Tutum ve Öz-Yeterliğin Matematik Başarısı Üzerindeki Etkilerinde Matematik Kaygısının Aracı Rolüne İlişkin Keşfedici Bir Çalışma

Yıl 2023, , 488 - 496, 29.09.2023

Muhammet Fatih Alkan , Şule Yılmaz Özkaya

https://doi.org/10.17556/erziefd.1218193

Öz

İlgili alanyazında matematik kaygısı, matematiğe yönelik tutum ve matematik öz-yeterliğinin matematik başarısına etkisine yönelik birçok çalışma olsa da bu yordayıcı değişkenlerin matematik başarısını açıklarken kendi aralarındaki ilişkilere yönelik çalışma sayısı oldukça sınırlıdır. Bu çalışma matematik başarısı, matematik kaygısı, matematik öz-yeterliği ve matematiğe yönelik tutum arasındaki yapısal ilişkileri incelemiştir. Bu kapsamda, matematik kaygısının matematik başarısı ile matematiğe yönelik tutum ve matematik öz-yeterliği arasındaki ilişkide aracı rolünü içeren bir tam aracılık modeli önerilmiştir. Analizler için 470 ortaokul öğrencisinden toplanan veriler kullanılmıştır. Önerilen ilişkiler, yapısal eşitlik modeli ve bootstrapping yöntemleri kullanılarak incelenmiştir. Ayrıca önerilen modelin matematik başarısını açıklamak ve görgül açıdan en iyi model olup olmadığını belirlemek için bir dizi alternatif model de test edilmiştir. Sonuçlar, önerilen modelin veri ile iyi uyum gösterdiğini ve alternatif modellerden daha üstün olduğunu göstermiştir. Buna göre, matematiğe yönelik tutum ve matematik öz-yeterliği, matematik başarısı üzerinde anlamlı ve olumlu dolaylı etkilere sahiptir ve bu etkilerde matematik kaygısının aracılık rolü bulunmaktadır. Sonuç olarak bu çalışma matematik başarısını açıklamak için güçlü bir kuramsal ve ampirik temele dayanan anlamlı bir model sunmuştur.

Anahtar Kelimeler

Matematik başarısı, matematik kaygısı, matematiğe yönelik tutum, matematik öz-yeterliği

An Exploratory Study on the Effects of Attitude and Self-Efficacy on Math Achievement as Mediated by Math Anxiety

Öz

Although the impacts of math anxiety, attitude toward math, and math self-efficacy on math achievement have been well-defined in the relevant literature, the interrelations among these predictors to explain math achievement are understudied. This study examined the structural relationships among math achievement, math anxiety, math self-efficacy, and attitude toward math. Within this scope, a full mediation model involving math anxiety as the mediator in the relationship of math achievement with attitude toward math and math self-efficacy was proposed. Data collected from 470 middle school students were used for the analyses. Structural equation modeling and bootstrapping methods were used to investigate the proposed relationships. Moreover, various alternative models were tested to see whether the proposed model was empirically the best model to explain math achievement. The findings showed that the proposed model fit the data well and was superior to alternative models. Accordingly, attitude toward math and math self-efficacy had significant and positive indirect effects on math achievement as mediated by math anxiety. In conclusion, the study provided a meaningful model based on a strong theoretical and empirical background to explain math achievement.

Anahtar Kelimeler

Math achievement, math anxiety, attitude toward math, math self-efficacy

Kaynakça

• Abalı Öztürk, Y., & Şahin, Ç. (2015). Matematiğe ilişkin akademik başarı, özyeterlik ve tutum arasındaki ilişkilerin belirlenmesi. The Journal of Academic Social Science Studies, 31, 343-366. http://dx.doi.org/10.9761/JASSS2621
• Adesoji, F. A., & Yara, P. O. (2008). Some student factors as correlates of achievement in mathematics in southwestern Nigeria. European Journal of Scientific Research, 19(3), 424-434.
• Adediwura, A. A. (2011). The development and confirmatory factor analysis of a scale for the measurement of gifted students attitude towards mathematics. World Journal of Education, 1(1), 52-62.
• Aiken, L. R. (1970). Attitudes toward mathematics. Review of Educational Research, 40(4), 551-596. https://doi.org/10.2307/1169746
• Aiken, L. R. (1976). Update on attitudes and other affective variables in learning mathematics. Review of Educational Research, 46(2), 293-311. https://doi.org/10.3102/00346543046002293
• Aiken, L. R., & Dreger, R. M. (1961). The effect of attitudes on performance in mathematics. Journal of Educational Psychology, 52(1), 19–24. https://doi.org/10.1037/h0041309
• Ajzen, I., & Fishbein, M. (1987). Attitude-behavior relations: A theoretical analysis and review of empirical research. Psychological Bulletin, 84(5), 888–918. https://doi.org/10.1037/0033-2909.84.5.888
• Akın, A., & Kurbanoğlu, İ. N. (2011). The relationships between math anxiety, math attitudes, and self-efficacy: A structural equation model. Studia Psychologica, 53(3), 263-273.
• Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103(3), 411-423.
• Ashcraft, M. H. (2022). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185. https://doi.org/10.1111/1467-8721.00196
• Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. https://doi.org/10.1037/0096-3445.130.2.224
• Aşkar, P. (1986). Matematik dersine yönelik tutumu ölçen likert-tipi bir ölçeğin geliştirilmesi. Eğitim ve Bilim(62), 31-36.
• Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W H Freeman & Company.
• Baumgartner, H., & Homburg, C. (1996). Applications of structural equation modeling in marketing and consumer research: A review. International Journal of Research in Marketing, 13(2), 139-161.
• Beilock, S. L., & Carr, T. H. (2005). When high-powered people fail working memory and “choking under pressure” in math. Psychological Science, 16, 101–105. https://doi.org/10.1111%2Fj.0956-7976.2005.00789.x
• Bindak, R. (2005). İlköğretim öğrencileri İçin matematik kaygı ölçeği. Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 17(2), 442-448.
• Brunyé, T. T., Mahoney, C. R., Giles, G. E., Rapp, D. N., Taylor, H. A., & Kanarek, R. B. (2013). Learning to relax: Evaluating four brief interventions for overcoming the negative emotions accompanying math anxiety. Learning and Individual Differences, 27, 1-7. https://doi.org/10.1016/j.lindif.2013.06.008
• Byrne, B. M. (2010). Structural equation modeling with AMOS: Basic concepts, applications, and programming. New York: Routledge.
• Carey, E., Hill, F., Devine, A., & Szücs, D. (2016). The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance. Frontiers in Psychology, 6(1987), 1-6. https://doi.org/10.3389/fpsyg.2015.01987
• Casanova, S., Vukovic, R. K., & Kieffer, M. J. (2021). Do girls pay an unequal price? Black and Latina girls' math attitudes, math anxiety, and mathematics achievement. Journal of Applied Developmental Psychology, 73, 101256. https://doi.org/10.1016/j.appdev.2021.101256
• Chen, L., Bae, S. R., Battista, C., Qin, S., Chen, T., Evans, T. M., & Menon, V. (2018). Positive attitude toward math supports early academic success: Behavioral evidence and neurocognitive mechanisms. Psychological Science, 29(3), 390–402. https://doi.org/10.1177/0956797617735528
• Chen, P. P. (2003). Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students. Learning and Individual Differences, 14(1), 77-90. https://doi.org/10.1016/j.lindif.2003.08.003
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates.
• Cohen, L., Manion, L., & Morrison, K. (2005). Research methods in education (5th ed.). USA: Taylor & Francis. Commodari, E., & La Rosa, V. L. (2021). General academic anxiety and math anxiety in primary school. The impact of math anxiety on calculation skills. Acta Psychologica, 220, 103413.
• Cook, D. A., & Artino, A. R. (2016). Motivation to learn: an overview of contemporary theories. Medical Education, 50(10), 997–1014. https://doi.org/10.1111/medu.13074
• Cvencek, D., Brečić, R., Gacesa, D., & Meltzoff, A. N. (2021). Development of math attitudes and math self‐concepts: Gender differences, implicit–explicit dissociations, and relations to math achievement. Child Development, 92(5), 1673-1678. https://doi.org/10.1111/cdev.13523
• Çavdar, D., & Şahan, H. H. (2019). Matematik dersinde akademik başarı, öz yeterlik ve matematik dersine yönelik tutum arasındaki ilişkinin incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 13(2), 979-999. https://doi.org/10.17522/balikesirnef.605618
• Daker, R. J., Gattas, S. U., Sokolowski, H. M., Green, A. E., & Lyons, I. M. (2021). First-year students’ math anxiety predicts STEM avoidance and underperformance throughout university, independently of math ability. npj Science of Learning, 6(17), 1-17. https://doi.org/10.1038/s41539-021-00095-7
• Devine, A., Fawcett, K., Szucs, D., & Dowker, A. (2012). Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and Brain Functions, 8(1), 33. https://doi.org/10.1186/1744-9081-8-33
• Du, C., Qin, K., Wang, Y., & Xin, T. (2021). Mathematics interest, anxiety, self-efficacy and achievement: Examining reciprocal relations. Learning and Individual Differences, 91, 102060. https://doi.org/10.1016/j.lindif.2021.102060
• European Commission. (2011, June 23). Math-Bridge: European remedial content for mathematics (Math-Bridge). https://joinup.ec.europa.eu/collection/education-culture-and-sport/document/math-bridge-european-remedial-content-mathematics-math-bridge
• Filiz, A., & Gür, H. (2020). Matematikte özyeterlik algılar, motivasyonlar, kaygılar ve tutumlar arasında ilişki. Balıkesir Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 23(44), 783-804. https://doi.org/10.31795/baunsobed.704334
• Forsblom, L., Pekrun, R., Loderer, K., & Peixoto, F. (2022). Cognitive appraisals, achievement emotions, and students’ math achievement: A longitudinal analysis. Journal of Educational Psychology, 114(2), 346–367. https://doi.org/10.1037/edu0000671
• Gula, T., Hoessler, C., & Maciejewski, W. (2015). Seeking mathematics success for college students: a randomized field trial of an adapted approach. International Journal of Mathematical Education in Science and Technology, 46(8), 1130-1148. https://doi.org/10.1080/0020739X.2015.1029026
• Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2006). Multivariate data analysis. Upper Saddle River: Pearson Prentice Hall.
• Hoffman, B., & Schraw, G. (2009). The influence of self-efficacy and working memory capacity on problem-solving efficiency. Learning and Individual Differences, 19(1), 91-100. https://doi.org/10.1016/j.lindif.2008.08.001
• Jain, S., & Dowson, M. (2009). Mathematics anxiety as a function of multidimensional self-regulation and self-efficacy. Contemporary Educational Psychology, 34(3), 240-249. https://doi.org/10.1016/j.cedpsych.2009.05.004
• Jansen, B. R., Louwerse, J., Straatemeier, M., Van der Ven, S. H., Klinkenberg, S., & Van Der Maas, H. L. (2013). The influence of experiencing success in math on math anxiety, perceived math competence, and math performance. Learning and Individual Differences, 24, 190-197. https://doi.org/10.1016/j.lindif.2012.12.014
• Kline, R. B. (2005). Principles and practice of structural equation modeling (2nd edition). The Guilford Press.
• Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd edition). The Guilford Press.
• Lane, J., & Lane, A. (2001). Self-efficacy and academic performance. Social Behavior and Personality: An International Journal, 29(7), 687–693. https://doi.org/10.2224/sbp.2001.29.7.687
• Larsen, N. E., & Jang , E. E. (2022). Instructional practices, students’ self-efficacy and math achievement: A multi-level factor score path analysis. Canadian Journal of Science, Mathematics and Technology Education(21), 803–823. https://doi.org/10.1007/s42330-021-00181-3
• Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9(2), 151-173. https://doi.org/10.1207/S15328007SEM0902_1
• Luttenberger, S., Wimmer, S., & Paechter, M. (2018). Spotlight on math anxiety. Psychology Research and Behavior Management, 11, 311–322. https://doi.org/10.2147/PRBM.S141421
• Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5), 520–540. https://doi.org/10.2307/749772
• MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130-149.
• MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: distribution of the product and resampling methods. Multivariate Behavioral Research, 39(1), 99-128. https://doi.org/10.1207/s15327906mbr3901_4
• Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling, 11(3), 320-341.
• Medikoğlu, O. (2020). İlkokul öğrencilerinin matematik öz yeterlik kaynakları ile matematik kaygı düzeyleri arasındaki ilişkinin incelenmesi. Eğitim Kuram ve Uygulama Araştırmaları Dergisi, 6(1), 35-52.
• Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents' course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82(1), 60–70. https://doi.org/10.1037/0022-0663.82.1.60
• Miller, H., & Bichsel, J. (2004). Anxiety, working memory, gender, and math performance. Personality and Individual Differences, 37(3), 591–606. https://doi.org/10.1016/j.paid.2003.09.029
• Moenikia, M., & Zahed-Babelan, A. (2010). A study of simple and multiple relations between mathematics attitude, academic motivation and intelligence quotient with mathematics achievement. Procedia - Social and Behavioral Sciences, 2(2), 1537-1542. https://doi.org/10.1016/j.sbspro.2010.03.231
• MoNE. (2013). Millî Eğitim Bakanlığı Ortaöğretim Kurumları Yönetmeliği. Resmi Gazete, 28758.
• MoNE. (2019). PISA 2018 Türkiye ön raporu. Ankara: T.C. Millî Eğitim Bakanlığı. http://pisa.meb.gov.tr/eski%20dosyalar/wp-content/uploads/2020/01/PISA_2018_Turkiye_On_Raporu.pdf
• MoNE. (2022, May 17). Matematik seferberliği başladı. https://www.meb.gov.tr/matematik-seferberligi-basladi/haber/26241/tr
• Mustoe, L., & Lawson, D. (2002). Mathematics for the European engineer. A curriculum for the twenty first century. Brussels: The European Society for Engineering Education. http://www.kmf.fgg.uni-lj.si/Matematika/Core%20Curriculum.pdf
• Oppenheimer, S. B., Mills, J. I., Zakeri, A., Payte, T. R., Lidgi, A., & Zavala, M. E. (2020). An approach to improving student success in science, technology, engineering, and mathematics (STEM ) career pathways. Ethnicity & Disease, 30(1), 33-40. https://doi.org/10.18865/ed.30.1.33
• Pajares, F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20(4), 426–443. https://doi.org/10.1006/ceps.1995.1029
• Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86(2), 193–203. https://doi.org/10.1037/0022-0663.86.2.193
• Pantoja, N., Schaeffer, M. W., Rozek, C. S., Beilock, S. L., & Levine, S. C. (2020). Children’s math anxiety predicts their math achievement over and above a key foundational math skill. Journal of Cognition and Development, 21(5), 709-728. https://doi.org/10.1080/15248372.2020.1832098
• Park, D., Ramirez, G., & Beilock, S. L. (2014). The role of expressive writing in math anxiety. Journal of Experimental Psychology: Applied, 20(2), 103–111. https://doi.org/10.1037/xap0000013
• Pekrun, R. (2006). The control-value theory of achievement emotions: Assumptions, corollaries, and implications for educational research and practice. Educational Psychology Review, 18(4), 315–341. https://doi.org/10.1007/s10648-006-9029-9
• Phan, H. P. (2012). Informational sources, self-efficacy and achievement: a temporally displaced approach. Educational Psychology, 32(6), 699-726. https://doi.org/10.1080/01443410.2012.708320
• Pinxten M., Marsh H. W., De Fraine B., Van Den Noortgate W., & Van Damme J. (2014). Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure. British Journal of Educational Psychology, 84(1), 152–174. https://doi.org/10.1111/bjep.12028
• Pohjolainen, S., Nykänen, O., Venho, J., & Kangas, J. (2018). Analysing and improving students’ mathematics skills using ICT-tools. EURASIA Journal of Mathematics, Science and Technology Education, 14(4), 1221-1227. https://doi.org/10.29333/ejmste/81869
• Pyzdrowski, L. J., Sun, Y., Curtis, R., Miller, D., Winn, G., & Hensel , R. A. (2013). Readiness and attitudes as indicators for success in college calculus. International Journal of Science and Mathematics Education, 11, 529–554. https://doi.org/10.1007/s10763-012-9352-1
• Recber, S., Isiksal, M., & Koç, Y. (2018). Investigating self-efficacy, anxiety, attitudes and mathematics achievement regarding gender and school type. Anales de Psicología, 34(1), 41-51. http://dx.doi.org/10.6018/analesps.34.1.229571
• Sağkal, A. S., & Sönmez, M. T. (2022). The effects of perceived parental math support on middle school students’ math engagement: The serial multiple mediation of math self-efficacy and math enjoyment. European Journal of Psychology of Education, 37(2), 341–354. https://doi.org/10.1007/s10212-020-00518-w
• Schumacker, R. E., & Lomax, R. G. (2004). A beginner's guide to structural equation modeling (2nd edition. Lawrence Erlbaum Associates.
• Skaalvik, E. M., Federici, R. A., & Klassen, R. M. (2015). Mathematics achievement and self-efficacy: Relations with motivation for mathematics. International Journal of Educational Research, 72, 129–136. https://doi.org/10.1016/j.ijer.2015.06.008
• Sorvo, R., Kiuru, N., Koponen, T., Aro, T., Viholainen, H., Ahonen, T., & Aro, M. (2022). Longitudinal and situational associations between math anxiety and performance among early adolescents. Annals of the New York Academy of Sciences, 1514(1), 174-186.
• Suárez-Pellicioni, M., Núñez-Peña, M. I., & Colomé, À. (2016). Math anxiety: a review of its cognitive consequences, psychophysiological correlates, and brain bases. Cognitive, Affective, & Behavioral Neuroscience, 16(1), 3–22. https://doi.org/10.3758/s13415-015-0370-7
• Tian, Y., Fang, Y., & Li, J. (2018). The effect of metacognitive knowledge on mathematics performance in self-regulated learning framework—multiple mediation of self-efficacy and motivation. Frontiers in Psychology, 9(2518), 1-11. https://doi.org/10.3389/fpsyg.2018.02518
• Tomasetto, C., Morsanyi, K., Guardabassi, V., & O'Connor, P. A. (2021). Math anxiety interferes with learning novel mathematics contents in early elementary school. Journal of Educational Psychology, 113(2), 315–329. https://doi.org/10.1037/edu0000602
• Umay, A. (2001). İlköğretim matematik öğretmenliği programının matematiğe karşı özyeterlik algısına etkisi. Journal of Qafqaz University(8).
• Weissgerber, S. C., Grünberg, C., Neufeld, L., Steppat, T., & Reinhard, M. (2022). The interplay of math anxiety and math competence for later performance. Social Psychology of Education. https://doi.org/10.1007/s11218-022-09700-y
• Xu, Z., & Jang, E. E. (2017). The role of math self-efficacy in the structural model of extracurricular technology-related activities and junior elementary school students' mathematics ability. Computers in Human Behavior, 68, 547–555. https://doi.org/10.1016/j.chb.2016.11.063
• Yu, X., Zhou, H., Sheng, P., Ren, B., Wang, Y., Wang, H., Zhou, X. (2023). Math anxiety is more closely associated with math performance in female students than in male students. Current Psychology. https://doi.org/10.1007/s12144-023-04349-y
• Yurt, E., & Sünbül, A. M. (2014). A structural equation model explaining 8th grade students’ mathematics achievements. Educational Sciences: Theory & Practice, 14(4), 1642-1652. https://doi.org/10.12738/estp.2014.4.2193
• Zhang, J., Zhao, N., & Kong, K. P. (2019). The relationship between math anxiety and math performance: A meta-analytic investigation. Frontiers in Psychology, 10(1613), 1-17. https://doi.org/10.3389/fpsyg.2019.01613
• Živković, M., Pellizzoni, S., Doz, E., Cuder, A., Mammarella, I., & Passolunghi, M. C. (2023). Math self-efficacy or anxiety? The role of emotional and motivational contribution in math performance. Social Psychology of Education, 1-23. https://doi.org/10.1007/s11218-023-09760-8