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Mobile-Supported Blended Learning for Fractions: Enhancing Conceptual and Procedural Knowledge in Primary School Students

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Submitted   Mar 20, 2025
Published   Jun 23, 2025
Issue    Vol 5 No 2 (2025)
DOI   10.25082/AMLER.2025.02.003

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Maria Arvanitaki corresponding author
Department of Preschool Education, University of Crete, Crete, Greece
Nicholas Zaranis
Department of Preschool Education, University of Crete, Crete, Greece
Michalis Linardakis
Department of Preschool Education, University of Crete, Crete, Greece
Michail Kalogiannakis
Department of Special Education, University of Thessaly, Thessaly, Greece

Abstract

This study explores the impact of a blended learning approach on fifth-grade students’ conceptual and procedural knowledge of fractions. A quasi-experimental design was implemented with 130 fifth grade students from public primary schools in socio-economically homogeneous areas of Heraklion, Crete (control group: n = 64; experimental group: n = 66). The intervention combined mobile-accessible H5P interactive tasks designed on e-Me learning platform, featuring dynamic environments in Geogebra, with hands-on activities using manipulatives and student-constructed models. Emphasis was placed on collaborative learning and verbal articulation of reasoning. Wilcoxon signed-rank tests revealed significant within-group improvements in both groups. However, the experimental group showed greater gains. Mann–Whitney U tests confirmed that improvements in conceptual and procedural knowledge were significantly higher in the experimental group (p = 0.003 and p = 0.008, respectively), with moderate effect sizes. These findings suggest that the blended learning approach substantially supports fraction learning by bridging conceptual and procedural aspects of knowledge. The use of browser-based, open-source software proved effective in creating personalised, engaging learning experiences. This study contributes to the growing discussion on technology-enhanced fraction learning by presenting a flexible, learner-centered approach that empowers teachers to design contextually responsive fraction learning experiences.

Keywords
blended learning, mobile learning, primary education, conceptual knowledge, procedural knowledge

Article Details

How to Cite
Arvanitaki, M., Zaranis, N., Linardakis, M., & Kalogiannakis, M. (2025). Mobile-Supported Blended Learning for Fractions: Enhancing Conceptual and Procedural Knowledge in Primary School Students. Advances in Mobile Learning Educational Research, 5(2), 1449-1462. https://doi.org/10.25082/AMLER.2025.02.003
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References

  1. Abdul Latif, N. H., Shahrill, M., & Hidayat, W. (2024). Mastering fractions and innovating with the station rotation model in blended learning. Infinity Journal, 13(2), 501–530. https://doi.org/10.22460/infinity.v13i2.p501-530
  2. Ampartzaki, M., Tassis, K., Kalogiannakis, M., Pavlidou, V., Christidis, K., Chatzoglidou, S., & Eleftherakis, G. (2024). Assessing the Initial Outcomes of a Blended Learning Course for Teachers Facilitating Astronomy Activities for Young Children. Education Sciences, 14(6), 606. https://doi.org/10.3390/educsci14060606
  3. Anat, K., Shirley, R., & Hanna, L.-Z. (2019). Building a computerized dynamic representation as an instrument for mathematical explanation of division of fractions. International Journal of Mathematical Education in Science and Technology, 51(2), 247–264. https://doi.org/10.1080/0020739x.2019.1648888
  4. Arcavi, A. (2003). Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/a:1024312321077
  5. Arvanitaki, M., & Zaranis, N. (2020). The use of ICT in teaching geometry in primary school. Education and Information Technologies, 25(6), 5003–5016. https://doi.org/10.1007/s10639-020-10210-7
  6. Attard, C., & Curry, C. (2012). Exploring the use of iPads to engage young students with mathematics. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: expanding horizons. Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia. (MERGA-35) (pp. 75-82). MERGA.
  7. Attard, C., & Orlando, J. (2014). Early career teachers, mathematics and technology: device conflict and emerging mathematical knowledge. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice. Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia. (MERGA-37) (pp. 71-78). MERGA.
  8. Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number. Ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. MacMillan.
  9. Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). Academic Press.
  10. Bulut, M., Akçakın, H. Ü., Kaya, G., & Akçakın, V. (2016). The Effects of GeoGebra On Third Grade Primary Students’ Academic Achievement in Fractions. International Electronic Journal of Mathematics Education, 11(2), 347–255. https://doi.org/10.29333/iejme/338
  11. Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777–786. https://doi.org/10.1037/0012-1649.27.5.777
  12. Charalambous, C. Y., & Pitta-Pantazi, D. (2006). Drawing on a Theoretical Model to Study Students’ Understandings of Fractions. Educational Studies in Mathematics, 64(3), 293–316. https://doi.org/10.1007/s10649-006-9036-2
  13. Chilivumbo, C. (2015). Mobile e-learning: The choice between Responsive/Mobile Websites and Mobile Applications for Virtual Learning Environments for increasing access to Higher Education in Malawi. 2015 IST-Africa Conference, 1–15. https://doi.org/10.1109/istafrica.2015.7190520
  14. Clarke, B., & Svanaes, S. (2014). An updated literature review on the use of tablets in education. Family kids and youth, 1-20. https://www.kidsandyouth.com
  15. Cleveland-Innes, M., & Wilton, D. (2018). Guide to Blended Learning. https://doi.org/10.56059/11599/3095
  16. Cohen, L., Manion, L., & Morrison, K. (2017). Research Methods in Education. Routledge. https://doi.org/10.4324/9781315456539
  17. Creswell, J. (2016) Research in Education: Design, conduct and evaluation of quantitative and qualitative research (Translated by Kouvarakou, N.). Ion. (Original work published 2012).
  18. Dogan, A., & IŞIK TERTEMİZ, N. (2020). Fraction models used by primary school teachers. İlköğretim Online, 1888–1901. https://doi.org/10.17051/ilkonline.2020.762538
  19. Ekeh, M. C., Venketsamy, R., Unamba, E. C., & Ugochukwu, N. J. (2021). Using blended-learning strategy in mathematics to strengthen the teaching of geometric 2D shapes and their properties to primary 6 learners. The Independent Journal of Teaching and Learning, 16(2). https://hdl.handle.net
  20. Escuder, A., & Furner, J. M. (2011). The impact of GeoGebra in math teachers’ professional development. In Proceedings of the International Conference on Technologies in Collegiate Mathematics (pp. 76-84). Pearson.
  21. Fabian, K., Topping, K. J., & Barron, I. G. (2015). Mobile technology and mathematics: effects on students’ attitudes, engagement, and achievement. Journal of Computers in Education, 3(1), 77–104. https://doi.org/10.1007/s40692-015-0048-8
  22. Fazal, M., & Bryant, M. M. (2019). Blended learning in middle school math: The question of effectiveness. Journal of Online Learning Research, 5(1), 49-64.
  23. Fütterer, T., Scheiter, K., Cheng, X., & Stürmer, K. (2022). Quality beats frequency? Investigating students’ effort in learning when introducing technology in classrooms. Contemporary Educational Psychology, 69, 102042. https://doi.org/10.1016/j.cedpsych.2022.102042
  24. Gazzawe, F., Mayouf, M., Lock, R., & Alturki, R. (2022). The Role of Machine Learning in E-Learning Using the Web and AI-Enabled Mobile Applications. Mobile Information Systems, 2022, 1–10. https://doi.org/10.1155/2022/3696140
  25. Goodwin, K. (2012). Use of Tablet Technology in the Classroom. NSW Curriculum and Learning Innovation Centre.
  26. Goodwin, K., & Highfield, K. (2012). iTouch and iLearn: An examination of “educational” apps. In Early education and technology for children conference (pp. 14-16). Salt Lake City, Utah, USA.
  27. Green, H., & Hannon, C. (2006). Their Space. Education for a digital generation. DEMOS.
  28. Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–859. https://doi.org/10.1037/a0019824
  29. Hiebert, J. (Ed.). (2013). Conceptual and Procedural Knowledge. Routledge. https://doi.org/10.4324/9780203063538
  30. Indrapangastuti, D., Surjono, H. D., . S., & Yanto, B. E. (2021). Effectiveness of the Blended Learning Model to Improve Students’ Achievement of Mathematical Concepts. Journal of Education and E-Learning Research, 8(4), 423–430. https://doi.org/10.20448/journal.509.2021.84.423.430
  31. Iroko, G. A., & Olaoye, A. A. (2021). Potency of Blended Strategy on Students’ Performance in Algebra at Senior Secondary Schools. International Journal of Innovative Research and Development, 10(3). https://doi.org/10.24940/ijird/2021/v10/i3/mar21039
  32. Jailani, N., Rosli, R., & Mahmud, M. S. (2025). Factors Influencing Mathematics Teachers’ Blended Learning: A Systematic Review. International Journal of Learning, Teaching and Educational Research, 24(1), 397–419. https://doi.org/10.26803/ijlter.24.1.20
  33. Kalogiannakis, M., & Papadakis, S. (2020). The Use of Developmentally Mobile Applications for Preparing Pre-Service Teachers to Promote STEM Activities in Preschool Classrooms. Mobile Learning Applications in Early Childhood Education, 82–100. https://doi.org/10.4018/978-1-7998-1486-3.ch005
  34. Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology, 62, 101896. https://doi.org/10.1016/j.cedpsych.2020.101896
  35. Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101-144). ERIC/SMEAC.
  36. Kieren, T. E. (1980). The rational number construct-its elements and mechanisms. In T. E. Kieren (Ed.), Recent research on number learning (pp. 125-150). Columus, ERIC/SMEAC.
  37. Kieren, T. E. (1993). Rational and fractional numbers: from quotient fields to recursive understanding. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 49-84). Lawrence Erlbaum.
  38. Koleza, E. (2000). Epistemological and didactical approach to elementary mathematical concepts [in Greek]. Leader Books.
  39. Kundu, A., Bej, T., & Rice, M. (2020). Time to engage: Implementing math and literacy blended learning routines in an Indian elementary classroom. Education and Information Technologies, 26(1), 1201–1220. https://doi.org/10.1007/s10639-020-10306-0
  40. Lamon, S. J. (2020). Teaching Fractions and Ratios for Understanding. Routledge. https://doi.org/10.4324/9781003008057
  41. Lamon, S.J. (2007). Rational numbers and proportional reasoning: Towards a theoretical framework for research. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). NCTM.
  42. Laskaris, D., Heretakis, E., Kalogiannakis, M., & Ampartzaki, M. (2019). Critical reflections on introducing e-learning within a blended education context. International Journal of Technology Enhanced Learning, 11(4), 413. https://doi.org/10.1504/ijtel.2019.102550
  43. Laskaris, D., Kalogiannakis, M., & Heretakis, E. (2017). “Interactive evaluation” of an e-learning course within the context of blended education. International Journal of Technology Enhanced Learning, 9(4), 339. https://doi.org/10.1504/ijtel.2017.087793
  44. Mayer, R. E. (2009). Multimedia learning (2nd ed.). Cambridge University Press.
  45. Mayer, R. E. (2014). Cognitive Theory of Multimedia Learning. The Cambridge Handbook of Multimedia Learning, 43–71. https://doi.org/10.1017/cbo9781139547369.005
  46. Moss, J. (2005). Pipes, tubes, and beakers: New approaches to teaching the rational-number system. In M. S. Donovan & J. D. Bransford (Eds.), How students learn: Mathematics in the classroom (pp. 121-162). National Academies Press.
  47. Motteram, G., & Sharma, P. (2009). Blending learning in a web 2.0 world. International Journal of Emerging Technologies and Society, 7(2), 83-112. https://www.academia.edu
  48. Moyer-Packenham, P. S., Ulmer, L. A., Anderson, K. L. (2012). Examining pictorial models and virtual manipulatives for third-grade fraction instruction. Interactive Online Learning. 11(3), 103-120.
  49. Nashiroh, F., & Zainuddin, A. (2023). Development of GeoGebra-Based Fraction Gap Learning Media to Improve Understanding of the Fraction Concept of Grade V Elementary School. DIDAKTIKA TAUHIDI: Jurnal Pendidikan Guru Sekolah Dasar, 10(1), 55–69. https://doi.org/10.30997/dt.v10i1.8238
  50. Ni, Y., & Zhou, Y.-D. (2005). Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias. Educational Psychologist, 40(1), 27–52. https://doi.org/10.1207/s15326985ep4001_3
  51. Niemi, D. (1996). Instructional influence on content area explanations and representational knowledge: Evidence for the construct validity of measures of principled understanding. (CSE Technical Report 403). National Center for Research on Evaluation, Standards, and Student Testing. University of California. https://cresst.org
  52. Obot, P. F. (2023). Impact of blended learning approach on students’ achievement in quadratic and simultaneous equations. International Journal of Trend in Scientific Research and Development, 7(6), 552-558. https://www.ijtsrd.com
  53. Palaigeorgiou, G., Tsolopani, X., Liakou, S., & Lemonidis, C. (2019). Movable, Resizable and Dynamic Number Lines for Fraction Learning in a Mixed Reality Environment. The Challenges of the Digital Transformation in Education, 118–129. https://doi.org/10.1007/978-3-030-11935-5_12
  54. Papadakis, S. (2020). Apps to Promote Computational Thinking Concepts and Coding Skills in Children of Preschool and Pre-Primary School Age. Mobile Learning Applications in Early Childhood Education, 101–121. https://doi.org/10.4018/978-1-7998-1486-3.ch006
  55. Papadakis, S., Alexandraki, F., & Zaranis, N. (2021). Mobile device use among preschool-aged children in Greece. Education and Information Technologies, 27(2), 2717–2750. https://doi.org/10.1007/s10639-021-10718-6
  56. Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2021). Teaching mathematics with mobile devices and the Realistic Mathematical Education (RME) approach in kindergarten. Advances in Mobile Learning Educational Research, 1(1), 5–18. https://doi.org/10.25082/amler.2021.01.002
  57. Papadakis, S., Trampas, A., Barianos, A., Kalogiannakis, M., & Vidakis, N. (2020). Evaluating the Learning Process: The “ThimelEdu” Educational Game Case Study. Proceedings of the 12th International Conference on Computer Supported Education. https://doi.org/10.5220/0009379902900298
  58. Poon, K. K. (2017). Learning fraction comparison by using a dynamic mathematics software – GeoGebra. International Journal of Mathematical Education in Science and Technology, 49(3), 469–479. https://doi.org/10.1080/0020739x.2017.1404649
  59. Post, T., Cramer, K., Behr, M., Lesh, R., & Harel, G. (1993). Curriculum implications of research on the learning, teaching and assessing of rational number concepts. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 327-361). Lawrence Erlbaum.
  60. Powell, A., Watson, J., Staley, P., Patrick, S., Horn, M., Fetzer, L., Hibbard, L., Oglesby, J., & Verma, S. (2015). Blending learning: The evolution of online and face-to-face education from 2008-2015. Promising Practices in Blended and Online Learning Series. https://files.eric.ed.gov
  61. Prensky, M. (2001). Digital Natives, Digital Immigrants Part 1. On the Horizon, 9(5), 1–6. https://doi.org/10.1108/10748120110424816
  62. Reimer, K., & Moyer-Packenham, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24(1), 5-25.
  63. Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175
  64. Rittle-Johnson, B., & Schneider, M. (2014). Developing Conceptual and Procedural Knowledge of Mathematics. The Oxford Handbook of Numerical Cognition, 1118–1134. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
  65. Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346
  66. Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227–1238. https://doi.org/10.1037/a0018170
  67. Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909–918. https://doi.org/10.1037/edu0000025
  68. Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: the new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. https://doi.org/10.1016/j.tics.2012.11.004
  69. Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503–518. https://doi.org/10.1016/j.learninstruc.2004.06.015
  70. Staker, H., & Horn, M.B. (2012). Classifying K-12 blended learning. Innosight Institute. https://www.christenseninstitute.org
  71. Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411. https://doi.org/10.2307/30034943
  72. Thambi, N., & Eu, L. K. (2013). Effect of students’ achievement in fractions using GeoGebra. SAINSAB, 16, 97-106.
  73. UNESCO. (2013). Policy guidelines for mobile learning. UNESCO. http://unesdoc.unesco.org
  74. Vamvakoussi, X., & Vosniadou, S. (2012). Bridging the Gap Between the Dense and the Discrete: The Number Line and the “Rubber Line” Bridging Analogy. Mathematical Thinking and Learning, 14(4), 265–284. https://doi.org/10.1080/10986065.2012.717378
  75. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: Teaching developmentally (9th Ed.). Pearson Education.
  76. Wilkie, K. J., & Roche, A. (2022). Primary teachers’ preferred fraction models and manipulatives for solving fraction tasks and for teaching. Journal of Mathematics Teacher Education, 26(6), 703–733. https://doi.org/10.1007/s10857-022-09542-7
  77. Yaghmour, K. S. (2016). Effectiveness of blended teaching strategy on the achievement of third grade students in mathematics. Journal of Education and Practice, 7(5), 65-73.
  78. Zaranis, N. (2014). The teaching of subtraction using ICT in kindergarten. In Proceedings of the 10th International Symposium EUTIC 2014 (pp. 563-574), Lisbon, Portugal.
  79. Zhang, X., Clements, M. A., & Ellerton, N. F. (2014). Conceptual mis(understandings) of fractions: From area models to multiple embodiments. Mathematics Education Research Journal, 27(2), 233–261. https://doi.org/10.1007/s13394-014-0133-8