategy Use of Eighth-Grade Students with and without Learning Disabilities During Mathematical Problem Solving: A Think-Aloud Analysis.” Journal of Learning Disabilities 44 (6): 508-520. doi:10.1177/0022219410378445 [Google Scholar] [Crossref] 
  51. Schneider, W., and C. Artelt. 2010. “Metacognition and Mathematics Education.” ZDM Mathematics Education 42: 149–161. doi:10.1007/s11858-010-0240-2. [Google Scholar] [Crossref] 
  52. Schoenfeld, A. H. 1987. “What’s all the Fuss about Metacognition?.” In Cognitive science and mathematics education, edited by A. H. Schoenfeld, 189-215. Hillsdale, NJ: Lawrence Erlbaum Associates. [Google Scholar]
  53. Schoenfeld, A. H. 1992. “Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics.” In Handbook for Research on Mathematics Teaching and Learning, edited by D. A. Grouws, 334- 370. New York: MacMillan [Google Scholar]
  54. Schraw, G., and D. Moshman. 1995. “Metacognitive Theories.” Educational Psychology Review 7 (4): 351-371. doi:10.1007/BF02212307  [Google Scholar] [Crossref] 
  55. Schunk, D. H. 2012. Learning theories: An educational perspective. Boston, MA: Pearson Education Inc.. [Google Scholar]
  56. Scott, B. M., and M. G. Levy. 2013. “Metacognition: Examining the Components of a Fuzzy Concept.” Educational Research 2 (2): 120-131. doi: 10.5838/erej.2013.22.04 [Google Scholar] [Crossref] 
  57. Serin, M. K., and Korkmaz, I. (2018). “Investigatıon of Cognitive-Metacognitive Behaviors of Primary School 4th Grade Students in Processes of Understanding the Problem and Prediction.” Adiyaman University Journal of Social Sciences 10 (28): 131-173. doi:10.14520/adyusbd.327680 [Google Scholar] [Crossref] 
  58. Shilo, A., and K. Kramarski. 2019. “Mathematical Metacognitive Discourse: How Can It be Developed Among Teachers and Their Students? Empirical Evidence From A Videotaped Lesson and Two Case Studies. ZDM Mathematics Education 51 (4): 625–640. doi:10.1007/s11858-018-01016-6 [Google Scholar] [Crossref] 
  59. Shorten, A., and J. Smith. 2017. “Mixed Methods Research: Expanding the Evidence Base. Evidence-Based Nursing 20 (3): 74-75. doi:10.1136/eb-2017-102699 [Google Scholar] [Crossref] 
  60. Smith, J. M. and R. Mancy. 2018. “Exploring the Relationship Between Metacognitive and Collaborative Talk During Group Mathematical Problem-Solving – What Do We Mean By Collaborative Metacognition?.” Research in Mathematics Education 20 (1): 14-36, doi:10.1080/14794802.2017.1410215 [Google Scholar] [Crossref] 
  61. Sorby S. A., and G. C. Panther. 2020. “Is the Key to Better PISA Math Scores Improving Spatial Skills?.” Mathematics Education Research Journal 32: 213-233. doi:10.1007/s13394-020- 00328-9  [Google Scholar] [Crossref] 
  62. Sperling, R. A., B. C. Howard, L. A. Miller, and C. Murphy. 2002. “Measures of Children’s Knowledge and Regulation of Cognition.” Contemporary Educational Psychology 27: 51-79. doi:10.1006/ceps.2001.1091, [Google Scholar] [Crossref] 
  63. Stillman, G., and Z. Mevarech. 2010. “Metacognition Research in Mathematics Education: From Hot Topic to Mature Field.” ZDM Mathematics Education 42: 145–148. doi:10.1007/s11858-010-0245-x [Google Scholar] [Crossref] 
  64. Susanto, S., and M. Irvan. 2018. “An Analysis of Students’ Metacognition Ability Through Jumping Task Strategy to Solve Geometry Problem.” International Journal of Advanced Research 6 (3): 1375-1381. doi:10.21474/IJAR01/6808 [Google Scholar] [Crossref] 
  65. Sutherland, L. 2002. “Developing Problem Solving Expertise: The Impact of Instruction in a Question Analysis Strategy.” Learning and Instruction 12: 155–187. www.elsevier.com/locate/learninstruc [Google Scholar]
  66. Swanson, H. L. 1990. Influence of Metacognitive Knowledge and Aptitude on Problem Solving.” Journal of Educational Psychology 82 (2): 306-314. https://doi.org/10.1037/0022-0663.82.2.306 [Google Scholar] [Crossref] 
  67. Teong, S. K. 2003. “The Effect of Metacognitive Training on Mathematical Word-Problem Solving.” Journal of Computer Assisted Learning 19: 46-55. doi:10.1046/j.0266-4909.2003.00005.x [Google Scholar] [Crossref] 
  68. Veenman, M. V. J. 2017. “Learning to Self-Monitor and Self-Regulate.” In Handbook Of Research On Learning and Instruction, edited by R. Mayer and P. Alexander, 233–257. New York: Routledge. [Google Scholar]
  69. Veenman, M. V. J., and D. V. Cleef. 2019. “Measuring Metacognitive Skills For Mathematics: Students’ Self-Reports vs. Online Assessment Methods.” ZDM The International Journal on Mathematics Education 51 (4): 691-701. doi:10.1007/s11858-018-1006-5 [Google Scholar] [Crossref] 
  70. Verschaffel, L., F. Depaepe, and Z. Mevarech. 2019. “Learning Mathematics in Metacognitively Oriented ICT-Based Learning Environments: A Systematic Review of the Literature.” Hindawi Education Research International 2019: 1-19. doi:10.1155/2019/3402035. [Google Scholar] [Crossref] 
  71. Wilson, J. 2001. “Methodological Difficulties of Assessing Metacognition: A New Approach. Australian Association for Research in Education Conference, 1-14. ERIC Number: ED460143. http://www.aare.edu.au/index.htm. [Google Scholar]
  72. Young, A. E., and F. C. Worrell. 2018. “Comparing Metacognition Assessments of Mathematics in Academically Talented Students.” Gifted Child Quarterly 62 (3): 259–275. doi:10.1177/0016986218755915 [Google Scholar] [Crossref] 
  73. Zhao, N., S. Teng, Y. Li, S. Wang, W. Li, H. Wen, and Y. Mengya. 2019. “A Path Model for Metacognition and Its Relation to Problem-Solving Strategies and Achievement for Different Tasks.” ZDM Mathematics Education 51 (4): 641-653. doi:10.1007/s11858-019-01067-3 [Google Scholar] [Crossref]