Research Article

Building students’ conceptual understanding of operations on fractions using manipulatives: A junior high school perspective

Kwadwo Amo-Asante 1 * , Ebenezer Bonyah 1
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1 Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, GHANA* Corresponding Author
Mediterranean Journal of Social & Behavioral Research, 7(3), October 2023, 151-159, https://doi.org/10.30935/mjosbr/13381
Published Online: 10 June 2023, Published: 01 October 2023
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ABSTRACT

Mathematics plays a key role because it is one of the important subjects within the foundation that constitute the core curriculum for basic and secondary education. Mathematics must therefore be taught in a way to engage learners to construct their knowledge, which helps them build conceptual understanding using modern teaching strategies. Fractions are the building blocks for a solid conceptual understanding of algebra and other concepts in mathematics, especially at the basic school. Therefore, teachers must use strategies that make lessons more realistic and practical, such as manipulatives. The purpose of the study was to use manipulatives to build students’ conceptual understanding of the operations of fractions. The study design was quasi-experimental, with a pre-/post-test method used for data collection to assess the impact of the intervention design. A sample of 50 junior high school students was selected purposively for the study. The data was analyzed using SPSS v.26. The researchers concluded that using manipulatives in the teaching of fractions improved the students’ performance and helped build their conceptual understanding of the operations of fractions.
Keywords: mathematics, fractions, manipulatives, conceptual understanding

CITATION (APA)

Amo-Asante, K., & Bonyah, E. (2023). Building students’ conceptual understanding of operations on fractions using manipulatives: A junior high school perspective. Mediterranean Journal of Social & Behavioral Research, 7(3), 151-159. https://doi.org/10.30935/mjosbr/13381

REFERENCES

  1. Abudu, A. M., & Mensah, M. A. (2016). Basic schoolteachers’ perceptions about curriculum design in Ghana. Journal of Education and Practice, 7(19), 21-29.
  2. Adendorff, S. A., Mntunjani, L. M., & Siyepu, S. W. (2018). Foundation phase teachers’ use of manipulatives to teach number concepts: A critical analysis. South African Journal of Childhood Education, 8(1), 1-9. https://doi.org/10.4102/sajce.v8i1.495
  3. Adu, E., Mereku, D. K., Assuah, C. K., & Okpoti, C. A. (2017). Effect of multimedia courseware with cooperative learning on senior high school students’ proficiency in solving linear equation word problems. African Journal of Educational Studies in Mathematics and Sciences, 13, 1-11.
  4. Adu-Gyamfi, S., Donkoh, W. J., & Addo, A. A. (2016). Educational reforms in Ghana: Past and present. Journal of Education and Human Development, 5(3), 158-172.
  5. Agyei, E., Agamah, D. C., & Entsie, G. (2022). Availability of manipulatives in teaching and learning of mathematics in colleges of education in Ghana. American Journal of Educational Research, 10(4), 188-193. https://doi.org/10.12691/education-10-4-5
  6. Ajai, J. T., & Imoko, B. I. (2015). Gender differences in mathematics achievement and retention scores: A case of problem-based learning method. International Journal of Research in Education and Science, 1(1), 45-50. https://doi.org/10.21890/ijres.76785
  7. Alkhateeb, H. M. (2001). Gender differences in mathematics achievement among high school students in the United Arab Emirates, 1991-2000. School Science and Mathematics, 101(1), 5-9. https://doi.org/10.1111/j.1949-8594.2001.tb18184.x
  8. Alolga, J. A., & Essel, H. B. (n. d.). Progressive mathematics initiative (PMI): An innovative approach to teaching and learning mathematics, evidence from three senior high schools in Ghana. International Journal of Innovative Science and Research Technology, 6(5), 1135-1143.
  9. Andamon, J. C., & Tan, D. A. (2018). Conceptual understanding, attitude and performance in mathematics of grade 7 students. International Journal of Scientific & Technology Research, 07(08), 96-105.
  10. Armah, S. E., Akayuure, P., & Armah, R. B. (2020). A comparative study of male and female distance learners’ mathematics achievement. Contemporary Mathematics and Science Education, 2(1), ep21001. https://doi.org/10.30935/conmaths/9288
  11. Baah-Duodu, S., Osei-Buabeng, V., Cornelius, E. F., Hegan, J. E., & Nabie, M. J. (2020). Review of literature on teaching and learning geometry and measurement: A case of Ghanaian standards based mathematics curriculum. International Journal of Advances in Scientific Research and Engineering, 6(3), 103-124. https://doi.org/10.31695/IJASRE.2020.33766
  12. Barnes, H. (2005). The theory of realistic mathematics education as a theoretical framework for teaching low attainers in mathematics. Pythagoras, 0(61), 42-57. https://doi.org/10.4102/pythagoras.v0i61.120
  13. Bartolini, M. G., & Martignone, F. (2020). Manipulatives in Mmathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 487-494). Springer. https://doi.org/10.1007/978-3-030-15789-0_93
  14. Berger, N., Mackenzie, E., & Holmes, K. (2020). Positive attitudes towards mathematics and science are mutually beneficial for student achievement: A latent profile analysis of TIMSS 2015. The Australian Educational Researcher, 47(3), 409-444. https://doi.org/10.1007/s13384-020-00379-8
  15. Bingham, T., & Rodriguez, R. C. (2019). Understanding fractions begins with literacy. Texas Association for Literacy Education Yearbook, 6, 9-18.
  16. Boakye, B. A. (2019). Explaining education reforms in Ghana: An institutional and ideational perspective [PhD thesis, University of Saskatchewan].
  17. Bosson-Amedenu, S. (2017). Pre-SHS students’ perception of difficult concepts in junior high school mathematics curriculum in Ghana. Asian Research Journal of Mathematics, 3(2), 1-11. https://doi.org/10.9734/ARJOM/2017/32329
  18. Bouck, E. C., Bassette, L., Shurr, J., Park, J., Kerr, J., & Whorley, A. (2017). Teaching equivalent fractions to secondary students with disabilities via the virtual–representational–abstract instructional sequence. Journal of Special Education Technology, 32(4), 220-231. https://doi.org/10.1177/0162643417727291
  19. Caglayan, G. (2019). Theory of polygonal numbers with Cuisenaire rods manipulatives: Understanding Theon of Smyrna’s arithmetic in a history of mathematics classroom. British Journal for the History of Mathematics, 34(1), 12-22. https://doi.org/10.1080/17498430.2018.1539375
  20. Cain, V. (2021). Schools and screens: A watchful history. The MIT Press. https://doi.org/10.7551/mitpress/12125.001.0001
  21. Cain-Caston, M. (1996). Manipulative queen. Journal of Instructional Psychology, 23(4), 270.
  22. Chappell, M. F., & Strutchens, M. E. (2001). Creating connections: Promoting algebraic thinking with concrete models. Mathematics Teaching in the Middle School, 7(1), 20-25. https://doi.org/10.5951/MTMS.7.1.0020
  23. Clements, D. H. (1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5(7), 400-405. https://doi.org/10.5951/TCM.5.7.0400
  24. Clements, D. H., Sarama, J., & Joswick, C. (2022). Learning and teaching geometry in early childhood. In Special issues in early childhood mathematics education research (pp. 95-131). Brill. https://doi.org/10.1163/9789004510685_005
  25. Collom, G. D. (2021). A quasi-experimental investigation of Tennessee promise and career and technical education postsecondary enrollment responses. Postsecondary Education Research Center. https://trace.tennessee.edu/cgi/viewcontent.cgi?article=1004&context=utk_edleadpubs
  26. Cramer, K., & Henry, A. (2002). Using manipulative models to build number sense for addition of fractions. In B. Litwiller, & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 yearbook (pp. 41-48). National Council of Teachers of Mathematics.
  27. Cramer, K., Monson, D., Whitney, S., Leavitt, S., & Wyberg, T. (2010). Dividing fractions and problem solving. Mathematics Teaching in the Middle School, 15(6), 338-346. https://doi.org/10.5951/MTMS.15.6.0338
  28. Dowling, A. P., Wright, K., & Bailey, K. (2018). Academic collaboration for experiential learning: Perspectives on using archival collections and information literacy in history education. College & Research Libraries News, 79(6), 323. https://doi.org/10.5860/crln.79.6.323
  29. Etikan, I., & Bala, K. (2017). Sampling and sampling methods. Biometrics & Biostatistics International Journal, 5(6), 00149. https://doi.org/10.15406/bbij.2017.05.00149
  30. Heddens, J. W. (1986). Bridging the gap between the concrete and the abstract. The Arithmetic Teacher, 33(6), 14-17. https://doi.org/10.5951/AT.33.6.0014
  31. Heuser, D. (2000). Mathematics workshop: Mathematics class becomes learner centered. Teaching Children Mathematics, 6(5), 288-295. https://doi.org/10.5951/TCM.6.5.0288
  32. Hodges, T. E., Cady, J., & Collins, R. L. (2008). Fraction representation: The not-so-common denominator among textbooks. Mathematics Teaching in the Middle School, 14(2), 78-84. https://doi.org/10.5951/MTMS.14.2.0078
  33. Jimenez, B. A., & Stanger, C. (2017). Math manipulatives for students with severe intellectual disability: A survey of special education teachers. Research, Advocacy, and Practice for Complex and Chronic Conditions, 36(1), 1-12.https://doi.org/10.14434/pders.v36i1.22172
  34. Johnson-Smith, L. (2022). Creatively cultivating a culturally-responsive mathematics classroom. In A. G. raj (Ed.), Creativity as progressive pedagogy: Examinations into culture, performance, and challenges (pp. 268-295). IGI Global. https://doi.org/10.4018/978-1-7998-8287-9.ch013
  35. Kontas, H. (2016). The effect of manipulatives on mathematics achievement and attitudes of secondary school students. Journal of Education and Learning, 5(3), 10. https://doi.org/10.5539/jel.v5n3p10
  36. Larbi, E., & Mavis, O. (2016). The use of manipulatives in mathematics education. Journal of Education and Practice, 7(36), 53-61.
  37. Lee, M. Y., Choy, B. H., & Mizzi, A. (2021). Exploring the introduction of fractions in Germany, Singapore, and South Korea mathematics textbooks. Research in Mathematical Education, 24(2), 111-130.
  38. Maldonado, S. I., Mosqueda, E., Capraro, R. M., & Capraro, M. M. (2018). Language minority students’ mathematics achievement in urban schools: Coursework, race-ethnicity, and English-language proficiency. Penn GSE Perspectives on Urban Education, 15(1), 1.
  39. Marsh, L. G., & Cooke, N. L. (1996). The effects of using manipulatives in teaching math problem solving to students with learning disabilities. Learning Disabilities Research and Practice, 11(1), 58-65.
  40. McNeil, N., & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulatives debate. Theory into Practice, 46(4), 309-316. https://doi.org/10.1080/00405840701593899
  41. Mereku, D. K. (2004). Mathematics curriculum implementation in Ghana. Danjoe Production.
  42. Mereku, D. K. (2010). Five decades of school mathematics in Ghana. Mathematics Connection, 9(8), 73-86. https://doi.org/10.4314/mc.v9i1.61558
  43. Moch, P. L. (2002). Manipulatives work! The Educational Forum, 66(1), 81-87. https://doi.org/10.1080/00131720108984802
  44. MOE, NaCCA. (2019). Ministry of Education Ghana new curriculum. National Council for Curriculum Assessment.
  45. Moore, S. D. (2014). Why teach mathematics with manipulatives? ETA Hand2mind. https://webringlearningtolife.com/media/contentmanager/content/Why_Teach_Math_with_Manips.pdf
  46. 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
  47. Nabie, M. J., Akayuure, P., & Sofo, S. (2013). Integrating problem solving and investigations in mathematics: Ghanaian teachers’ assessment practices. International Journal of Humanities and Social Science, 3(15), 46-56.
  48. NCSM (2013). Improving student achievement in mathematics by using manipulatives with classroom instruction. National Council of Supervisors of Mathematics.
  49. NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  50. Niemi, D. (1996). Assessing conceptual understanding in mathematics: Representations, problem solutions, justifications, and explanations. The Journal of Educational Research, 89(6), 351-363. https://doi.org/10.1080/00220671.1996.9941339
  51. Nikiforidou, Z. (2019). Probabilities and preschoolers: Do tangible versus virtual manipulatives, sample space, and repetition matter? Early Childhood Education Journal, 47(6), 769-777. https://doi.org/10.1007/s10643-019-00964-2
  52. OECD. (2017). OECD science, technology and innovation outlook 2016. OECD Publishing. https://doi.org/10.1787/sti_in_outlook-2016-en
  53. Ross, R., & Kurtz, R. (1993). Making manipulatives work: A strategy for success. The Arithmetic Teacher, 40(5), 254-257. https://doi.org/10.5951/AT.40.5.0254
  54. Ruzic, R., & O’Connell, K. (2001). Manipulatives. National Center of Accessing the General Curriculum.
  55. Sebesta, L. M., & Martin, S. R. M. (2004). Fractions: Building a foundation with concrete manipulatives. Illinois Schools Journal, 83(2), 3-23.
  56. Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Houghton Mifflin,.
  57. Shaw, J. M. (2002). Manipulatives enhance the learning of mathematics.
  58. Stein, M. K., & Bovalino, J. W. (2001). Reflections on practice: Manipulatives: One piece of the puzzle. Mathematics Teaching in the Middle School, 6(6), 356-359. https://doi.org/10.5951/MTMS.6.6.0356
  59. Sulistyaningsih, D., Mawarsari, V. D., & Hidayah, I. (2017). Manipulatives implementation for supporting learning of mathematics for prospective teachers. Journal of Physics: Conference Series, 824(1), 012047. https://doi.org/10.1088/1742-6596/824/1/012047