Title: A case of teacher and student mathematical problem-solving behaviors from the perspective of a cognitive-metacognitive framework
Source document: Studia paedagogica. 2019, vol. 24, iss. 4, pp. [221]-243
Extent
[221]-243
-
ISSN1803-7437 (print)2336-4521 (online)
Persistent identifier (DOI): https://doi.org/10.5817/SP2019-4-10
Stable URL (handle): https://hdl.handle.net/11222.digilib/142247
Type: Article
Language
License: Not specified license
Notice: These citations are automatically created and might not follow citation rules properly.
Abstract(s)
This study aims to investigate the problem-solving behaviors of a teacher and his students based on a cognitive – metacognitive framework. The problem-solving behaviors of 6-8th-grade students and a mathematics teacher were recorded and encoded during task-based interview sessions about solving problems, and semi-structured interviews were used to obtain information regarding the mathematics teacher's perceptions of mathematical problem-solving processes. They solved the problems in a learning environment, and their problem-solving processes were investigated using the think-aloud method. The results indicated that the students and the teacher followed a similar path involving reading, understanding, exploring, planning, and implementing. Furthermore, not all episodes occurred in each problem-solving task and the behaviors that represented given episodes changed according to the participants. Students with different problem-solving skill levels were found to exhibit different frequencies of cognitive and metacognitive behaviors while solving problems. The problemsolving behaviors of the teacher and the students revealed information related to metacognitive behaviors that are to be developed in further studies.
References
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[35] Polya, G. (2004). How to solve it: A new aspect of mathematical method. USA: Princeton University Press.
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[38] Schoenfeld, A. H. (1981). Episodes and executive decisions in mathematical problem solving. Paper presented at the meeting of the American Educational Research Association, Los Angeles.
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[40] Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
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[42] Veenman, M. V. J., Kerseboom, L., & Imthorn, C. (2000). Test anxiety and metacognitive skillfulness: Availability versus production deficiencies. Anxiety, Stress and Coping, 13(4), 391–412. | DOI 10.1080/10615800008248343
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[2] Artzt, A. F., & Armour-Thomas, E. (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
[3] Artzt, A. F., & Armour-Thomas, E. (2001). Mathematics teaching as problem solving: A framework for studying teacher metacognition underlying instructional practice in mathematics. In H. J. Hartman (Ed.), Metacognition in learning and instruction (pp. 127–148). Netherlands: Kluwer Academic Publishers.
[4] Baten, E., Praet, M., & Desoete, A. (2017). The relevance and efficacy of metacognition for instructional design in the domain of mathematics. ZDM-The International Journal on Mathematics Education, 49(4), 613–623. | DOI 10.1007/s11858-017-0851-y
[5] Blum, B., & Niss, M., (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects. Educational Studies in Mathematics, 22(1), 37–68. | DOI 10.1007/BF00302716
[6] Cai, J., & Brook, M. (2006). Looking back in problem solving. Mathematics Teaching Incorporating Micromath, 196, 42–45.
[7] Cho, K. L., & Jonassen, D. H. (2002). The effects of argumentation scaffolds on argumentation and problem solving. Educational Technology Research and Development, 50(3), 5–22. | DOI 10.1007/BF02505022
[8] Curwen, M. S., Miller, R. G., White-Smith, K. A., & Calfee, R. C. (2010). Teachers' metacognition develops students' higher learning during content area literacy instruction: Findings from the read-write cycle project. Issues in Teacher Education, 19(2), 127–151.
[9] Department for Education. (2000). Mathematics programmes of study: Key stages 1 and 2 National curriculum in England – Statutory guidance to July 2015. Retrieved from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/286343/Primary_maths_curriculum_to_July_2015_RS.pdf
[10] Desoete, A. (2007). Evaluating and improving the mathematics teaching-learning process through metacognition. Electronic Journal of Research in Educational Psychology, 5(3), 705–730.
[11] Desoete, A., & De Craene, B. (2019). Metacognition and mathematics education: An overview. ZDM, 51(4), 565–575. | DOI 10.1007/s11858-019-01060-w
[12] Erbas, A. K., & Okur, S. (2012). Researching students' strategies, episodes, and metacognitions in mathematical problem solving. Quality and Quantity, 46(1), 89–102. | DOI 10.1007/s11135-010-9329-5
[13] Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. Resnick (Ed.), The nature of intelligence (pp. 231–236). Hillsdale: Erlbaum.
[14] Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American Psychologist, 34(10), 906–911. | DOI 10.1037/0003-066X.34.10.906
[15] García, T., Rodríguez, C., González-Castro, P., González-Pienda, J. A., & Torrance, M. (2016). Elementary students' metacognitive processes and post-performance calibration on mathematical problem-solving tasks. Metacognition and Learning, 11(2), 139–170. | DOI 10.1007/s11409-015-9139-1
[16] Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176. | DOI 10.2307/748391
[17] Hartman, H., & Sternberg, J. (1993). A broad BACEIS for improving thinking. Instructional Science, 21(5), 401–425. | DOI 10.1007/BF00121204
[18] Jacobse, A. E., & Harskamp, E. G. (2012). Towards efficient measurement of metacognition in mathematical problem solving. Metacognition and Learning, 7(2), 133–149. | DOI 10.1007/s11409-012-9088-x
[19] Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63–85. | DOI 10.1007/BF02300500
[20] Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom two episodes and related theoretical abductions. Journal of Mathematical Behavior, 26(1), 60–82. | DOI 10.1016/j.jmathb.2007.02.001
[21] Ku, K. Y., & Ho, I. T. (2010). Metacognitive strategies that enhance critical thinking. Metacognition and Learning, 5(3), 251–267. | DOI 10.1007/s11409-010-9060-6
[22] Kuhn, D. (1991). The skills of argument. Cambridge: Cambridge University Press.
[23] Kuhn, D., Zillmer, N., Crowell, A., & Zavala, J. (2013). Developing norms of argumentation: Metacognitive, epistemological, and social dimensions of developing argumentative competence. Cognition and Instruction, 31(4), 456–496. | DOI 10.1080/07370008.2013.830618
[24] Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40.
[25] Latterell, C. (2003). Testing the problem-solving skills of students in an NCTM-oriented curriculum. The Mathematics Educator, 13(1), 5–14.
[26] Mayer, R. E. (1998). Cognitive, metacognitive and motivational aspects of problem solving. Instructional Science, 26(1-2), 49–63. | DOI 10.1023/A:1003088013286
[27] Ministry of National Education. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı (Mathematics curricula program for middle grades). Retrieved from http://ttkb.meb.gov.tr/www/guncellenen-ogretim-programlari-ve-kurul-kararlari/icerik/150
[28] Montague, M., & Applegate, B. (1993). Middle school students' mathematical problem solving: An analysis of think-aloud protocols. Learning Disability Quarterly, 16(1), 19–32. | DOI 10.2307/1511157
[29] National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
[30] Olkin, I., & Schoenfeld, A. (1994). A discussion of Bruce Reznick's chapter. In A. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 39–51). Hillsdale: Lawrence Erlbaum Associates.
[31] OECD Programme for International Student Assessment 2012. (2013). PISA 2012 released mathematics items. Retrieved from https://www.oecd.org/pisa/pisaproducts/pisa2012-2006-rel-items-maths-ENG.pdf
[32] Özsoy, D. (2007). İlkögretim beşinci sınıfta üstbiliş stratejileri öğretiminin problem çözme basarısına etkisi (Unpublished Doctoral Dissertation). Turkey: Gazi University.
[33] Özsoy, G. (2011). An investigation of the relationship between metacognition and mathematics achievement. Asia Pacific Educational Review, 12(2), 227–235. | DOI 10.1007/s12564-010-9129-6
[34] Papaleontiou-Louca, E. (2003). The concept and instruction of metacognition. Teacher Development, 7(1), 9–30. | DOI 10.1080/13664530300200184
[35] Polya, G. (2004). How to solve it: A new aspect of mathematical method. USA: Princeton University Press.
[36] Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students' problem solving processes. Educational Studies in Mathematics, 55(1-3), 27–47. | DOI 10.1023/B:EDUC.0000017666.11367.c7
[37] Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM, 42(2), 149–161. | DOI 10.1007/s11858-010-0240-2
[38] Schoenfeld, A. H. (1981). Episodes and executive decisions in mathematical problem solving. Paper presented at the meeting of the American Educational Research Association, Los Angeles.
[39] Schoenfeld, A. H. (1985). Making sense of "out loud" problem-solving protocols. The Journal of Mathematical Behavior, 4(2), 171–191.
[40] Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
[41] Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26(1-2), 113–125. | DOI 10.1023/A:1003044231033
[42] Veenman, M. V. J., Kerseboom, L., & Imthorn, C. (2000). Test anxiety and metacognitive skillfulness: Availability versus production deficiencies. Anxiety, Stress and Coping, 13(4), 391–412. | DOI 10.1080/10615800008248343
[43] Veenman, M. V. J., Kok, R., & Blöte, A. W. (2005). The relation between intellectual and meta-cognitive skills in early adolescence. Instructional Science: An International Journal of Learning and Cognition, 33(3), 193–211. | DOI 10.1007/s11251-004-2274-8
[44] Welsh Government. (2012). A guide to using PISA as a learning context. Cardiff: Welsh Government.