The impact of discovery-based learning with physical manipulatives in teaching the area of triangles and quadrilaterals on students’ achievement
Aleksandar Milenković 1 * , Jelena Stevanić 1, Natali Zdravković 2
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1 Faculty of Science, University of Kragujevac Serbia, Serbia
2 Elementary School “Žarko Zrenjanin – Uča,” Serbia
* Corresponding Author

Abstract

Discovery-based learning is characterized by a learning environment where students are not passive observers but actively construct new knowledge, which is expected to contribute to their cognitive development. Since it is desirable for students to reflect on their physical actions during this process and considering the positive effects of using physical manipulatives in the teaching process, it naturally follows that discovery-based learning with manipulatives in mathematics education could potentially have a positive impact on students' knowledge acquisition and skill development. The aim of this research is to examine the impact of discovery-based learning with manipulatives, specifically tangram models made from cardboard, on sixth-grade students' achievements in learning the area of triangles and quadrilaterals. The sample consisted of students from four classes at an elementary school in Vranje, Serbia. The research results indicate that discovery-based learning with physical manipulatives leads to better student performance in solving higher-complexity mathematical problems, specifically those that require applying the key property of finite additivity. Also, results support previously observed characteristics in literature - the positive impact of the heuristic approach to teaching on the retention of acquired mathematical knowledge.

Keywords

References

  • Abonyi, O. S., & Umeh, V. O. (2014). Effects of heuristic method of teaching on students’ achievement in algebra. International Journal of Scientific & Engineering Research, 5(2), 1735-1740.
  • Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenebaum, H. R. (2011). Does Discovery-Based Instruction Enhance Learning? Journal of Educational Psychology, 103(1), 1-18. https://doi.org/10.1037/a0021017
  • Baki, A., Kösa, T., & Güven, B. (2011). A comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualization skills of pre-service mathematics teachers. British Journal of Educational Technology, 42(2), 291–310. https://doi.org/10.1111/j.1467-8535.2009.01012.x
  • Baruiz, M., & Dioso, E. (2023). The use of manipulatives and its effects on the students’ mathematics achievement: An experimental study. EPRA International Journal of Environmental Economics, Commerce and Educational Management, 10(8), 55-65. https://doi.org/10.36713/epra14015.
  • Battista, M. T. (1999). The importance of spatial structuring in geometric reasoning. Teaching Children Mathematics, 6(3), 170-177. https://doi.org/10.5951/TCM.6.3.0170
  • Bower, C., Zimmermann, L., Verdine, B., Toub, T. S., Islam, S., Foster, L., ... & Golinkoff, R. M. (2020). Piecing together the role of a spatial assembly intervention in preschoolers’ spatial and mathematics learning: Influences of gesture, spatial language, and socioeconomic status. Developmental Psychology, 56(4), 686-698. https://doi.org/10.1037/dev0000899
  • Carbonneau, K., Marley, S. C., & Selig, J. P. (2012). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380-400. https://doi.org/10.1037/a0031084
  • Clements, D. H. (1999). 'Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60. https://doi.org/10.2304/ciec.2000.1.1.7
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 420-464). Macmillan Publishing.
  • Damjanović, R. (2008). Konkretno iskustvo kao snažan oslonac u formiranju formalnog, apstraktnog mišljenja [Concrete experience as a strong foundation for the development of formal, abstract thinking]. Metodički obzori, 3(2), 35-45.
  • Diano Jr., F. M., Monterde, N. Y., & Diaz, J. M. (2021). Discovery approach in teaching mathematics among Grade Six Students. Solid State Technology, 64(2), 5157-5162.
  • Eby, J. W., Herrel, A. L., & Jordan, M. L. (2005). Teaching K-12 schools: A reflective action approach. Prentice Hall.
  • Gurung, R. K., & Chaudhary, D. K. (2022). Effectiveness of instruction with manipulative materials on fourth graders’ geometry learning achievement. Journal of Bhuwanishankar, 1(1), 69-84. https://doi.org/10.3126/jobs.v1i1.49495
  • Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112. https://doi.org/10.3102/003465430298487
  • Hilbert, T. S., Renkl, A., & Reiss, K. (2008). Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction, 18(1), 54-65. https://doi.org/10.1016/j.learninstruc.2006.10.008
  • Hoon, T. S., Singh, P., Han, C. T., & Kee, K. L. (2013). Heuristic approach experience in solving mathematical problems. Educational Research, 4(8), 607-611.
  • Ikodinović, N., & Dimitrijević, S. (2022). Matematika 6 - udžbenik za šesti razred osnovne škole [Mathematics 6 – Textbook for the Sixth Grade of Primary School]. Klett.
  • In'am, A., & Hajar, S. (2017). Learning geometry through discovery learning using a scientific approach. International Journal of Instruction, 10(1), 55-70. https://doi.org/10.12973/iji.2017.1014a
  • Kablan, Z. (2016). The effect of manipulatives on mathematics achievement across different learning styles. Educational Psychology, 36(2), 277 - 296. https://doi.org/10.1080/01443410.2014.946889.
  • Kamaluddin, M., & Widjajanti, D. B. (2019). The impact of discovery learning on students’ mathematics learning outcomes. Journal of Physics: Conference Series, 1320, 012038. https://doi.org/10.1088/1742-6596/1320/1/012038
  • Khairunnisa, K., & Juandi, D. (2022). Meta-analysis: The effect of discovery learning models on students' mathematical ability. Jurnal Riset Pendidikan Matematika, 9(2), 201-211. https://doi.org/10.21831/jrpm.v9i2.49147
  • Kirschner, P. A., Sweller, J., & Clark, R. J. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86. https://doi.org/10.1207/s15326985ep4102_1
  • Kontaş, H. (2016). The effect of manipulatives on mathematics achievement and attitudes of secondary school students. Journal of Education and Learning, 5(3), 10-20. https://doi.org/10.5539/jel.v5n3p10
  • Maarif, S., & Soebagyo, J. (2024). Discovery learning in geometry class: The implementation of learning to build pre-service teachers' conceptual understanding of geometry based on sociomathematical norms. IndoMath: Indonesia Mathematics Education, 7(1), 20-34. https://doi.org/10.30738/indomath.v7i1.87
  • Milenković, A., & Dimitrijević, S. (2019). Advantages and disadvantages of heuristic teaching in relation to traditional teaching - the case of the parallelogram surface. In J. Milinković, & Z. Kadelburg (Eds.), Research in mathematics education (pp. 74-87). Mathematical Society of Serbia.
  • Mousoulides, N., & Sriraman, B. (2020). Heuristics in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 331-333). Springer. https://doi.org/10.1007/978-3-030-15789-0_172
  • Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197. https://doi.org/10.1023/A:1014596316942
  • Ojose, B., & Sexton, L. (2009). The effect of manipulative materials on mathematics achievement of first grade students. The Mathematics Educator, 12(1), 3-14.
  • Pallant, J. (2020). SPSS survival manual: A step by step guide to data analysis using IBM SPSS. Routledge.
  • Pólya, G. (1954). How to solve it. Princeton University Press.
  • Ponte, R., Viseu, F., Neto, T. B., & Aires, A. P. (2023). Revisiting manipulatives in the learning of geometric figures. Frontiers in Education 8, 1217680. https://doi.org/10.3389/feduc.2023.1217680
  • Pugosa, C. M., Yumol, C., Nogadas, C., & Etcuban, J. (2024). Effects of heuristic method on students’ performance in mathematics. British Journal of Teacher Education and Pedagogy, 3(2), 69-86. https://doi.org/10.32996/bjtep.2024.3.2.8
  • Ramadhani, M. H., Kartono, & Haryani, S. (2023). The effect of using discovery learning-based mathematics learning modules on students' interest in learning mathematics. International Journal of Research and Review, 10(4), 476-480. https://doi.org/10.52403/ijrr.20230458
  • Rosyada, M. N., & Retnawati, H. (2021). Challenges of mathematics learning with heuristic strategies. Al-Jabar: Jurnal Pendidikan Matematika, 12(1), 161-173. https://doi.org/10.24042/ajpm.v12i1.8730
  • Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
  • Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
  • Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498-505. https://doi.org/10.2307/749423
  • Von Glasersfeld, E. (1995). A constructivist approach to teaching. In L. P. Steffe, & J. Gale, Constructivism in Education (pp. 3-15). Erlbaum.
  • Westwood, P. (2008). What teachers need to know about teaching methods. ACER Press.

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