Pre-service primary school teachers’ metacognitive awareness and beliefs about mathematical problem solving

Alper Yorulmaz(1), Hümeyra Uysal(2), Halil Çokçaliskan(3*)

(1) Faculty of Education, Mugla Sıtkı Kocman University, Turkey
(2) Institute of Education Science, Marmara University, Turkey
(3) Faculty of Education, Mugla Sıtkı Kocman University, Turkey
(*) Corresponding Author

Abstract

Metacognitive awareness is a variable that is thought to affect beliefs in  problem solving. When the literature is examined, it is seen that the studies mostly focus on metacognitive awareness and problem solving skills. Therefore, the aim is to determine pre-service primary school teachers’ metacognitive awareness and beliefs in mathematical problem solving. In this study, it is thought that it will contribute to the researches that will be carried out regarding the investigation of the relationship between metacognitive awareness and beliefs about problem solving and its implementation with pre-service primary school teachers. The study, designed as the correlational survey model, included a total of 284 pre-service primary school teachers attending a university in the Aegean Region of Turkey. The data were collected with the “Metacognitive Awareness Inventory” and the “Scale of Beliefs about Mathematical Problem Solving”. In the analysis, descriptive statistics, difference test, correlation and regression analyses were used. As a result, the pre-service primary school teachers’ metacognitive awareness was found to be high and their beliefs about mathematical problem solving were found to be medium. While metacognitive awareness was found to be not varying significantly by gender, beliefs about mathematical problem solving were found to be varying significantly by gender in favor of the male pre-service teachers. Moreover, a medium and significant correlation was found between metacognitive awareness and beliefs about mathematical problem solving. It was also found that metacognitive awareness explained 13% of the variance in the dependent variable of beliefs about mathematical problem solving.

Keywords

Metacognitive awareness, mathematical problem solving, beliefs, pre-service primary school teachers, primary education

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References

Abrosse, R., Clement, L., Philipp, R., & Chauvot, J. (2004). Assessing prospective elementary school teachers‟ beliefs about mathematics and mathematics learning: Rationale and development of a Constructed-Response-Format Belief Survey. School Science and Mathematics Journal, 104(2), 56–69. https://doi.org/10.1111/j.1949-8594.2004.tb17983.x

Akın, A. & Abacı, R. (2011). Biliş ötesi [Metacognition]. Ankara: Nobel Yayınları

Akın, A., Abacı, R. &Çetin, B. (2007). The Validity and Reliability of the Turkish Version of the Metacognitive Awareness Inventory. Educational Sciences: Theory & Practice, 7(2), 655-680. https://toad.halileksi.net/sites/default/files/pdf/bilisotesi-farkindalik-envanteri-toad.pdf

Altun, M. (2008). Eğitim fakülteleri ve sınıf öğretmenleri için matematik öğretimi[Teaching maths to education faculty and primary school teachers]. Ankara: Alfa Yayıncılık

Baker, L. & Brown, A. L. (1980). Metacognitive skills and reading. Handbook of Reading Research, New York: Longman.

Baki, A. (2018). Matematiği öğretme bilgisi [The knowledge of teaching maths]. Ankara: Pegem Akademi.

Baş, F., Özturan-Sağırlı, M., & Bekdemir, M. (2016). The metacognitive awarenesses of pre-service secondary school mathematics teachers, beliefs, attitudes on problem solvıng, and relationshıp between them. Journal of Theory and Practice in Education, 12(2), 464-482. https://dergipark.org.tr/tr/download/article-file/262376

Baydar, C. ve Bulut. S. (2002). Öğretmenlerin matematiğin doğası ve öğretimi ile ilgili inançlarının matematik eğitimindeki önemi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23, 62-66. https://dergipark.org.tr/tr/pub/hunefd/issue/7815/102626

Baykara, K. (2011). A study on “teacher effıcacy perceptıons” and “metacognitive learning strategies” of prospective teachers. Hacettepe University the Journal of Education, 40, 80-92. http://efdergi.hacettepe.edu.tr/yonetim/icerik/makaleler/396-published.pdf

Baykul, Y. (2016). İlkokulda matematik öğretimi [Teaching maths in primary school].(13rd edition). Ankara: Pegem Akademi.

Baysal, Z. N., Ayvaz, A., Çekirdekçi, S., and Malbeleği, F. (2013). An analysis of metacognitive awareness of pre-service primary school teachers in terms of various variables. Marmara University Atatürk Education Faculty Journal of Educational Sciences, 37, 68-81. https://dergipark.org.tr/tr/download/article-file/2153

Belet, S. D., and Güven, M. (2011). Meta-cognitive strategy usage and epistemological beliefs of primary school teacher trainees. Educational Sciences: Theory and Practice, 11(1), 51-57. https://files.eric.ed.gov/fulltext/EJ919889.pdf

Büyüköztürk, Ş. (2012). Sosyal bilimler için veri analizi el kitabı istatistik, araştırma deseni SPSS ugulamaları ve yorum [Data analysis handbook for social sciences: Statistics, research design, SPSS applications and interpretation]. Ankara: Pegem Akademi.

Byron, M.K. (1995). Confronting the Verbal/Visual Issue: The Mathematical problem-solving processes of a small group of female junior secondary students. Unpublished Doctoral Thesis, The Ohio State University, Ohio, USA.

Charles, R., and Lester, F. (1982). Teaching problem solving: What, why and how. Palo Alto, California: Dale Seymour Publications.

Cüceloğlu, D. (2012). İnsan ve davranışı [Human behavior]. İstanbul: Remzi Kitabevi.

Çeliköz, N., Erişen,Y. and Şahin, M. (2012). Bilişsel öğrenme kuramları [Cognitive learning theories]. In Kaya, Z. (Ed.), Öğrenme ve öğretme kuramlar-yaklaşımlar-modeller [Learning and teaching theories-approaches-models] (pp. 49-74). Ankara: Pegem Akademi Yayınları

Çubukçu, Z. (2011). Düşünme becerileri [Thinking skills]. In Filiz, S.B. (Ed.), Öğrenme öğretme kuram ve yaklaşımları [The theories and approaches of learning and teaching](s. 279-334). Ankara: Pegem Akademi Yayınları

Dağlı, A. (2004). Problem solving and decision making. Electronic Journal of Social Science, 3(7), 41-49. https://dergipark.org.tr/tr/pub/esosder

Davis, R.B. (1984). Learning mathematics: The cognitive science approach to mathematics education. New Jersey: Ablex Publishing Corporation

Desoete, A., Roeyers, H. & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities 34(5): 435-449. https://doi.org/10.1177/002221940103400505

Demirsöz, E. S. (2014). Metacognitive awareness and its developing. Trakya University Journal of Education, 4, 112-123. https://dergipark.org.tr/tr/download/article-file/200398

Deniz, D., Küçük, B., Cansız, Ş., Akgün, L. and İşleyen, T. (2014). Examining metacognitive awareness of prospective secondary school mathematics teachers in terms of some variables. Kastamonu Education Journal, 22(1), 305-320. https://dergipark.org.tr/tr/download/article-file/209952

Deringöl, Y. (2018). An analysis of prospective primary school teachers’ problem solving beliefs and problem posing self-efficacy beliefs. Turkish Journal of Computer and Mathematics Education, 9(1), 31-53. https://doi.org/10.16949/turkbilmat.336386

Deryakulu, D. (2004). Epistemolojik inançlar. In Y. Kuzgun, and D. Deyakulu (Ed.), Eğitimde bireysel farklılıklar (pp. 259-287). Ankara: Nobel Akademik Yayıncılık.

Dilci, T. and Kaya, S. (2012). Examination of meta-cognitive awareness levels of primary school teachers teaching 4th and 5th grades in terms of various variables. SDU Faculty of Arts and Sciences Journal of Social Sciences, 247-267. https://dergipark.org.tr/tr/download/article-file/117833

Duatepe-Paksu, A. (2008). Comparing teachers’ beliefs about mathematics in terms of their branches and gender. Hacettepe University Journal of Education, 35, 87-97. https://dergipark.org.tr/tr/pub/hunefd/issue/7803/102277

Erbaş, A. A., Karaduman, G. B. & Yavuz, G. (2018). The ınvestıgatıon of the relatıonshıp between the primary school teacher candıdates' cognıtıve levels, creatıvıty levels and problem solvıng skılls. Turkish Stuedies, 13, 551-568. https://doi.org/10.7827/TurkishStudies.12816

Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34(10), 906-911. https://doi.org/10.1037/0003-066X.34.10.906

Frykholm, J. (2003). Teachers’ Tolerance for Discomfort: Implications for Curricular Reform in Mathematics, Journal of Curriculum and Supervision, 19(2), 125-149. http://www.ascd.org/publications/jcs/winter2004/Teachers'-Tolerance-for-Discomfort@-Implications-for-Curricular-Reform-in-Mathematics.aspx

Gelbal, S. (1991). Problem çözme. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 6(6), 167-173. https://dergipark.org.tr/tr/pub/hunefd/issue/7831/103054

Grouws, D. A. (1996). Critical İssues in Problem Solving İnstruction in Mathematics. In D. Zhang, T. Sawada, & J. P. Becker (Eds.), Proceedings of the China-Japan-U.S. seminar on mathematical education (70-93). Carbondale, IL: Board of Trustees of Southern Illinois University.

Gül, Ş., Köse, E. Ö., & Yılmaz, S. S. (2014). Compared to different variables of prospective biology teachers’ metacognitive awareness. HAYEF: Journal of Education, 12-1(23), 83-91. https://dergipark.org.tr/tr/download/article-file/93203

Gülten, D. Ç. & Soytürk, İ. (2012). An investigation of primary school mathematics teacher candidates’ mathematical problem solving beliefs through some variables. The Journal of Academic Social Science Studies, 5(8), 641-656. https://arastirmax.com/tr/system/files/dergiler/79201/makaleler/5/8/arastrmx_79201_5_pp_641-656.pdf

Hacıömeroğlu, G. (2011a). Turkish adaptation of beliefs about mathematical problem solving instrument . Dicle University Journal of Ziya Gökalp Faculty of Education, 17, 119-132. https://dergipark.org.tr/en/download/article-file/787037

Hacıömeroğlu, G. (2011b). Examining elementary pre-service teachers’ epistemological beliefs as predictors of beliefs about mathematical problem solving. Buca Faculty of Education Journal, 30, 206-220. https://dergipark.org.tr/tr/download/article-file/231663

Heppner, P. P. & Peterson, C. H. (1982). The development and implications of a personal problem solving inventory. Journal of Counseling Psychology, 29, 66- 75. https://doi.org/10.1037/0022-0167.29.1.66

House, J. D. (2006). Mathematics beliefs and achievement of elementary school students in Japan and the United States: results from the third international mathematics and science study. The Journal of Genetic Psychology, 167(1), 31-45. https://doi.org/10.3200/GNTP.167.1.31-45

Izgar, H., Gürsel, M., Kesici, Ş. and Negiş, A. (2004). Önder davranışlarının problem çözme becerisine etkisi [The effect of leader behaviors on problem solving skills].. XIII. Ulusal Eğitim Bilimleri Kurultayı, İnönü Üniversitesi Eğitim Fakültesi, Malatya, Turkey.

Kana, F. (2015). Motivational, cognitive and metacognitive competences of pre-service Turkish language teachers. The Journal of International Education Science, 2(4), 395-407. https://dergipark.org.tr/tr/download/article-file/562689

Kapa, E. (2001). A metacognitive support during the process of problem solving in a computerized environment. Educational Studies in Mathematics, 47, 317-336. https://link.springer.com/content/pdf/10.1023/A:1015124013119.pdf

Karasar, N. (2014). Bilimsel araştırma yöntemi [Scientific research methods](26th edition).Ankara: Nobel Akademik Yayıncılık.

Kayaaslan, A. (2006). 4th and 5th grade elementary school students' beliefs about the nature of mathematics and the teaching of mathematics. Unpublished Master Thesis, Gazi University, Institute of Education Sciences, Ankara, Turkey.

Kayan, F., & Çakıroğlu, E. (2008). Pre-service elementary mathematics teachers’ mathematical problem solving beliefs. Hacettepe Unıversity The Journal Of Education (35), 218–226. https://dergipark.org.tr/tr/pub/hunefd/issue/7803/102288

Kışkır, G. (2011). Investigation of the relationship between metacognitive awareness levels and problem solving skills of prospective teachers. Unpublished Master Thesis, Atatürk University, Institute of Education Sciences, Erzurum, Turkey.

Kloosterman, P., & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving. School Science and Mathematics, 92(3), 109–115. https://doi.org/10.1111/j.1949-8594.1992.tb12154.x

Kramarski, B., Mevarech, Z.R. & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49, 225-250. https://www.jstor.org/stable/3483076

Krulik, S. & Rudnick, J.A. (1996). The new sourcebook for teaching reasoning and problem solving in junior and senior high school. Boston: Allyn & Bacon.

Lai, A. F. & Yang, S. M. (2011). The learning effect of visualized programming learning on 6 th graders' problem solving and logical reasoning abilities. Electrical and Control Engineering (ICECE), 2011 International Conference on. IEEE.

Lin, X., Schwartz, D. L., & Hatano, G. (2005). Toward teachers' adaptive metacognition. Educational Psychologist, 40(4), 245-255. https://doi.org/10.1207/s15326985ep4004_6

Lloyd, G., and Wilson, S. (1998). Supporting innovation: The impact of a teacher’s conceptions of functions on his implementations of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248-274. https://doi.org/10.2307/749790

Mason, L., and Scrivani, L. (2004). Enhancing students' mathematical beliefs: An intervention study. Learning and Instruction, 14, 153-176. https://doi.org/10.1016/j.learninstruc.2004.01.002

McLeod, D. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grouwsm (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York: Macmillan.

McLeod, D. B., & McLeod, S. H. (2002). Synthesis – beliefs and mathematics education: Implications for learning, teaching, and research. In G. C. Leder, E. Pehkonen, and G. Törner (Ed.), Beliefs: A hidden variable in mathematics education? (pp. 115-127). Dordrecht: Kluwer Acedemic.

Memnun, D. S., & Akkaya, R. (2012). An investigation of pre-service primary school mathematics, science and primary school teachers’ metacognitive awareness in terms of knowledge of and regulation of cognition. Journal of Theoretical Educational Science, 5(3), 312-329.https://dergipark.org.tr/tr/pub/akukeg/issue/29346/314038

Montague, M., Applegate, B. & Marquard, K. (1993). Cognitive strategy instruction and mathematical problem-solving performance of students with learning disabilities. Learning Disabilities Research and Practice, 8(4), 223-232.

https://doi.org/10.1177/002221949703000204

Morgan, J., and Williams, B. C. (2007). Overview of problem solving. In S. W. Beyerlein, C. Holmes, and D. K. Apple (Eds.), Faculty guidebook: A comprehensive tool for improving facultyperformance (pp. 181-184). Lisle, IL: Pacific Crest.

Özkubat, U. & Özmen, E.R. (2020). Turkish adaptation of the metacognitive experiences questionnaire in solving math problems. OPUS International Journal of Society Researches, 16(31), 3958-3984. https://doi.org/10.26466/opus.736793

Özsoy, G. (2014). The Relationship Between Problem Solving Skills and Mathematical Achievement. Gazi UniversityJournal of Gazi Education Faculty, 25(3), 179-190. http://www.gefad.gazi.edu.tr/tr/download/article-file/77235

Özsoy, G. and Günindi, Y. (2011). Prospective preschool teachers’ metacognitive awareness. Elementary Education Online, 10(2),430-440. https://www.ilkogretim-online.org/fulltext/218-1596869645.pdf?1618759255

Özturan-Sağırlı, M., Baş, F. &Bekdemir, M. (2020). The Relationship between teacher candidates’ metacognitive awareness levels and achievements. Journal of BayburtEducation Faculty, 15(29), 1-22. https://doi.org/10.35675/befdergi.464806

Öztürk, S., &Serin, M. K. (2020). Examination of pre-service primary school teachers’ metacognitive awareness with anxiety towards mathematics teaching. Kastamonu Education Journal, 28(2), 1013-1025. https://doi.org/10.24106/kefdergi.705074

Pajares, M. F. (1992). Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332. https://doi.org/10.3102/00346543062003307

Polya G.. (1957). How to solve it: A new aspect of mathematical method. Ed. ke-2. New Jersey: Princeton University Press.

Polya, G. (1981). Mathematical discovery: On understanding, learning, and teaching problem solving. New York: John Wiley.

Posamentier, A. S. & Krulik, S. (2016). Matematikte problem çözme [Problem solving in mathematics](L. Akgün, T. Kar and M. F. Öçal, Trans.). Ankara: Pegem Akademi.

Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practices. Journal for Research in Mathematics Education, 28(6), 550-576. https://doi.org/10.2307/749691

Reeve, R. A., & Brown, A. L. (1985). Metacognition reconsidered: Implications for intervention research. Journal of Abnormal Child Psychology, 13(3), 343-356.https://doi.org/10.1007/BF00912721

Sağlam, Y. & Dost, S. (2014). Preservice science and mathematics teachers’ beliefs about mathematical problem solving. Procedia-Social and Behavioral Sciences, 116, 303-306. https://doi.org/10.1016/j.sbspro.2014.01.212

Schoenfeld, A. H. (1985). Mathematical problem solving (1st edition). Orlando: Academic Press.

Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338-355. https://doi.org/10.2307/749440

Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26, 113-125. https://doi.org/10.1023/A:1003044231033

Schraw, G. & Dennison, R.S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19(4), 460-475. https://doi.org/10.1006/ceps.1994.1033

Schraw, G. and Moshman, D., (1995). Metacognitive theories. Educational Psychology Review, 7(4), 351–371. https://doi.org/10.1007/BF02212307

Schunk, D. H. (2009). Öğrenme teorileri eğitimsel bir bakışla [Learning theories: An educational perspective](M. Şahin, Trans.). Ankara: Nobel Yayın Dağıtım.

Schunk, D. H. (1989). Self-efficacy and achievement behaviors. Educational Psychology Review, 1,173–208. https://doi.org/10.1007%2FBF01320134

Silik, Y. (2016). Effect of educational robotics applications on problem solving skills of science teacher candidates. Unpublished Master Thesis, Karadeniz Technical University, Institute of Education Sciences, Trabzon, Turkey.

Smith, E., E. & Kosslyn, S.M. (2014). Bilişsel psikoloji [Cognitive psychology](Şahin, M., Trans.)Ankara: Nobel Akademik Yayınları

Stillman, G.A. & Galbraith, P.L. (1998). Applying mathematics with real world connections: metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36, 157-195. https://www.jstor.org/stable/3482790

Stylianou, D.A. (2002). On the interaction of visualization and analysis: the negotiation of a visual representation in expert problem solving. Journal of Mathematical Behavior, 21, 303- 317. https://doi.org/10.1016/S0732-3123(02)00131-1

Soytürk, İ. (2011). An investigation of pre-service primary school teachers’ self-efficacy about mathematical literacy and their beliefs about mathematical problem solving. Unpublished Master Thesis, İstanbul University, Social Sciences Institute, İstanbul, Turkey.

Thompson, A. G. (1992). Teachers’ belief and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 12-146). New York: Macmillan.

Toptaş, V. & Gözel, E. (2017). Beliefs and the mathematical problem solutions of primary school teacher candidates. Kırıkkale University Journal of Social Sciences, 7(2), 439-459. https://dergipark.org.tr/tr/download/article-file/338040

Tunçer, B. K. (2013). The relationship between pre-service teachers' academic achievement toward initial reading writing course, metacognitive awareness level, thinking style and attitudes toward course. Unpublished Master Thesis, Çanakkale 18 Mart University, Institute of Education Sciences, Çanakkale, Turkey.

Ünlü, M. & Sarpkaya Aktaş, G. (2016). Pre-service elementary mathematics teachers' self-efficacy beliefs about problem posing and beliefs about problem solving. Abant Izzet Baysal University Journal of Faculty of Education, 16(4), 2040-2059. https://dergipark.org.tr/tr/download/article-file/291960

Wilkins, J., & Brand, B. (2004). Change in pre-service teachers’ beliefs: An evaluation of a mathematics methods course. School Science & Mathematics, 104(5), 226-232. https://doi.org/10.1111/j.1949-8594.2004.tb18245.x

Wilson, N. S., &Bai, H. (2010).The relationships and impact of teachers’ metacognitive knowledge and pedagogical understandings of metacognition. Metacognition and Learning, 5(3), 269-288. https://doi.org/10.1007/s11409-010-9062-4

Van De Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2016). Problem çözme ile öğretim [Teaching through problem solving] (S. Durmuş, Trans.). In S. Durmuş (Ed.), İlkokul ve ortaokul matematiği [Elementary and middle school mathematics] (pp. 32-57). Ankara: Nobel Kitap.

Yavuz, G. & Erbay, H. N. (2015). The analysis of pre-service teachers’ beliefs about mathematical problem solving. Procedia - Social and Behavioral Sciences, 174, 2687 – 2692. https://doi.org/10.1016/j.sbspro.2015.01.953

Yıldırım, S. & Ersözlü, Z. N. (2013). The relationship between students’ metacognitive awareness and their solutions to similar types of mathematical problems. Eurasia Journal of Mathematics, Science and Technology Education, 9(4), 411-415. https://doi.org/10.12973/eurasia.2013.946a

DOI: 10.23917/jramathedu.v6i3.14349

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