Research Article

An atomic approach to mathematical modeling in sixth-grade students’ process of creating real-life situation

Mehmet Bekdemir 1 * , Fatih Baş 1
More Detail
1 Department of Mathematics and Science Education, Faculty of Education, Erzincan Binali Yıldırım University, Erzincan, TURKEY* Corresponding Author
International Journal of Professional Development, Learners and Learning, 8(2), 2026, e2611, https://doi.org/10.30935/ijpdll/18751
Submitted: 17 November 2025, Published: 13 June 2026
OPEN ACCESS   16 Views   8 Downloads
Download Full Text (PDF)

ABSTRACT

This study aims to examine the mathematical modeling process of sixth-grade students based on the atomic approach in the context of generating real-life situations related to given mathematical models. The study, which used the case study method, was conducted with the participation of 19 sixth-grade students (successful students in mathematics). During the data collection process, instructional experiment practices were employed, and participants were asked to write about real-life situations related to 15 mathematical models (line graphs) provided to them. Video recordings and group worksheets obtained during the process were subjected to content analysis. According to the first result of this study, sixth-grade students, when generating real-life scenarios related to mathematical models based on the atomic approach, use their own experiences (experiential knowledge) as primary sources and the information they gain from sources such as television and social media (environmental knowledge) as secondary sources. However, students show a more active and productive attitude in modeling processes related to their own experiences. According to the second result of the study, mathematical modeling activities based on the atomic approach contribute to students’ learning and meaningful use of mathematical concepts they have not yet been formally taught. This result supports the idea that such mathematical modeling activities help students learn abstract mathematical concepts by making them concrete. In light of these results, it is recommended that mathematical modeling activities based on the atomic approach be used not only at the sixth-grade level but also in other middle school grades.
Keywords: atomic approach, mathematical modeling, real-life situations, sixth-grade students

CITATION (APA)

Bekdemir, M., & Baş, F. (2026). An atomic approach to mathematical modeling in sixth-grade students’ process of creating real-life situation. International Journal of Professional Development, Learners and Learning, 8(2), e2611. https://doi.org/10.30935/ijpdll/18751

REFERENCES

  1. Albarracín, L., & Gorgorió, N. (2019). Using large number estimation problems in primary education classrooms to introduce mathematical modeling. International Journal of Innovation in Science and Mathematics Education, 27(2), 45-57. https://doi.org/10.30722/IJISME.27.02.004
  2. Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19, 523-545. https://doi.org/10.1007/s10857-015-9309-8
  3. Bekdemir, M., Sağlam Kaya, Y., & Manouchehri, A. (2024). Developing a scale to determine the knowledge of the preservice teachers related to mathematical modelling. Hacettepe University Journal of Education, 39(4), 353-365. https://doi.org/10.16986/huje.2024.529
  4. Garfunkel, S., & Montgomery, M. (Eds.) (2016). GAIMME: Guidelines for assessment & instruction in mathematical modeling education. Consortium for Mathematics and Its Applications & Society for Industrial and Applied Mathematics. https://www.siam.org/media/n2tinywa/gaimme-2nd-ed-final-download-print-bw.pdf
  5. 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
  6. Blomhøj, M., & Kjeldsen, T. H. (2007). Learning the integral concept through mathematical modelling. In CERME 5–Proceedings of the fourth congress of the European Society for Research in Mathematics Education (pp. 2070-2079). https://erme.site/wp-content/uploads/CERME5/WG13.pdf
  7. Blum, W., & Borromeo Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45-58. https://eclass.uoa.gr/modules/document/file.php/MATH601/3rd%20&%204rth%20unit/3rd%20unit_Modelling%20cycle.pdf
  8. Blum, W., & Leiß, D. (2007). How do students’ and teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 222-231). Horwood Publishing. https://doi.org/10.1533/9780857099419.5.221
  9. Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (2007). Modeling and applications in mathematics education. Springer. https://doi.org/10.1007/978-0-387-29822-1
  10. Cakmak Gurel, Z., & Bekdemir, M. (2022). The teacher and peer intervention for pre-service mathematics teachers on the validity of mathematical models. Pedagogical Research, 7(2), Article em0120. https://doi.org/10.29333/pr/11800
  11. Carlisle, W. R., Jung, H., Wickstrom, M. H., Sutcliffe, K., & Kim, H. J. (2025). Insights into pothole damage: Exploring culturally responsive mathematical modeling. International Journal of Science and Mathematics Education, 23(4), 1013-1032. https://doi.org/10.1007/s10763-024-10492-0
  12. Carlson, M. A., Wickstrom, M. H., Burroughs, E. A., & Fulton, E. W. (2016). A case for mathematical modeling in the elementary school classroom. In C. R. Hirsch and A. R. McDuffie (Eds.), Annual Perspectives in mathematics education 2016: Mathematical modeling (pp. 121-129). National Council of Teachers of Mathematics. https://www.nctm.org/Store/Products/Annual-Perspectives-in-Mathematics-Education-2016--Mathematical-Modeling/
  13. Carpenter, T. P., & Romberg, T. A. (2004). Powerful practices in mathematics and science: Research-based practice for teaching and learning. Learning Point https://www.amazon.com/Powerful-Practices-Mathematics-Science-Book/dp/B003UV1IPM
  14. Common Core State Standards Initiative (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices and Council of Chief State School Officers. https://corestandards.org/mathematics-standards/
  15. Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. R. Hirsch, & A. R. McDuffie (Eds.), Annual perspectives in mathematics education 2016: Mathematical modeling (pp. 3-16). National Council of Teachers of Mathematics. https://www.nctm.org/Handlers/AttachmentHandler.ashx?attachmentID=fePJMG5zJqM%3D
  16. Czocher, J. A., White, A., Kularajan, S. S., Roan, E., & Baas, A. (2025). Quantizing and visualizing the influence of scaffolding moves on mathematical modeling competencies. Methods in Psychology, 13, Article 100210. https://doi.org/10.1016/j.metip.2025.100210
  17. Durandt, R., & Lautenbach, G. (2020). Strategic support to students’ competency development in the mathematical modeling process: A qualitative study. Perspectives in Education, 38(1), 211-223. https://doi.org/10.18820/2519593X/pie.v38i1.15
  18. English, L. D. (2012). Data modeling with first-grade students. Educational Studies in Mathematics, 81(1), 15-30. https://doi.org/10.1007/s10649-011-9377-3
  19. English, L. D. (2021). Mathematical and interdisciplinary modeling in optimizing young children’s learning. In J. M. Suh, M. H. Wickstrom, & L. D. English (Eds.), Exploring mathematical modeling with young learners, early mathematics learning and development (pp. 3-23). Springer. https://doi.org/10.1007/978-3-030-63900-6_1
  20. English, L. D., & Doerr, H. M. (2003, July 13-18). Perspective-taking in middle school mathematical modeling: A teacher case study [Conference presentation]. Proceedings of the 27th International Group for the Psychology of Mathematics Education Conference, 2, 357-364. https://eric.ed.gov/?id=ED500952
  21. English, L. D., & Watters, J. J. (2005). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(3), 58-79. https://doi.org/10.1007/BF03217401
  22. English, L. D., Ärlebäck, J. B., & Mousoulides, N. (2016). Reflections on progress in mathematical modeling research. In Á. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education: The journey continues (pp. 383-413). Sense Publishers. https://doi.org/10.1007/978-94-6300-561-6_11
  23. Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621-1627. https://eric.ed.gov/?id=EJ1045031
  24. Galbraith, P., Henn. H.-W., & Niss, M. (2007). Modeling and applications in mathematics education. Springer. https://doi.org/10.1007/978-0-387-29822-1
  25. Geiger, V., Bergman, J., & Frejd, P. (2016). Interpreting curricula to find opportunities for modeling: Case studies from Australia and Sweden. In C. R. Hirsch & A. R. McDuffie (Eds.), Annual perspectives in mathematics education 2016: Mathematical modeling (pp. 207-216). National Council of Teachers of Mathematics. https://www.nctm.org/Store/Products/Annual-Perspectives-in-Mathematics-Education-2016--Mathematical-Modeling/
  26. Gould, H. T. (2013). Teachers’ conceptions of mathematical modeling [PhD thesis, Columbia University]. https://academiccommons.columbia.edu/doi/10.7916/D87D32BS
  27. Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modeling: Approaches and developments from German speaking countries. In G. Greefrath & K. Vorhölter (Eds.), Teaching and learning mathematical modelling. ICME-13 Topical Surveys (pp. 1-42). Springer. https://doi.org/10.1007/978-3-319-45004-9_1
  28. Haines, C., Crouch, R., & Fitzharris, A. (2003). Deconstructing mathematical modelling: Approaches to problem solving. In Q.-X. Ye, W. Blum, K. Houston, & Q.-Y. Jiang (Eds.), Mathematical modelling in education and culture (pp. 41–53). Woodhead Publishing. https://doi.org/10.1533/9780857099556.1.41
  29. Kaiser, G. (2017). The teaching and learning of mathematical modeling. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 267-291). National Council of Teachers of Mathematics. https://www.nctm.org/Store/Products/Compendium-for-Research-in-Mathematics-Education/
  30. Leavy, A., & Hourigan, M. (2018). The role of perceptual similarity, context, and situation when selecting attributes: Considerations made by 5-6-year-olds in data modeling environments. Educational Studies in Mathematics, 97(2), 163-183. https://doi.org/10.1007/s10649-017-9791-2
  31. Lehrer, R., & Schauble, L. (2007). Scientific thinking and scientific literacy: Supporting development in learning in context. In W. Damon, R. M. Lerner, K. A. Renninger, & I. E. Sigel (Eds.), Handbook of child psychology (pp. 153-196). John Wiley and Sons. https://doi.org/10.1002/9780470147658.chpsy0405
  32. Leiß, D., & Wiegand, B., (2005). A classification of teacher interventions in mathematics teaching. ZDM Mathematics Education, 37, 240-245. https://doi.org/10.1007/s11858-005-0015-3
  33. 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. https://doi.org/10.4324/9781410607713
  34. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2-3), 157-189. https://doi.org/10.1080/
  35. 10986065.2003.9679998
  36. Lesh, R., & Lehrer, 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
  37. Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models & modeling perspectives on mathematics problem solving, learning, and teaching? In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education (pp. 161-170). Springer. https://doi.org/10.1007/978-0-387-29822-1_15
  38. Lingefjärd, T. (2007). Mathematical modeling in teacher education—Necessity or unnecessarily. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education (pp. 333-340). Springer. https://doi.org/10.1007/978-0-387-29822-1_35
  39. Manouchehri, A. (2017). Implementing Mathematical Modeling: The challenge of teacher educating. In G. A. Stillman (Ed.), Mathematical modeling and applications: Crossing and Researching Boundaries in Mathematics Education (pp. 421-432). Springer. https://www.researchgate.net/publication/320899350_Implementing_Mathematical_Modelling_The_Challenge_of_Teacher_Educating
  40. Manouchehri, A., Bekdemir, M., & Yao, X. (2020). Facilitating modeling activities in a grade 5 classroom. In G. A. Stillman, G. K. Christine & E. Lampen (Eds.), Mathematical modeling education and sense-making (pp. 187-197). Springer. https://link.springer.com/chapter/10.1007/978-3-030-37673-4_17
  41. Merriam, S. B., & Grenier, R. S. (2019). Qualitative research in practice: Examples for discussion and analysis. Jossey-Bass Publishers. https://www.wiley.com/en-no/shop/general-introductory-education/qualitative-research-in-practice-examples-for-discussion-and-analysis-2nd-edition-p-9781119452027
  42. 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
  43. Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 3-32). Springer. https://doi.org/10.1007/978-0-387-29822-1_1
  44. Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage Publications. https://study.sagepub.com/patton4e
  45. Sokolowski, A. (2015). The effects of mathematical modeling on students’ achievement-meta-analysis of research. IAFOR Journal of Education, 3(1), 93-114. https://doi.org
  46. /10.22492/ije.3.1.06
  47. Steen, L. A., Turner, R., & Burkhardt, H. (2007). Developing mathematical literacy. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education: The 14th ICMI study (pp. 285-294). Springer. https://doi.org/10.1007/978-0-387-29822-1_30
  48. Stender, P., & Kaiser, G. (2015). Scaffolding in complex modeling situations. ZDM Mathematics Education, 47, 1255-1267. https://doi.org/10.1007/s11858-015-0741-0
  49. Stillman, G. (2000). Impact of prior knowledge of task context on approaches to applications tasks. The Journal of Mathematical Behavior, 19(3), 333-361. https://doi.org
  50. /10.1016/S0732-3123(00)00049-3
  51. 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), Article 62. https://doi.org/10.3390/educsci7020062
  52. Wickstrom, M. H. (2017, October 5-8). Mathematical modeling: Challenging the figured worlds of elementary mathematics [Conference session]. Paper presented at the Annual Meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 685-692), Indianapolis, IN, United States. https://eric.ed.gov/?id=ED581352
  53. Zawojewski, J. (2013). Problem solving versus modeling. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 237-243). Springer. https://doi.org/10.1007/978-94-007-6271-8_20