Research Article

The Effects of Balance Model and Algebra Tiles Manipulative in Solving Linear Equations in One Variable

Anas Seidu Salifu 1 *
More Detail
1 E. P. College of Education, Bimbilla, GHANA* Corresponding Author
Contemporary Mathematics and Science Education, 3(2), July 2022, ep22012, https://doi.org/10.30935/conmaths/12028
Submitted: 21 October 2021, Published: 17 April 2022
OPEN ACCESS   2165 Views   2747 Downloads
Download Full Text (PDF)

ABSTRACT

The purpose of the study is to compare the achievements of Basic 9 pupils, taught using balance model and algebra tile, with control group who were taught without any manipulative in linear equations involving one variable. The research design is quasi-experimental methods, specifically the nonequivalent group’s pre-test–post-test control or comparison group designs, with all Basic 9 pupils of Bimbilla Municipality forming the population. The sample used was 120 Basic 9 pupils comprising of 70 males and 50 females. Multi-stage cluster sampling procedures was adopted to select the schools in the various circuits in the Municipality and three intact classrooms for the study. The instrument used was achievement test with 10 essay questions on linear equations in one variable. The independent variables were teaching methods using algebra tiles, balance model and traditional method. While the dependent variable is the achievement scores from the pre- and post-test. The results of the ANOVA and independent sample t-test of the study revealed that, there was significant difference between the balance model, algebra tiles groups compared to the control group in post-test analysis, which favored the balance model and algebra tiles groups with large effect size. The study recommends that Basic School mathematics teachers should use the balance model and algebra tiles in the teaching and learning of linear equations in one variable because it will help improve performance in mathematics.

CITATION (APA)

Salifu, A. S. (2022). The Effects of Balance Model and Algebra Tiles Manipulative in Solving Linear Equations in One Variable. Contemporary Mathematics and Science Education, 3(2), ep22012. https://doi.org/10.30935/conmaths/12028

REFERENCES

  1. Aburime, F. E. (2007). How manipulatives affect the mathematics achievement of students in Nigerian schools. Educational Research Quarterly, 31(1), 3-15.
  2. Akkus, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representation preference [Unpublished doctoral dissertation]. Middle East Technical University.
  3. Amoako, J. (2013). Using the balance model to improve the understanding of the principles of solving linear equations in one variable at Buasi Roman Catholic Junior High School [Master’s thesis, University of Education, Winneba].
  4. Atteh, E., Andam, E. A., Amoako, J., Denteh, W., & Wiafe, F. (2017). The impact of using balance model in teaching linear equation. Archives of Current Research International, 11(3), ACRI.35310. https://doi.org/10.9734/ACRI/2017/35310
  5. Battle, T. S. (2007). Infusing math manipulatives: The key to an increase in academic achievement in the mathematics classroom. https://files.eric.ed.gov/fulltext/ED498579.pdf
  6. Brahier, D. J. (2016). Teaching secondary and middle school mathematics. Routledge. https://doi.org/10.4324/9781315685502
  7. Brizuela, B., & Schliemann, A. (2004). Ten-year old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40. http://flm-journal.org/articles/1B12DE724121000F472E47AF244AE3.pdf
  8. Cass, M., Cates, D., Smith, M., & Jackson, C. (2003). Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learning Disabilities: Research & Practice, 18(2), 112-120. https://doi.org/10.1111/1540-5826.00067
  9. 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
  10. Doias, E. D. (2013). The effect of manipulatives on achievement scores in the middle school mathematics class [Ed.D. dissertation, Lindenwood University].
  11. Dugopolski, M. (2002). Elementary and intermediate algebra. McGraw Hill.
  12. Dugopolski, M. (2006). Algebra for college students. McGraw Hill.
  13. Fiakumah, W. K. (2012). Using beam balance to assist DBE students to improve on their conceptual knowledge of linear inequalities in one variable [Master’s thesis, University of Education, Winneba].
  14. Gurbuz, R. (2010). The effort of activity based instruction on conceptual development of seventh grade students in probability. International Journal of Mathematics Education in Science and Technology, 41, 743-767. https://doi.org/10.1080/00207391003675158
  15. Gurbuz, R., & Toprak, Z. (2014). Designation, implementation and evaluation of activities to ensure transition from arithmetic to algebra. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 8(1), 178-203. https://doi.org/10.12973/nefmed.2014.8.1.a8
  16. Heddens, J. W. (1986). Bridging the gap between the concrete and the abstract. The Arithmetic Teacher, 33, 14-17. https://doi.org/10.5951/AT.33.6.0014
  17. Johnson, K. A. (1993). Manipulatives allow everyone to learn mathematics. Contemporary Education, 65, 10-11.
  18. Kog, O., & Baser, N. (2012). The role of visualization approach on students’ attitudes towards and achievements in mathematics. Elementary Education Online, 11(4), 945-957.
  19. Larbi, E. (2011). The effect of algebra tiles on students’ performance in algebra at the junior high school [Unpublished master’s thesis]. University of Cape Coast.
  20. Larbi, E., & Okyere, M. (2014). Algebra tiles manipulative and gender differences in learning and achievement in mathematics: A case of Sunyani West Municipality. Journal of Education and Practice, 5(38), 1-7.
  21. Larbi, E., & Okyere, M. (2016). The use of manipulatives in mathematics education. Journal of Education and Practice, 7(36), 53-61.
  22. Leitze, A. R., & Kitt, N. A. (2000). Using homemade algebra tiles to develop algebra and prealgebra concepts. Mathematics Teacher, 93(6), 462-520. https://doi.org/10.5951/MT.93.6.0462
  23. Magruder, R. L. (2012). Solving linear equations: A comparison of concreate and virtual manipulatives in middle school mathematics [Doctoral dissertation, University of Kentucky].
  24. Mathematical Sciences Education Board. (1998). The nature and role of algebra in the K-14 curriculum: Proceedings of a national symposium (Washington, DC, May 27-28, 1997). National Research Council. https://files.eric.ed.gov/fulltext/ED429801.pdf
  25. Mereku, K. D. (2001). An investigation into factors that influence teachers’ content coverage in primary mathematics. Africa Journal of Educational Studies in Mathematics and Sciences, 1(1), 53-72. https://doi.org/10.4314/ajesms.v1i1.38577
  26. Ogg, B. (2010). What is the impact of math manipulatives on student learning? Master research project of Ohio University.
  27. Palabiyik, U., & Akkus, O. (2011). Algebraic thinking of students in pattern-based algebra teaching their effects on their skills and attitudes towards mathematics. Pamukkale University Faculty of Education Journal, 30, 111-123.
  28. Picciotto, H. (1998). Operation sense, tool-based pedagogy, curricular breadth: A proposal. https://www.mathed.page/early-math/early.html
  29. Salifu, A. S. (2018). The geometric thinking levels of mathematics pre-service teachers’ in Northern Ghana Colleges of Education. Researchjournali’s Journal of Mathematics, 5(3),1-19.
  30. Saraswati, S. (2016). Supporting students’ understanding of linear equations with one variable using algebra tiles. Journal on Mathematics Education, 7(1), 21-32. https://doi.org/10.22342/jme.7.1.2814.19-30
  31. Sebesta, L. M., & Martin, S. R. M. (2004). Fractions: Building a foundation with concrete manipulatives. Illinois Schools Journal, 83(2), 3-23.
  32. Swan, P., & Marshall, L. 2010. Revisiting mathematics manipulative materials. Australian Primary Mathematics Classroom, 15(2),13-19.
  33. Vlassis, J. (2002). The balance model: Hindrance or support for the solving of linear equation with one known. Education Studies in Mathematics, 49(3), 341-359.
  34. WAEC. (2011). WAEC result checker. The West African Examinations Council. https://www.waecdirect.org/
  35. White, K. M. (2012). The effect of an instructional model utilizing hands-on learning and manipulatives on math achievement of middle school students in Georgia [Doctoral dissertation, Liberty University].