Research Article

Fostering cognitive mathematical modeling competencies in 4th-grade students: Cooperative learning strategies

H. Beyza Albayrak 1 * , M. Sencer Özsezer 1 , Kamuran Tarım 1
More Detail
1 Faculty of Education, Çukurova University, Adana, TÜRKİYE* Corresponding Author
European Journal of Science and Mathematics Education, 14(4), October 2026, 665-689, https://doi.org/10.30935/scimath/19598
Published: 13 October 2026
OPEN ACCESS   58 Views   14 Downloads
Download Full Text (PDF)

ABSTRACT

The study aims to explore how 4th-grade students’ cognitive mathematical modeling competencies develop during the implementation of model-eliciting activities within a cooperative learning framework. The study was designed as a qualitative teaching experiment involving eight 4th-grade students, with the longitudinal analysis focusing on three purposively selected focal students representing different initial modeling competency levels. Data were collected through six teaching episodes, four clinical interviews, students’ written solution papers, solution letters, and audio-video recordings, and analyzed using descriptive analysis of the rubric for the assessment of modelling skills. The findings indicate progressive development in the focal students’ cognitive mathematical modeling competencies. In particular, the cooperative learning strategies (think-talk-write, think-pair-share, and timed pair-share) supported students’ progression from result-oriented approaches toward more systematic processes of understanding the task, simplifying, mathematizing, interpreting, and validating. These findings have implications for integrating cooperative learning with model-eliciting activities to support mathematical modeling instruction in elementary mathematics education.
Keywords: mathematical modeling, cognitive modeling competence, cooperative learning strategies, elementary school

CITATION (APA)

Albayrak, H. B., Özsezer, M. S., & Tarım, K. (2026). Fostering cognitive mathematical modeling competencies in 4th-grade students: Cooperative learning strategies. European Journal of Science and Mathematics Education, 14(4), 665-689. https://doi.org/10.30935/scimath/19598

REFERENCES

  1. Afthina, H., & Pramudya, I. (2017). Think pair share using realistic mathematics education approach in geometry learning. Journal of Physics: Conference Series, 895, Article 012025. https://doi.org/10.1088/1742-6596/895/1/012025
  2. Asempapa, R. S. (2015). Mathematical modeling: Essential for elementary and middle school students. Journal of Mathematics Education, 8(1), 16-29.
  3. Astuti, E. P. (2014). Improving students’ writing skill of recount texts by using think-talk-write strategy at grade VIII-B of MTs SMQ Bangko. Journal English Language Teaching, 2(1)38-46.
  4. Biccard, P., & Wessels, D. C. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 375-383). Springer. https://doi.org/10.1007/978-94-007-0910-2_37
  5. Blomhøj, M. (2011). Modelling competency: Teaching, learning and assessing competencies-overview. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 343-347). Springer. https://doi.org/10.1007/978-94-007-0910-2_34
  6. Blum, W. (2011). Can modelling 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 modelling. International perspectives on the teaching and learning of mathematical modelling, vol 1 (pp. 15-30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3
  7. Blum, W. (2015). Quality teaching of mathematical modelling: What do we know? What can we do? In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 73-96). Springer. https://doi.org/10.1007/978-3-319-12688-3
  8. Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  9. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38, 86-95. https://doi.org/10.1007/BF02655883
  10. Canbazoğlu-Albayrak, H. B., & Tarım, K. (2025). How are the cognitive mathematical modelling processes of third grade elementary school students? Asia Pacific Education Review, 26(4), 885-899. https://doi.org/10.1007/s12564-024-10015-0
  11. Chan, C. M. E., Ng, K. E. D., Widjaja, W., & Seto, C. (2012). Assessment of primary 5 students’ mathematical modelling competencies. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 146-178.
  12. Cobb, P., & Steffe, L. (2011). The constructivist researcher as teacher and model builder. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A journey in mathematics education research. Mathematics education library, vol 48 (pp. 19-30). Springer. https://doi.org/10.1007/978-90-481-9729-3_3
  13. Creswell, J. W., & Poth, C. N. (2016). Qualitative inquiry and research design: Choosing among five approaches. SAGE.
  14. Czarnocha, B., & Maj, B. (2008). A teaching experiment. In B. Czarnocha (Ed.), Handbook of mathematics teaching research – a tool for teachers – researchers (pp. 47-58). University of Reszów.
  15. 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
  16. English, L. D. (2006). Mathematical modeling in the elementary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323. https://doi.org/10.1007/s10649-005-9013-1
  17. English, L. D. (2007). Interdisciplinary modelling in the elementary mathematics curriculum. In J. Watson, & K. Beswick (Eds.), Mathematics: Essential research, essential practice (pp. 275-284). MERGA Inc.
  18. English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24-47. https://doi.org/10.1007/BF03217564
  19. English, L. D., & Watters, J. J. (2004). Mathematical modelling with young children. In M. J. Høines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 335-342). PME.
  20. Goldin, G. (2000). A scientific perspective on structures, task-based interviews in mathematics education research. In R. Lesh, & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 547-590). Lawrence Erlbaum Associates, Publishers.
  21. Greefrath, G. (2015). Problem solving methods for mathematical modeling. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice. International perspectives on the teaching and learning of mathematical modelling (pp. 173-183). Springer. https://doi.org/10.1007/978-3-319-18272-8_13
  22. Guswinda, G., Yuanita, P., & Hutapea, N. M. (2019). Improvement of mathematical problem solving and disposition ability of MTs students through strategies think talk write in cooperative learning in Kuantan Singingi Regency. Journal of Educational Sciences, 3(3), 377-389. https://doi.org/10.31258/jes.3.3.p.377-389
  23. Haas, B., Kreis, Y., & Lavicza, Z. (2020). Connecting the real world to mathematical models in elementary schools in Luxemburg. Proceedings of the British Society for Research into Learning Mathematics, 40(2), 1-6.
  24. Haines, C., & Crouch, R. (2007). Mathematical modelling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. New ICMI Study Series, vol 10 (pp. 417-424). Springer. https://doi.org/10.1007/978-0-387-29822-1_46
  25. Herget, W. Jahnke, T., & Kroll, W. (2000). Produktive aufgaben für den mathematikunterricht in der sekundarstufe I [Productive tasks for mathematics lessons in lower secondary education]. Cornelsen.
  26. Huda, S., Munifah, M., & Umam, R. (2020). Think talk write (TTW) learning model on thinking skills, creativity, and problem solving. Journal of Gifted Education and Creativity, 7(1), 25-32.
  27. Indahyanti, R. (2017). Think talk write strategy toward students’ writing ability. Ethical Lingua: Journal of Language Teaching and Literature, 4(2), 139-150. https://doi.org/10.30605/ethicallingua.v4i2.627
  28. Kothiyal, A., Majumdar, R., Murthy, S., & Iyer, S. (2013). Effect of think-pair-share in a large CS1 class: 83% sustained engagement. In Proceedings of the 9th Annual International ACM Conference on International Computing Education Research. https://doi.org/10.1145/2493394.2493408
  29. Leiss, D., Schukajlo, S., Blum, W., Messner, R., & and Pekrun, R. (2010). The role of the situation model in mathematical model- Task analyses, student competencies, and interventions. Journal für Mathematik-Didaktik, 31, 119-141. https://doi.org/10.1007/s13138-010-0006-y
  30. Lesh, R., & Doerr, H. (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 perspective on mathematics problem solving, learning, and teaching (pp. 3-34). Lawrence Erlbaum Associates, Publishers.
  31. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-646). Lawrence Erlbaum Associates, Publishers.
  32. Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. SAGE.
  33. Maaß, J., O’Meara, N., Johnson, P., & O’Donoghue, J. (2018). Mathematical modelling for teachers. Springer. https://doi.org/10.1007/978-3-030-00431-6
  34. Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38, 113-142. https://doi.org/10.1007/BF02655885
  35. Maaß, K., & Mischo, C. (2011). Implementing modelling into day-to-day teaching practice – The project STRATUM and its framework. Journal für Mathematik-Didaktik, 32(1), 103-131. https://doi.org/10.1007/s13138-010-0015-x
  36. Maher, C. A., Powell, A. B., & Uptegrove, E. (2011). Combinatorics and reasoning: Representing, justifying and building isomorphisms. Springer. https://doi.org/10.1007/978-0-387-98132-1
  37. Miles, M. B., & Huberman, A. M. (2016). Qualitative data analysis: An expanded sourcebook. SAGE.
  38. Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293-304. https://doi.org/10.1080/10986060802218132
  39. Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 2-32). Springer. https://doi.org/10.1007/978-0-387-29822-1_1
  40. Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. SAGE.
  41. Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. In I. Putt, R. Farragher, & M. McLean (Eds.), Mathematics education for the third millenium: Towards 2010 (pp. 454-461). MERGA.
  42. Pratiwi, V. U. (2019). Implementing think talk write strategy to enhance students of high school’s writing skill in narrative text. European Journal of Social Sciences, 57(4), 408-418.
  43. Rosyida, F., Zubaidah, S., & Mahanal, S. (2016). Memberdayakan keterampilan berpikir kritis dengan model pembelajaran remap TMPS (reading concept map timed pair share) [Empowering critical thinking skills through the remap TMPS (reading, concept map, timed pair share) learning model]. Biologi, Sains, Lingkungan, dan Pembelajarannya Dalam Upaya Peningkatan Daya Saing Bangsa, 13(1), 209-214. https://doi.org/10.17977/jp.v1i4.6207
  44. Sekerak, J. (2010). Phases of mathematical modelling and competence of high school students. The Teaching of Mathematics, 13(2), 105-112.
  45. Sharma, H. L., & Saarsar, P. (2018). TPS (think-pair-share): An effective cooperative learning strategy for unleashing discussion in classroom interaction. International Journal of Research in Social Sciences, 8(5), 91-100.
  46. Steen, L. A., Turner, R., & Burkhardt, H. (2007). Developing mathematical literacy. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss, (Eds.) Modelling and applications in mathematics education. New ICMI study series, vol 10 (pp. 285-294). Springer. https://doi.org/10.1007/978-0-387-29822-1_30
  47. Steffe, L. P., & Ulrich, C. (2014). Constructivist teaching experiment. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 102-109). Springer. https://doi.org/10.1007/978-94-007-4978-8_32
  48. Sugiarto, D., & Sumarsono, P. (2014). The implementation of think-pair-share model to improve students’ ability in reading narrative texts. International journal of English and Education, 3(3), 206-215.
  49. Suh, J. M., Matson, K., & Seshaiyer, P. (2017). Engaging elementary students in the creative process of mathematizing their world through mathematical modeling. Education Sciences, 7(2), 61-83. https://doi.org/10.3390/educsci7020062
  50. Suh, J., Matson, K., Seshaiyer, P., Jamieson, S., & Tate, H. (2021). Mathematical modeling as a catalyst for equitable mathematics instruction: Preparing teachers and young learners with 21st century skills. Mathematics, 9(2), Article 162. https://doi.org/10.3390/math9020162
  51. Susanto, A. S., Bharata, H., & Dahlan, S. (2018). The effect of cooperative learning model think-talk-write (TTW) type on mathematical problem-solving abilities in terms of learning habits. Al-Jabar: Jurnal Pendidikan Matematika, 9(1), 33-40. https://doi.org/10.24042/ajpm.v9i1.2235
  52. Tekin-Dede, A., & Bukova-Güzel, E. (2018). A rubric development study for the assessment of modeling skills. The Mathematics Educator, 27(2), 33-72. https://doi.org/10.63301/tme.v27i2.2040
  53. Tran, D., & Dougherty, B. J. (2014). Authenticity of mathematical modeling. The Mathematics Teacher, 107(9), 672-678. https://doi.org/10.5951/mathteacher.107.9.0672
  54. Wahyuni, R., Efuansyah, E., & Sukasno, S. (2020). Developing student worksheet based on missouri mathematics project model by using think-talk-write strategy of class VIII. Infinity Journal, 9(1), 81-92. https://doi.org/10.22460/infinity.v9i1.p81-92
  55. Wickstrom, M. H., & Aytes, T. (2018). Elementary modeling: Connecting counting with sharing. Teaching Children Mathematics, 24(5), 300-307. https://doi.org/10.5951/teacchilmath.24.5.0300