### A Case of Teacher and Student Mathematical Problem-Solving Behaviors from the Perspective of a Cognitive-Metacognitive Framework

#### Abstrakt

#### Klíčová slova

#### Celý článek:

PDF (English)#### Reference

Ader, E. (2013). A framework for understanding teachers' promotion of students' metacognition. International Journal for Mathematics Teaching & Learning, 5, 1-45.

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

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.

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

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

Cai, J., & Brook, M. (2006). Looking back in problem solving. Mathematics Teaching Incorporating Micromath, 196, 42–45.

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

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.

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

Desoete, A. (2007). Evaluating and improving the mathematics teaching-learning process through metacognition. Electronic Journal of Research in Educational Psychology, 5(3), 705–730.

Desoete, A., & De Craene, B. (2019). Metacognition and mathematics education: An overview. ZDM, 51(4), 565–575. | DOI 10.1007/s11858-019-01060-w

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

Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. Resnick (Ed.), The nature of intelligence (pp. 231–236). Hillsdale: Erlbaum.

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

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

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

Hartman, H., & Sternberg, J. (1993). A broad BACEIS for improving thinking. Instructional Science, 21(5), 401–425. | DOI 10.1007/BF00121204

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

Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63–85. | DOI 10.1007/BF02300500

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

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

Kuhn, D. (1991). The skills of argument. Cambridge: Cambridge University Press.

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

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.

Latterell, C. (2003). Testing the problem-solving skills of students in an NCTM-oriented curriculum. The Mathematics Educator, 13(1), 5–14.

Mayer, R. E. (1998). Cognitive, metacognitive and motivational aspects of problem solving. Instructional Science, 26(1-2), 49–63. | DOI 10.1023/A:1003088013286

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

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

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.

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.

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

Özsoy, D. (2007). İlkögretim beşinci sınıfta üstbiliş stratejileri öğretiminin problem çözme basarısına etkisi (Unpublished Doctoral Dissertation). Turkey: Gazi University.

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

Papaleontiou-Louca, E. (2003). The concept and instruction of metacognition. Teacher Development, 7(1), 9–30. | DOI 10.1080/13664530300200184

Polya, G. (2004). How to solve it: A new aspect of mathematical method. USA: Princeton University Press.

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

Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM, 42(2), 149–161. | DOI 10.1007/s11858-010-0240-2

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.

Schoenfeld, A. H. (1985). Making sense of "out loud" problem-solving protocols. The Journal of Mathematical Behavior, 4(2), 171–191.

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.

Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26(1-2), 113–125. | DOI 10.1023/A:1003044231033

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

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

Welsh Government. (2012). A guide to using PISA as a learning context. Cardiff: Welsh Government.