Mathematical Thinking and Problem Solving Performance: The Mediating Role of Hope

Year 2024, Volume: 12 Issue: 23, 148 - 163, 21.03.2024

Tuğba Uygun Rahime Dere Elif Ertem Akbaş

https://doi.org/10.18009/jcer.1389816

Abstract

The purpose of the present study is to provide a mediation model by exploring the relationships among mathematical thinking, hope and problem solving performance in mathematics. The participants of the present study were composed of 311 preservice mathematics teachers. In this mixed method research, these preservice mathematics teachers were conducted to the scales of Dispositional Hope and Mathematical Thinking, and Problem Solving Test. Based on the quantitative data analysis, it was observed that statistically significant relationships among the variables of hope, mathematical thinking and problem solving performance. The quantitative data collected through these instruments were also analyzed by mediation analysis techniques. The qualitative data gathered through semi-structured interviews were analyzed by content analysis technique. These data encouraged the findings acquired from quantitative data analysis. The qualitative findings confirmed the findings of the mediator role of hope. The qualitative findings encouraged the relationships among the variables and the role of mediator.

Keywords

Hope, mathematical thinking, mixed design, preservice mathematics teachers, problem solving performance

Ethical Statement

Since the data of this study were collected before 2020, there is no ethics committee approval.

References

• Arnau, R. C., Rosen, D. H., Finch, J. F., Rhudy, J. L. & Fortunato, V. J. (2007). Longitudinal effects of hope on depression and anxiety: A latent variable analysis. Journal of Personality, 75(1), 1-21.
• Arnett, J. J. (2000). Emerging adulthood: A theory of development from the late teens through the twenties. American Psychologist, 469-480.
• Aspinwall, L. G. & Leaf, S. L. (2002). In search of the unique aspects of hope: Pinning our hopes on positive emotions, future-oriented thinking, hard times, and other people. Psychological Inquiry, 13, 276-288.
• Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody and A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 1–34). Lawrence Erlbaum Associates.
• Benn, L., Harvey, J. E, Gilbert, P., & Irons, C. (2005). Social rank, interpersonal trust and recall of parental rearing in relation to homesickness. Personality and Individual Differences, 8(38), 1813–1822.
• Bowlby, J. (1982). Attachment and loss, Vol. 1, Attachment. Basic Books.
• Bowlby, J. (1973). Attachment and loss, Vol. 2, Separation. Basic Books.
• Cai, J., Moyer, J. C., & Wang, N. (1999). Parental roles in students’ learning of mathematics: An exploratory study. Research in Middle Level Education Quarterly, 22(3), 1–18.
• Chang, E. C. (1998). Hope, problem-solving ability, and coping in a college student population: Some implications for theory and practice. Journal of Clinical Psychology, 54, 953–962.
• Creswell, J. W. (2013). Research design qualitative, quantitative, and mixed method approaches. Sage Publications.
• Cokluk, O., Sekercioglu, G., & Buyukozturk, S. (2012). Sosyal bilimler için çok değişkenli istatistik: SPSS ve LISREL uygulamaları (Vol. 2) [Multivariate statistics for social sciences: SPSS and LISREL applications]. Pegem Akademi.
• Ersoy, E., & Baser, N. (2012). Matematiksel dusunme olceginin gelistirilmesi [The development of mathematical thinking scale]. Kastamonu Egitim Dergisi, 21(49), 1471-1486.
• Grouws, D. A. (1996). Critical issues in problem solving instruction in mathematics. In D. Zhang, T. Sawada, and J. P. Becker (Eds.), Proceedings of the China-Japan-U.S. seminar on mathematical education (pp. 70-93). Carbondale, IL: Board of Trustees of Southern Illinois University.
• Henderson, K. B. & Pingry, R. E. (1953). Problem solving in mathematics. In H. F. Fehr (Ed.), The learning of mathematics: Its theory and practice (21st Yearbook of the National Council of Teachers of Mathematics) (pp. 228-270). National Council of Teachers of Mathematics.
• Irwanto, Saputro, A. D., Rohaeti, E., & Prodjosantoso, A. K. (2018). Promoting critical thinking and problem solving skills of preservice elementary teachers through process-oriented guided-inquiry learning (POGIL). International Journal of Instruction, 11(4), 777-794.
• Karakoca, A. (2011). Altıncı sınıf öğrencilerinin problem çözmede matematiksel düşünmeyi kullanma durumları [Using of mathematical thinking of sixth grade students in problem-solving]. Unpublished master thesis. Eskişehir Osmangazi University, Turkey.
• Kolodner, J., Simpson, R., & Sycara-Cyransky, K. A. (1985). Process Model of Case-Based Reasoning in Problem Solving. Proceedings of IJCAI-85, Los Angeles, CA, 1985, 284-290.
• Köseoğlu, E., Demirci, F., Demir, B. and Özyürek, C. (2017). 7. sınıf öğrencilerinin problem çözmeye yönelik yansıtıcı düşünme becerilerinin incelenmesi: Ordu ili örneği. International e-Journal of Educational Studies (IEJES), 1(1), 60-68.
• Lincoln, Y. S., & Guba, E. G. (1990). Judging the quality of case study reports. Qualitative Studies in Education 3(1), 53-59.
• Marshall, C., & Rossman, G. B. (1989). Designing qualitative research. Sage.
• Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically. Pearson Education Limited.
• Menninger, K. (1939). The academic lecture on hope. The American Journal of Psychiatry, 109, 481-49.
• Oettingen, G., & Gollwitzer P. M. (2002). Turning hope thoughts into goal-directed behavior. Psychological Inquiry, 13, 304-7.
• Parade, S. H., Leerkes, E. M., & Blankson, A. N. (2010). Attachment to parents, social anxiety, and close relationships of female students over the transition to college. Journal of Youth and Adolescence, 39(2), 127-137.
• Peterson, C., & Seligman, M. E. P. (2004). Introduction to a manual of the sanities. In Character strengths and virtues: A handbook and classification (pp. 3–32). American Psychological Association and Oxford University Press.
• Polya, G. (1990). How to solve it: A new aspect of mathematical method.
• Posamentier, A.S., & S. Krulik. 1998. Problem-solving strategies for efficient and elegant solutions: A resource for the mathematics teacher. Corwin Press.
• Quick, J. D., Nelson, D., Matuszek, P., Whittington, J. L. & Quick, J. C. (1996). Social support, secure attachments, and health. In C. L. Cooper, Handbook of Stress, Medicine and Health. CRC Press.
• Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. Oxford University Press.
• Schoenfeld, A. H. (1992): Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In: Grouws, D. A. (Ed.): Handbook of Research on Mathematics, Teaching and Learning (NCTM). – New York, 334–370.
• Snyder, C. R., Harris, C., Anderson, J. R., Holleran, S. A., Irving, L. M., Sigmon, S. T., et al. (1991). The will and theways: Development and validation of an individual-differences measure of hope. Journal of Personality and Social Psychology, 60, 570–585.
• Snyder, C. R., Lapointe, A. B., Crowson, J. J. Jr., & Early, S. (1998). Preferences of high- and low-hope people for self-referential input. Cognition and Emotion, 12, 807–823.
• Snyder, C. R., Lehman, K. A., Kluck, B., & Monsson, Y. (2006). Hope for rehabilitation and vice versa. Rehabilitation Psychology, 51, 89-112.
• Snyder, C. R., Lopez, S. J., Shorey, H. S., Rand, K. L. & Feldman, D. B. (2003). Hope theory, measurements, and applications to school psychology. Psychology Quarterly, 18, 122-139.
• Snyder, C. R., McDermott, D., Cook, W., & Rapoff, M. A. (1997). Hope for the journey: Helping children through good times and bad. Boulder, CO: Westview.
• Snyder, C. R., Rand, K. L., & Sigmon, D. R. (2002). Hope theory: A member of the positive psychology family. In C. R. Snyder, & S. Lopez (Eds.), Handbook of positive psychology (pp. 257–266). OxfordUniversity Press.
• Sookman D., & Pinard, G. (1997).Vulnerability and response to unpredictability, Newness and Change in Obsessive Compulsive Disorder. Congress of European Association of Behavioral and Cognitive Therapies. Venezia (Italy).
• Sullivan, L. E. (2009). The glossary of the social and behavioral sciences. Sage.
• Tabachnick, B.G. & Fidell, L.S. (1996). Using Multivariate Statistics, 3rd ed., CSU, Harper‐Collins, Northridge, CA.
• Tarhan, S. & Bacanlı, H. (2015). Sürekli umut ölçeği’nin Türkçe’ye uyarlanması: Geçerlik ve güvenirlik çalışması [Adaptation of dispositional hope scale into Turkish: Validity and reliability study]. The Journal of Happiness and Well-being 3(1), 1-14.
• Taşdemir, A. (2008). Matematiksel düşünme becerilerinin ilköğretim öğrencilerinin fen ve teknoloji dersindeki akademik başarilari, problem çözme becerileri ve tutumlari üzerine etkileri [The effects of mathematical thinking skills on primary school students' academic achievements, problem-solving skills and attitudes in science and technology courses]. Unpublished doctoral dissertation, Gazi University, Turkey.
• Van de Walle, J. A. (1994). Elementary school mathematics teaching developmentally. Longman.
• Woolfolk, A. E. (1993). Educational psychology. Allyn and Bacon.