Araştırma Makalesi
BibTex RIS Kaynak Göster

Mathematical Modeling Self-Efficacy of Middle School and High School Students

Yıl 2024, Cilt: 11 Sayı: 4, 99 - 114, 07.07.2024
https://doi.org/10.17275/per.24.51.11.4

Öz

Mathematical modeling is a cyclical process involving the competencies of understanding the problem, simplifying, mathematizing, working mathematically, interpreting, and validating. Mathematical modeling self-efficacy beliefs are essential to students’ mathematical modeling performance. This study examined middle and high school students’ mathematical modeling self-efficacy beliefs. The participants consisted of 1091 middle school students and 974 high school students. The data were collected through the “Mathematical Modeling Self-Efficacy Scale [MMSS]”. T-tests and ANOVA test statistics were used to determine the effect of gender, school level, grade level and previous engagement in model-eliciting activities on the mathematical modeling self-efficacy beliefs. The results showed that the mathematical modeling self-efficacy beliefs of middle school students were significantly higher than those of high school students. Furthermore, middle school students’ mathematical modeling self-efficacy beliefs did not differ significantly by gender, while at the high school level there was a significant difference in favor of males. Regarding grade levels, only a statistically significant difference was found between the mathematical modeling self-efficacy beliefs of seventh- and eighth-grade students. Moreover, middle and high school students who had previously engaged in model-eliciting activities had significantly higher mathematical modeling self-efficacy beliefs than those who had not. In the accessible literature, there is no study on the mathematical modeling self-efficacy beliefs of middle and high school students. Therefore, we believe this study’s results will contribute to the literature on mathematical modeling.

Kaynakça

  • Adal, A. A., & Yavuz, İ. (2017). The relationship between mathematics self-efficacy and mathematics anxiety levels of middle school students. International Journal of Field Education, 3(1), 20–41.
  • Albayrak, H. B., & Tarım, K. (2022). Sınıf öğretmeni adaylarının matematiksel modelleme yeterlikleri: Okulda zaman problemi [Mathematical modelling competencies of pre-service primary school teachers: The time at school]. Eğitimde Kuram ve Uygulama [Journal of Theory and Practice in Education], 18(2), 95–112. https://doi.org/10.17244/eku.1163414
  • Artino, A. R. (2012). Academic self-efficacy: from educational theory to instructional practice. Perspectives on Medical Education, 1, 76–85. https://doi.org/10.1007/s40037-012-0012-5
  • Aztekin, S., & Taşpınar Şener, Z. (2015). Türkiye’de matematik eğitimi alanındaki matematiksel modelleme araştırmalarının içerik analizi: Bir meta-sentez çalışması [The content analysis of mathematical modelling studies in Turkey: A meta-synthesis study]. Eğitim ve Bilim [Education and Science], 40(178), 139–161. http://dx.doi.org/10.15390/EB.2015.4125
  • Bandura, A. (1997). Self-efficacy: The exercise of control. W.H. Freeman.
  • Berry, J., & Davies, A. (1996). Written reports. In C. R. Haines & S. Dunthorne (Eds.), Mathematics learning and assessment: Sharing innovative practices. Arnold.
  • Berry, J., & Houston, K. (1995). Mathematical modeling. J. W. Arrowsmith Ltd.
  • Bilgili, S., & Çiltaş, A. (2019). Similarity and differences in visuals in mathematical modeling of primary and secondary mathematics teachers. International Journal of Eurasia Social Sciences, 10(35), 334–353.
  • Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modeling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123–139. https://doi.org/10.1093/teamat/22.3.123
  • Blum, W. (2011). Can modeling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 15–30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45–58.
  • Blum, W., & Leiss, D. (2007). How do students and teachers deal with modeling problems. Mathematical modeling: Education, engineering and economics, 222–231. https://doi.org/10.1533/9780857099419.5.221
  • Boaler, J. (2001). Mathematical modeling and new theories of learning. Teaching Mathematics and Its Applications: International Journal of the IMA, 20(3), 121–128. https://doi.org/10.1093/teamat/20.3.121
  • Bong, M., & Clark, R. E. (1999). Comparison between self-concept and self-efficacy in academic motivation research. Educational Psychologist, 34(3), 139–153. https://doi.org/10.1207/s15326985ep3403_1
  • Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM Mathematics Education, 38, 86–95. https://doi.org/10.1007/BF02655883
  • Borromeo-Ferri, R. (2007). Personal experiences and extra-mathematical knowledge as an influence factor on modeling routes of pupils. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (p. 2080–2089). Zypern.
  • Borromeo-Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. https://doi.org/10.1007/978-3-319-68072-9
  • Brady, C. (2018). Modeling and the representational imagination. ZDM Mathematics Education, 50, 45–59. https://doi.org/10.1007/s11858-018-0926-4
  • Cooper, S. E., & Robinson, D. A. G. (1991). The relationship of mathematics selfefficacy beliefs, mathematics anxiety and performances. Measurement and Evaluation in Counseling and Development, 24(1), 4–11.
  • Dede, Y., Akçakın, V., & Kaya, G. (2018). Examining mathematical modeling competencies of pre-service middle school mathematics teachers by gender: Multidimensional item response theory. Adıyaman University Journal of Educational Sciences, 8(2), 150–169. https://doi.org/10.17984/adyuebd.456626
  • Deniz, D., & Akgün, L. (2018). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi [Investigation of prospective secondary mathematics teachers’ mathematical modelling skills]. Akdeniz Eğitim Araştırmaları Dergisi [Mediterranean Journal of Educational Research], 12(24), 294–312. https://doi.org/10.29329/mjer.2018.147.16
  • Doerr, H. M. (1997). Experiment, simulation and analysis: An integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265–282. https://doi.org/10.1080/0950069970190302
  • Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. https://doi.org/10.2307/30034902
  • Doerr, H. M., Delmas, R., & Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal, 16(2), 86–115. https://doi.org/10.52041/serj.v16i2.186
  • English, L. D. (2009). Promoting interdisciplinarity through mathematical modeling. ZDM Mathematics Education, 41(1–2), 161–181. https://doi.org/10.1007/s11858-008-0106-z
  • English, L. D., & Watters, J. J. (2004). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(16), 58–79. https://doi.org/10.1007/BF03217401
  • Erbas, A. K., Kertil, M., Çetinkaya, B., Cakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621–1627.
  • Erdoğan, F. (2019). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme özyeterliklerinin belirlenmesi [Determination of mathematical modeling self-efficacy of pre-service elementary mathematics teachers]. Mersin Üniversitesi Eğitim Fakültesi Dergisi [Mersin University Journal of the Faculty of Education], 15(1), 118–130. https://doi.org/10.17860/mersinefd.480866
  • Ergene, Ö. (2019). Matematik öğretmeni adaylarının Riemann toplamlarını kullanarak modelleme yoluyla belirli integrali anlama durumlarının incelenmesi. [Investigation of pre-service mathematics teachers’ understanding of definite integral through modelling by using riemann sums]. (Unpublished doctoral dissertation). Marmara Üniversitesi.
  • Ergene, Ö., & Özdemir, A. Ş. (2020). Investigating pre-service elementary mathematics teachers’ perception of integral. Marmara University Atatürk Education Faculty Journal of Educational Sciences, 51(51), 155-176. https://doi.org/10.15285/maruaebd.622149
  • Erkek, Ö., & Işiksal-Bostan, M. (2015). The role of spatial anxiety, geometry self-efficacy and gender in predicting geometry achievement. Elementary Education Online, 14(1), 164–180. https://doi.org/10.17051/io.2015.18256
  • Ferri, R. B., & Blum, W. (2013). Insights into teachers’ unconscious behaviour in modeling contexts. In R. Lesh, P. Galbraith, C. Haines & A. Hurford (Eds.), Modeling Students’ Mathematical Modeling Competencies: ICTMA 13 (pp. 423–432). Springer. https://doi.org/10.1007/978-1-4419-0561-1_36
  • Frejd, P., & Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’ mathematical modeling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modeling (Vol. 1, pp. 407–416). Springer. https://doi.org/10.1007/978-94-007-0910-2_40
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modeling process. ZDM Mathematics Education, 38, 143–162. https://doi.org/10.1007/BF02655886
  • George, D., & Mallery, M. (2010). SPSS for windows step by step: A simple guide and reference, 17.0 update. Pearson.
  • Gravemeijer, K., & Stephan, M. (2002). Emergent models as an instructional design heuristic. In K. Gravemeijer, R. Lehrer, B. Oers & L. Verschaffel (Eds.), Symbolizing, modelling and tool use in mathematics education (pp. 145–169). The Netherlands.
  • Hacıömeroğlu, G., & Elmalı, Ö. (2021). Ortaokul öğrencilerinin matematik öz yeterlik düzeylerinin incelenmesi [Examining middle school students’ mathematics self-efficacy levels]. Journal of Computer and Education Research, 9(17), 353–379. https://doi.org/10.18009/jcer.866760
  • Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self efficacy/mathematics performance correspondence. Journal for Research Mathematics Education, 20(3), 261–273. https://doi.org/10.2307/749515
  • Harrison, G. A. (2001). How do teachers and textbook writers model scientific ideas for students? Research in Science Education, 31, 401–435. https://doi.org/10.1023/A:1013120312331
  • Hiller, S. E., Kitsantas, A., Cheema, J. E., & Poulou, M. (2022). Mathematics anxiety and self-efficacy as predictors of mathematics literacy. International Journal of Mathematical Education in Science and Technology, 53(8), 2133–2151. https://doi.org/10.1080/0020739X.2020.1868589
  • Holenstein, M., Bruckmaier, G., & Grob, A. (2022). How do self-efficacy and self-concept impact mathematical achievement? The case of mathematical modelling. British Journal of Educational Psychology, 92(1), 155–174. https://doi.org/10.1111/bjep.12443
  • Işıksal, M., & Aşkar, P. (2003). İlköğretim öğrencileri için matematik ve bilgisayar özyeterlik algısı ölçekleri [The scales of perceived mathematics and computer self-efficacy for elementary students]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Hacettepe University Journal of Education], 25, 109–118.
  • Kaiser, G., & Maaß, K. (2007). Modeling in lower secondary mathematics classroom-problems and opportunities. In W. Blum, P. Galbraith, H-W. Henn & M. Niss (Eds.), Modeling and Applications in Mathematics Education (Vol.10, pp. 99–108). Springer. https://doi.org/10.1007/978-0-387-29822-1_8
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM Mathematics Education, 38(3), 302–310. https://doi.org/10.1007/BF02652813
  • Karahan, M. & Ergene, Ö. (2023). Bitkisel ürün sigortası modelleme etkinliği bağlamında matematik öğretmen adaylarının modelleme süreçlerinin incelenmesi [Investigation of pre-service mathematics teachers’ modeling processes in the context of crop insurance model-eliciting activity]. Sakarya University Journal of Education Faculty, 23(1), 1-22. https://doi.org/10.53629/sakaefd.1271618
  • Karasar, N. (2006). Bilimsel araştırma yöntemi [Scientific research method]. Nobel Yayınları.
  • Kelly, G. J. (2014). Discourse practices in science learning and teaching. In N. G. Lederman & S. K. Abell (Eds.), Handbook of Research on Science Education (Vol. 2, pp. 321–336). Taylor and Francis. https://doi.org/10.4324/9780203097267
  • Koyuncu, İ., Güzeller, C. O., & Akyüz, D. (2017). The development of a self-efficacy scale for mathematical modeling competencies. International Journal of Assessment Tools in Education, 4(1), 19–36. https://doi.org/10.21449/ijate.256552
  • Lau, W. W. F. (2022). Predicting pre-service mathematics teachers’ teaching and learning conceptions: The role of mathematical beliefs, mathematics self-efficacy, and mathematics teaching efficacy. International Journal of Science and Mathematics Education, 20(6), 1141–1160. https://doi.org/10.1007/s10763-021-10204-y
  • Lesh, R., & Lehler, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2&3), 109–129. https://doi.org/10.1080/10986065.2003.9679996
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 3–33). Lawrence Erlbaum.
  • Ludwig, M., & Xu, B. (2010). A comparative study of modeling competencies among Chinese and German students. Journal für Mathematik-Didaktik, 31(1), 77–97. https://doi.org/10.1007/s13138-010-0005-z
  • Maaß, K. (2006). What are modeling competencies? ZDM Mathematics Education, 38(2), 113–142. https://doi.org/10.1007/BF02655885
  • Mehraein, S., & Gatabi, A. R. (2014). Gender and mathematical modeling competency: primary students’ performance and their attitude. Procedia-Social and Behavioral Sciences, 128, 198–203.
  • Ministry of National Education (MoNE) (2018). Mathematics curriculum (Primary and middle school Grades 1, 2, 3, 4, 5, 6, 7 and 8). MoNE.
  • Muşlu, M., & Çiltaş, A. (2016). The impact of the mathematical modeling method at teaching the subject of the process on natural numbers on the student success. Journal of Bayburt Education Faculty, 11(2), 329–343.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. NCTM.
  • Niss, M. (1989). Aims and scope of applications and modeling in mathematics curricula. In W. Blum, J. S. Berry, R. Biehler, I. Huntley, G. Kaiser-Messmer & L. Profke (Eds.), Applications and Modeling in Learning and Teaching Mathematics (pp. 22–31). Ellis Horwood.
  • Özer, A. Ö., & Bukova Guzel, E. (2016). Öğrenci, öğretmen adayı ve öğretmenlerin bakış açısından matematiksel modelleme problemleri [Mathematical modelling problems from the viewpoint of students, prospective teachers and teachers]. Manisa Celal Bayar Üniversitesi Eğitim Fakültesi Dergisi [Manisa Celal Bayar University Journal of the Faculty of Education], 4(1), 57–73.
  • Özgen, K., & Şeker, İ. (2021). 6. sınıf öğrencilerinin farklı matematiksel modelleme problemlerindeki beceri gelişimlerinin incelenmesi [Investigation of the skill developments of 6th grade students in different mathematical modeling]. Milli Eğitim Dergisi [JAournal of Millî Eğitim], 50(230), 329–358. https://doi.org/10.37669/milliegitim.680760
  • Pajares, F. (2005). Gender differences in mathematics self-efficacy beliefs. In A. Gallagher & J. Kaufman (Eds.), Mind Gap: Gender Differences in Mathematics (pp. 294–315). Cambridge University Press.
  • Pajares, F., & Miller, D. M. (1997). Mathematics self-efficacy and mathematics problem solving: Implications of using different forms of assessments. Journal of Experimental Education, 65(3), 213–228.
  • 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
  • Pajeres, F., & Kranzler, J. H. (1995). An exploraty factor analysis of the Mathematics Self–efficacy Scale–Revised (MSES-R). Measurement and Evaluation in Counseling and Development, 29, 215–228. https://doi.org/10.1080/07481756.1997.12068906
  • Perry, D. R., & Steck, A. K. (2015). Increasing student engagement, self-efficacy, and meta-cognitive self-regulation in the high school geometry classroom: Do iPads help?. Computers in the Schools, 32(2), 122–143. https://doi.org/10.1080/07380569.2015.1036650
  • Pollak, H. (1979). The interaction between mathematics and other school subjects. New Trends in Mathematics Teaching. UNESCO.
  • Potvin, P., & Hasni, A. (2014). Analysis of the decline in interest towards school science and technology from grades 5 through 11. Journal of Science Education and Technology, 23(6), 784–802. https://doi.org/10.1007/s10956-014-9512-x
  • Richardson, J. T. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135-147. https://doi.org/10.1016/j.edurev.2010.12.001
  • Schöber, C., Schütte, K., Köller, O., McElvany, N., & Gebauer, M. M. (2018). Reciprocal effects between self-efficacy and achievement in mathematics and reading. Learning and Individual Differences, 63, 1–11. https://doi.org/10.1016/j.lindif.2018.01.008
  • Siller, H. S., & Kuntze, S. (2011). Modeling as a big idea in mathematics: Knowledge and views of pre-service and in-service teachers. Journal of Mathematical Modeling and Application, 1(6), 33–39.
  • Simamora, R. E., & Saragih, S. (2019). Improving students’ mathematical problem solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966
  • Smith, J. P., di Sessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: a constructivist analysis of knowledge in transition. The Journal of Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
  • Tabachnick, B. G., Fidell, L. S., & Ullman, J. B. (2013). Using multivariate statistics. Pearson.
  • Tekin Dede, A. (2015). Matematik derslerinde öğrencilerin modelleme yeterliklerinin geliştirilmesi: Bir eylem araştırması [Developing students’ modelling competencies in mathematics lessons: An action research study] [Unpublished doctoral dissertation]. Dokuz Eylül Üniversitesi.
  • Tella, A. (2011). An assessment of mathematics self-efficacy of secondary school students in Osun State, Nigeria. IFE Psychologia: An International Journal, 19(1), 430–440. https://doi.org/10.4314/ifep.v19i1.64611
  • Uzar, F. N. (2010). Exploring sources of middle school students’ mathematics self-efficacy with respect to different variables [Unpublished master’s thesis]. Hacettepe Üniversitesi.
  • Uzun H., Ergene, Ö., & Masal, E. (2023). İlköğretim beşinci sınıf öğrencilerinin matematiksel modelleme süreçlerinin incelenmesi: Matematik Köyü’ne gidiyoruz etkinliği [Investigation of mathematical modelling processes of fifth grade students: We are going to the Mathematics Village model-eliciting activity]. Kocaeli University Journal of Education, 6(2), 494-521. http://doi.org/10.33400/kuje.1316782
  • Yel, Ü. (2021). Matematik öğretmen adaylarının matematiksel modelleme öz yeterliklerinin ve bilgi işlemsel düşünme becerilerinin incelenmesi [Examination of pre-service mathematics teachers’ mathematics modeling self-efficacy and computational thinking skills] [Unpublished master’s thesis]. Balıkesir Üniversitesi.
  • Yenilmez, K., & Yıldız, Ş. (2019). Matematiksel modelleme ile ilgili lisansüstü tezlerin tematik içerik analizi [Thematic content analysis of graduate theses related to mathematical modelling]. Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi [Eskişehir Osmangazi University Journal of Social Sciences], 20, 1–22. https://doi.org/10.17494/ogusbd.548180
  • Yıldırım, Z., & Işık, A. (2015). Matematiksel modelleme etkinliklerinin 5. sınıf öğrencilerinin matematik dersindeki akademik başarılarına etkisi [The effects of mathematical modelling activities to academic achievement of the fifth grade students in mathematics course]. Kastamonu Eğitim Dergisi [Kastamonu Education Journal], 23(2), 581–600.
  • Yıldız, E., & Yetim, S. (2024). Mathematical modeling measuring self-efficacy: A scale adaptation study. International Journal of Educational Studies in Mathematics, 11(1), 23–38. https://doi.org/10.17278/ijesim.1438228
  • Zuya, H. E., Kwalat, S. K., & Attah, B. G. (2016). Pre-service teachers’ mathematics self-efficacy and mathematics teaching self-efficacy. Journal of Education and Practice, 7(14), 93–98.
Yıl 2024, Cilt: 11 Sayı: 4, 99 - 114, 07.07.2024
https://doi.org/10.17275/per.24.51.11.4

Öz

Kaynakça

  • Adal, A. A., & Yavuz, İ. (2017). The relationship between mathematics self-efficacy and mathematics anxiety levels of middle school students. International Journal of Field Education, 3(1), 20–41.
  • Albayrak, H. B., & Tarım, K. (2022). Sınıf öğretmeni adaylarının matematiksel modelleme yeterlikleri: Okulda zaman problemi [Mathematical modelling competencies of pre-service primary school teachers: The time at school]. Eğitimde Kuram ve Uygulama [Journal of Theory and Practice in Education], 18(2), 95–112. https://doi.org/10.17244/eku.1163414
  • Artino, A. R. (2012). Academic self-efficacy: from educational theory to instructional practice. Perspectives on Medical Education, 1, 76–85. https://doi.org/10.1007/s40037-012-0012-5
  • Aztekin, S., & Taşpınar Şener, Z. (2015). Türkiye’de matematik eğitimi alanındaki matematiksel modelleme araştırmalarının içerik analizi: Bir meta-sentez çalışması [The content analysis of mathematical modelling studies in Turkey: A meta-synthesis study]. Eğitim ve Bilim [Education and Science], 40(178), 139–161. http://dx.doi.org/10.15390/EB.2015.4125
  • Bandura, A. (1997). Self-efficacy: The exercise of control. W.H. Freeman.
  • Berry, J., & Davies, A. (1996). Written reports. In C. R. Haines & S. Dunthorne (Eds.), Mathematics learning and assessment: Sharing innovative practices. Arnold.
  • Berry, J., & Houston, K. (1995). Mathematical modeling. J. W. Arrowsmith Ltd.
  • Bilgili, S., & Çiltaş, A. (2019). Similarity and differences in visuals in mathematical modeling of primary and secondary mathematics teachers. International Journal of Eurasia Social Sciences, 10(35), 334–353.
  • Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modeling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123–139. https://doi.org/10.1093/teamat/22.3.123
  • Blum, W. (2011). Can modeling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 15–30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45–58.
  • Blum, W., & Leiss, D. (2007). How do students and teachers deal with modeling problems. Mathematical modeling: Education, engineering and economics, 222–231. https://doi.org/10.1533/9780857099419.5.221
  • Boaler, J. (2001). Mathematical modeling and new theories of learning. Teaching Mathematics and Its Applications: International Journal of the IMA, 20(3), 121–128. https://doi.org/10.1093/teamat/20.3.121
  • Bong, M., & Clark, R. E. (1999). Comparison between self-concept and self-efficacy in academic motivation research. Educational Psychologist, 34(3), 139–153. https://doi.org/10.1207/s15326985ep3403_1
  • Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM Mathematics Education, 38, 86–95. https://doi.org/10.1007/BF02655883
  • Borromeo-Ferri, R. (2007). Personal experiences and extra-mathematical knowledge as an influence factor on modeling routes of pupils. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (p. 2080–2089). Zypern.
  • Borromeo-Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. https://doi.org/10.1007/978-3-319-68072-9
  • Brady, C. (2018). Modeling and the representational imagination. ZDM Mathematics Education, 50, 45–59. https://doi.org/10.1007/s11858-018-0926-4
  • Cooper, S. E., & Robinson, D. A. G. (1991). The relationship of mathematics selfefficacy beliefs, mathematics anxiety and performances. Measurement and Evaluation in Counseling and Development, 24(1), 4–11.
  • Dede, Y., Akçakın, V., & Kaya, G. (2018). Examining mathematical modeling competencies of pre-service middle school mathematics teachers by gender: Multidimensional item response theory. Adıyaman University Journal of Educational Sciences, 8(2), 150–169. https://doi.org/10.17984/adyuebd.456626
  • Deniz, D., & Akgün, L. (2018). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi [Investigation of prospective secondary mathematics teachers’ mathematical modelling skills]. Akdeniz Eğitim Araştırmaları Dergisi [Mediterranean Journal of Educational Research], 12(24), 294–312. https://doi.org/10.29329/mjer.2018.147.16
  • Doerr, H. M. (1997). Experiment, simulation and analysis: An integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265–282. https://doi.org/10.1080/0950069970190302
  • Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. https://doi.org/10.2307/30034902
  • Doerr, H. M., Delmas, R., & Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal, 16(2), 86–115. https://doi.org/10.52041/serj.v16i2.186
  • English, L. D. (2009). Promoting interdisciplinarity through mathematical modeling. ZDM Mathematics Education, 41(1–2), 161–181. https://doi.org/10.1007/s11858-008-0106-z
  • English, L. D., & Watters, J. J. (2004). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(16), 58–79. https://doi.org/10.1007/BF03217401
  • Erbas, A. K., Kertil, M., Çetinkaya, B., Cakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621–1627.
  • Erdoğan, F. (2019). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme özyeterliklerinin belirlenmesi [Determination of mathematical modeling self-efficacy of pre-service elementary mathematics teachers]. Mersin Üniversitesi Eğitim Fakültesi Dergisi [Mersin University Journal of the Faculty of Education], 15(1), 118–130. https://doi.org/10.17860/mersinefd.480866
  • Ergene, Ö. (2019). Matematik öğretmeni adaylarının Riemann toplamlarını kullanarak modelleme yoluyla belirli integrali anlama durumlarının incelenmesi. [Investigation of pre-service mathematics teachers’ understanding of definite integral through modelling by using riemann sums]. (Unpublished doctoral dissertation). Marmara Üniversitesi.
  • Ergene, Ö., & Özdemir, A. Ş. (2020). Investigating pre-service elementary mathematics teachers’ perception of integral. Marmara University Atatürk Education Faculty Journal of Educational Sciences, 51(51), 155-176. https://doi.org/10.15285/maruaebd.622149
  • Erkek, Ö., & Işiksal-Bostan, M. (2015). The role of spatial anxiety, geometry self-efficacy and gender in predicting geometry achievement. Elementary Education Online, 14(1), 164–180. https://doi.org/10.17051/io.2015.18256
  • Ferri, R. B., & Blum, W. (2013). Insights into teachers’ unconscious behaviour in modeling contexts. In R. Lesh, P. Galbraith, C. Haines & A. Hurford (Eds.), Modeling Students’ Mathematical Modeling Competencies: ICTMA 13 (pp. 423–432). Springer. https://doi.org/10.1007/978-1-4419-0561-1_36
  • Frejd, P., & Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’ mathematical modeling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modeling (Vol. 1, pp. 407–416). Springer. https://doi.org/10.1007/978-94-007-0910-2_40
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modeling process. ZDM Mathematics Education, 38, 143–162. https://doi.org/10.1007/BF02655886
  • George, D., & Mallery, M. (2010). SPSS for windows step by step: A simple guide and reference, 17.0 update. Pearson.
  • Gravemeijer, K., & Stephan, M. (2002). Emergent models as an instructional design heuristic. In K. Gravemeijer, R. Lehrer, B. Oers & L. Verschaffel (Eds.), Symbolizing, modelling and tool use in mathematics education (pp. 145–169). The Netherlands.
  • Hacıömeroğlu, G., & Elmalı, Ö. (2021). Ortaokul öğrencilerinin matematik öz yeterlik düzeylerinin incelenmesi [Examining middle school students’ mathematics self-efficacy levels]. Journal of Computer and Education Research, 9(17), 353–379. https://doi.org/10.18009/jcer.866760
  • Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self efficacy/mathematics performance correspondence. Journal for Research Mathematics Education, 20(3), 261–273. https://doi.org/10.2307/749515
  • Harrison, G. A. (2001). How do teachers and textbook writers model scientific ideas for students? Research in Science Education, 31, 401–435. https://doi.org/10.1023/A:1013120312331
  • Hiller, S. E., Kitsantas, A., Cheema, J. E., & Poulou, M. (2022). Mathematics anxiety and self-efficacy as predictors of mathematics literacy. International Journal of Mathematical Education in Science and Technology, 53(8), 2133–2151. https://doi.org/10.1080/0020739X.2020.1868589
  • Holenstein, M., Bruckmaier, G., & Grob, A. (2022). How do self-efficacy and self-concept impact mathematical achievement? The case of mathematical modelling. British Journal of Educational Psychology, 92(1), 155–174. https://doi.org/10.1111/bjep.12443
  • Işıksal, M., & Aşkar, P. (2003). İlköğretim öğrencileri için matematik ve bilgisayar özyeterlik algısı ölçekleri [The scales of perceived mathematics and computer self-efficacy for elementary students]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Hacettepe University Journal of Education], 25, 109–118.
  • Kaiser, G., & Maaß, K. (2007). Modeling in lower secondary mathematics classroom-problems and opportunities. In W. Blum, P. Galbraith, H-W. Henn & M. Niss (Eds.), Modeling and Applications in Mathematics Education (Vol.10, pp. 99–108). Springer. https://doi.org/10.1007/978-0-387-29822-1_8
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM Mathematics Education, 38(3), 302–310. https://doi.org/10.1007/BF02652813
  • Karahan, M. & Ergene, Ö. (2023). Bitkisel ürün sigortası modelleme etkinliği bağlamında matematik öğretmen adaylarının modelleme süreçlerinin incelenmesi [Investigation of pre-service mathematics teachers’ modeling processes in the context of crop insurance model-eliciting activity]. Sakarya University Journal of Education Faculty, 23(1), 1-22. https://doi.org/10.53629/sakaefd.1271618
  • Karasar, N. (2006). Bilimsel araştırma yöntemi [Scientific research method]. Nobel Yayınları.
  • Kelly, G. J. (2014). Discourse practices in science learning and teaching. In N. G. Lederman & S. K. Abell (Eds.), Handbook of Research on Science Education (Vol. 2, pp. 321–336). Taylor and Francis. https://doi.org/10.4324/9780203097267
  • Koyuncu, İ., Güzeller, C. O., & Akyüz, D. (2017). The development of a self-efficacy scale for mathematical modeling competencies. International Journal of Assessment Tools in Education, 4(1), 19–36. https://doi.org/10.21449/ijate.256552
  • Lau, W. W. F. (2022). Predicting pre-service mathematics teachers’ teaching and learning conceptions: The role of mathematical beliefs, mathematics self-efficacy, and mathematics teaching efficacy. International Journal of Science and Mathematics Education, 20(6), 1141–1160. https://doi.org/10.1007/s10763-021-10204-y
  • Lesh, R., & Lehler, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2&3), 109–129. https://doi.org/10.1080/10986065.2003.9679996
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 3–33). Lawrence Erlbaum.
  • Ludwig, M., & Xu, B. (2010). A comparative study of modeling competencies among Chinese and German students. Journal für Mathematik-Didaktik, 31(1), 77–97. https://doi.org/10.1007/s13138-010-0005-z
  • Maaß, K. (2006). What are modeling competencies? ZDM Mathematics Education, 38(2), 113–142. https://doi.org/10.1007/BF02655885
  • Mehraein, S., & Gatabi, A. R. (2014). Gender and mathematical modeling competency: primary students’ performance and their attitude. Procedia-Social and Behavioral Sciences, 128, 198–203.
  • Ministry of National Education (MoNE) (2018). Mathematics curriculum (Primary and middle school Grades 1, 2, 3, 4, 5, 6, 7 and 8). MoNE.
  • Muşlu, M., & Çiltaş, A. (2016). The impact of the mathematical modeling method at teaching the subject of the process on natural numbers on the student success. Journal of Bayburt Education Faculty, 11(2), 329–343.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. NCTM.
  • Niss, M. (1989). Aims and scope of applications and modeling in mathematics curricula. In W. Blum, J. S. Berry, R. Biehler, I. Huntley, G. Kaiser-Messmer & L. Profke (Eds.), Applications and Modeling in Learning and Teaching Mathematics (pp. 22–31). Ellis Horwood.
  • Özer, A. Ö., & Bukova Guzel, E. (2016). Öğrenci, öğretmen adayı ve öğretmenlerin bakış açısından matematiksel modelleme problemleri [Mathematical modelling problems from the viewpoint of students, prospective teachers and teachers]. Manisa Celal Bayar Üniversitesi Eğitim Fakültesi Dergisi [Manisa Celal Bayar University Journal of the Faculty of Education], 4(1), 57–73.
  • Özgen, K., & Şeker, İ. (2021). 6. sınıf öğrencilerinin farklı matematiksel modelleme problemlerindeki beceri gelişimlerinin incelenmesi [Investigation of the skill developments of 6th grade students in different mathematical modeling]. Milli Eğitim Dergisi [JAournal of Millî Eğitim], 50(230), 329–358. https://doi.org/10.37669/milliegitim.680760
  • Pajares, F. (2005). Gender differences in mathematics self-efficacy beliefs. In A. Gallagher & J. Kaufman (Eds.), Mind Gap: Gender Differences in Mathematics (pp. 294–315). Cambridge University Press.
  • Pajares, F., & Miller, D. M. (1997). Mathematics self-efficacy and mathematics problem solving: Implications of using different forms of assessments. Journal of Experimental Education, 65(3), 213–228.
  • 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
  • Pajeres, F., & Kranzler, J. H. (1995). An exploraty factor analysis of the Mathematics Self–efficacy Scale–Revised (MSES-R). Measurement and Evaluation in Counseling and Development, 29, 215–228. https://doi.org/10.1080/07481756.1997.12068906
  • Perry, D. R., & Steck, A. K. (2015). Increasing student engagement, self-efficacy, and meta-cognitive self-regulation in the high school geometry classroom: Do iPads help?. Computers in the Schools, 32(2), 122–143. https://doi.org/10.1080/07380569.2015.1036650
  • Pollak, H. (1979). The interaction between mathematics and other school subjects. New Trends in Mathematics Teaching. UNESCO.
  • Potvin, P., & Hasni, A. (2014). Analysis of the decline in interest towards school science and technology from grades 5 through 11. Journal of Science Education and Technology, 23(6), 784–802. https://doi.org/10.1007/s10956-014-9512-x
  • Richardson, J. T. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135-147. https://doi.org/10.1016/j.edurev.2010.12.001
  • Schöber, C., Schütte, K., Köller, O., McElvany, N., & Gebauer, M. M. (2018). Reciprocal effects between self-efficacy and achievement in mathematics and reading. Learning and Individual Differences, 63, 1–11. https://doi.org/10.1016/j.lindif.2018.01.008
  • Siller, H. S., & Kuntze, S. (2011). Modeling as a big idea in mathematics: Knowledge and views of pre-service and in-service teachers. Journal of Mathematical Modeling and Application, 1(6), 33–39.
  • Simamora, R. E., & Saragih, S. (2019). Improving students’ mathematical problem solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966
  • Smith, J. P., di Sessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: a constructivist analysis of knowledge in transition. The Journal of Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
  • Tabachnick, B. G., Fidell, L. S., & Ullman, J. B. (2013). Using multivariate statistics. Pearson.
  • Tekin Dede, A. (2015). Matematik derslerinde öğrencilerin modelleme yeterliklerinin geliştirilmesi: Bir eylem araştırması [Developing students’ modelling competencies in mathematics lessons: An action research study] [Unpublished doctoral dissertation]. Dokuz Eylül Üniversitesi.
  • Tella, A. (2011). An assessment of mathematics self-efficacy of secondary school students in Osun State, Nigeria. IFE Psychologia: An International Journal, 19(1), 430–440. https://doi.org/10.4314/ifep.v19i1.64611
  • Uzar, F. N. (2010). Exploring sources of middle school students’ mathematics self-efficacy with respect to different variables [Unpublished master’s thesis]. Hacettepe Üniversitesi.
  • Uzun H., Ergene, Ö., & Masal, E. (2023). İlköğretim beşinci sınıf öğrencilerinin matematiksel modelleme süreçlerinin incelenmesi: Matematik Köyü’ne gidiyoruz etkinliği [Investigation of mathematical modelling processes of fifth grade students: We are going to the Mathematics Village model-eliciting activity]. Kocaeli University Journal of Education, 6(2), 494-521. http://doi.org/10.33400/kuje.1316782
  • Yel, Ü. (2021). Matematik öğretmen adaylarının matematiksel modelleme öz yeterliklerinin ve bilgi işlemsel düşünme becerilerinin incelenmesi [Examination of pre-service mathematics teachers’ mathematics modeling self-efficacy and computational thinking skills] [Unpublished master’s thesis]. Balıkesir Üniversitesi.
  • Yenilmez, K., & Yıldız, Ş. (2019). Matematiksel modelleme ile ilgili lisansüstü tezlerin tematik içerik analizi [Thematic content analysis of graduate theses related to mathematical modelling]. Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi [Eskişehir Osmangazi University Journal of Social Sciences], 20, 1–22. https://doi.org/10.17494/ogusbd.548180
  • Yıldırım, Z., & Işık, A. (2015). Matematiksel modelleme etkinliklerinin 5. sınıf öğrencilerinin matematik dersindeki akademik başarılarına etkisi [The effects of mathematical modelling activities to academic achievement of the fifth grade students in mathematics course]. Kastamonu Eğitim Dergisi [Kastamonu Education Journal], 23(2), 581–600.
  • Yıldız, E., & Yetim, S. (2024). Mathematical modeling measuring self-efficacy: A scale adaptation study. International Journal of Educational Studies in Mathematics, 11(1), 23–38. https://doi.org/10.17278/ijesim.1438228
  • Zuya, H. E., Kwalat, S. K., & Attah, B. G. (2016). Pre-service teachers’ mathematics self-efficacy and mathematics teaching self-efficacy. Journal of Education and Practice, 7(14), 93–98.
Toplam 82 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Eğitim Üzerine Çalışmalar (Diğer)
Bölüm Research Articles
Yazarlar

Büşra Çaylan Ergene 0000-0002-5567-6791

Özkan Ergene 0000-0001-5119-2813

Erken Görünüm Tarihi 14 Temmuz 2024
Yayımlanma Tarihi 7 Temmuz 2024
Gönderilme Tarihi 23 Mayıs 2024
Kabul Tarihi 10 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 11 Sayı: 4

Kaynak Göster

APA Çaylan Ergene, B., & Ergene, Ö. (2024). Mathematical Modeling Self-Efficacy of Middle School and High School Students. Participatory Educational Research, 11(4), 99-114. https://doi.org/10.17275/per.24.51.11.4