Research Article

Learning through virtual manipulatives: Investigating the impact of Gizmos-based lessons on students’ performance in integers

Nur Fatin Haji Ismail 1, Masitah Shahrill 1 * , Daniel Asamoah 1
More Detail
1 Sultan Hassanal Bolkiah Institute of Education, Universiti Brunei Darussalam, Gadong, BRUNEI DARUSSALAM* Corresponding Author
Contemporary Mathematics and Science Education, 4(1), 2023, ep23009,
Published: 20 January 2023
OPEN ACCESS   84 Views   92 Downloads
Download Full Text (PDF)


Understanding integers is critical for further learning in mathematics. However, most students have difficulty understanding integers, especially how to apply sign rules. This study adopted a mixed-method and action research approach to investigate the impact of a virtual manipulative tool (Gizmos) on students’ performance in addition and subtraction of integers. It also explored students’ perceptions of the Gizmos-based intervention. A multistage sampling was used to select 44 year 9 students in one of the secondary schools in Brunei, who were subjected to a Gizmos-based lesson intervention on addition and subtraction of integers. Data were collected through pre-test, post-test, and interviews. Our paired sample t-test showed that student performance after the intervention improved significantly. The results also revealed that the Gizmos-based intervention provided an opportunity for students to play, learn, and visualize integers, enhancing their confidence, understanding, and performance. However, they found it challenging to memorize the rules during Gizmos-based lessons. Based on our results, Gizmos can be an effective tool that can help improve student performance in addition and subtraction of integers when carefully implemented. It has dynamic representative features that provide quick feedback to students when dealing with integers. It is recommended that teachers should continuously guide students to understand and apply sign rules and instructions in using Gizmos.


Haji Ismail, N. F., Shahrill, M., & Asamoah, D. (2023). Learning through virtual manipulatives: Investigating the impact of Gizmos-based lessons on students’ performance in integers. Contemporary Mathematics and Science Education, 4(1), ep23009.


  1. Al-Balushi, S. M., Ambusaidi, A. K., Al-Balushi, K. A., Al-Hajri, F. H., & Al-Sinani, M. S. (2020). Student-centred and teacher-centred science classrooms as visualised by science teachers and their supervisors. Teaching and Teacher Education, 89, 103014.
  2. Ali, H. M. H. H. M., Asamoah, D., & Shahrill, M. (2022). Flipped classroom model through multimedia technology and student performance in directed numbers. Infinity Journal, 11(2), 193-210.
  3. Bofferding, L. (2010). Addition and subtraction with negatives: Acknowledging the multiple meanings of the minus sign. In Proceedings of the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 703-710).
  4. Bolyard, J., & Moyer-Packenham, P. (2006). The impact of virtual manipulatives on student achievement in integer addition and subtraction. In S. Alatorre, J. L. Cortina, M. Saiz, & A. Mendez (Eds.)., Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 879-881). Merida.
  5. Bouck, E. C., & Park, J. (2020). App-based manipulatives and the system of least prompts to support acquisition, maintenance, and generalization of adding integers. Education and Training in Autism and Developmental Disabilities, 55(2), 158-172.
  6. Braun, V., & Clarke, V. (2012). Thematic analysis. In H. Cooper, P. M. Camic, D. L. Long, A. T. Panter, D. Rindskopf, & K. J. Sher (Eds.), APA handbook of research methods in psychology. Research designs: Quantitative, qualitative, neuropsychological, and biological (pp. 57-71). American Psychological Association.
  7. Cai, J., & Knuth, E. J. (2005). Introduction: The development of students’ algebraic thinking in earlier grades from curricular, instructional and learning perspectives. ZDM: The International Journal on Mathematics Education, 37(1), 1-4.
  8. Cetin, H. (2019). Explaining the concept and operations of integer in primary school Mathematics teaching: Opposite model sample. Universal Journal of Educational Research, 7(2), 365-370.
  9. Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education. Routledge.
  10. Chong, W. W. N., Shahrill, M., Asamoah, D., & Latif, S. N. A. (2022). Non-digital card game and year 8 students’ performance in integers. Journal of Mathematics and Science Teacher, 2(1), em007.
  11. Coman, E., Picho, K., McArdle, J., Villagra, V., Dierker, L., & Iordache, E. (2013). The paired t-test as a simple latent change score model. Frontiers in Psychology, 4, 738.
  12. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE.
  13. Durmus, S., & Karakirik, E. (2006). Virtual manipulatives in Mathematics education. The Turkish Online Journal of Educational Technology, 5(1), 117-123.
  14. Eyyam, R., & Yaratan, H. S. (2014). Impact of use of technology in Mathematics lessons on student achievement and attitudes. Social Behavior and Personality: An International Journal, 42(1), 31S-42S.
  15. Finti, H. N. F. M. M., Shahrill, M., & Salleh, S. M. (2016). Integrating virtual manipulative with the use of iPad in the teaching and learning of fractions. Knowledge Management & E-Learning, 8(4), 581-601.
  16. Fisher, M. J., & Marshall, A. P. (2009). Understanding descriptive statistics. Australian Critical Care, 22(2), 93-97.
  17. Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of The National Academy of Sciences, 111(23), 8410-8415.
  18. Fuadiah, N. F., & Suryadi, D. (2019). Teaching and learning activities in classroom and their impact on student misunderstanding: A case study on negative integers. International Journal of Instruction, 12(1), 407-424.
  19. Gningue, S. M., Park, B., West, B., & Fuchs, E. (2014). Applying Bruner’s theory of representation to teach pre-algebra and algebra concepts to community college students using virtual manipulatives. The Electronic Journal of Mathematics and Technology, 8(3), 159-178.
  20. Goh, L. S., Tengah, K. A., Shahrill, M., Tan, A., & Leong, E. (2017). Teaching and learning of integers using hands-on versus virtual manipulatives. In S. De Silva (Ed.), Proceedings of the 3rd International Conference on Education 2017 (Vol. 3, pp. 174-185). The International Institute of Knowledge Management.
  21. Golafshani, N. (2013). Teachers’ beliefs and teaching mathematics with manipulatives. Canadian Journal of Education, 36(3), 137-159.
  22. Hiebert, J. (Ed.). (2013). Conceptual and procedural knowledge: The case of mathematics. Routledge.
  23. Inman, B. L. (2018). Gizmos computer simulations in the mathematics classroom [PhD thesis, Morehead State University].
  24. Japar, I., Asamoah, D., & Shahrill, M. (2022). Addressing student learning gaps in fractions: How effective is synchronous videoconferencing? Jurnal Pendidikan Matematika, 16(1), 103-120.
  25. Kay, R., & Lauricella, S. (2018). Exploring the use of mathematics apps for elementary school students. In T. Bastiaens, J. Van Braak, M. Brown, L. Cantoni, M. Castro, R. Christensen, G. Davidson-Shivers, K. DePryck, M. Ebner, M. Fominykh, C. Fulford, S. Hatzipanagos, G. Knezek, K. Kreijns, G. Marks, E. Sointu, E. Korsgaard Sorensen, J. Viteli, J. Voogt, …, & O. Zawacki-Richter (Eds.), Proceedings of EdMedia: World Conference on Educational Media and Technology (pp. 206-211). Association for the Advancement of Computing in Education.
  26. Khalid, M., & Embong, Z. (2019). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568.
  27. Kolb, D., & Kolb, A. (2008). Experiential learning theory: A dynamic, holistic approach to management learning, education and development. SAGE.
  28. Lamb, L. C., & Thanheiser, E. (2006). Understanding integers: Using balloons and weights software. Algebraic Thinking, 2, 163-164.
  29. Liebeck, P. (1990). Scores and forfeits: An intuitive model for integer arithmetic. Educational Studies in Mathematics, 21, 221-239.
  30. Lim, C. S. (2011). Assessment in Malaysian school mathematics: Issues and concerns [Paper presentation]. The Meeting of the APEC-Tsukuba International Conference.
  31. Michaelides, M. P., Brown, G. T. L., Eklöf, H., & Papanastasiou, E. C. (2019). The relationship of motivation with achievement in Mathematics. Springer.
  32. Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372-377.
  33. Ogunleye, B. O. (2019). Effects of concrete-representational-abstract instructional strategy on chemistry performance of students with mathematics learning difficulties in Ogun State, Nigeria. Kampala International University Journal of Education, 14(2), 135-151.
  34. Piaget, J. (1965). The child’s conception of the world. Littlefield, Adams & Co.
  35. Raines, J. M., & Clark, L. M. (2011). A brief overview on using technology to engage students in mathematics. Current Issues in Education, 14(2), 1-8.
  36. Sahat, N., Tengah, K. A., & Prahmana, R. C. I. (2018). The teaching and learning of addition and subtraction of integers through manipulative in Brunei Darussalam. Journal of Physics: Conference Series, 1088(1), 1-7.
  37. Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 2014, 1-10.
  38. Saunders, M., Lewis, P., & Thornhill, A. (2016). Research methods for business students. Pearson.
  39. Serin, H. (2019), Project based learning in mathematics context. International Journal of Social Sciences & Educational Studies, 5(3), 232-236.
  40. Shanty, N. O. (2016). Investigating students’ development of learning. Journal on Mathematics Education, 7(2), 57-72.
  41. Stephan, M., & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428-464.
  42. Toh, T. S., Tengah, K. A., Shahrill, M., Tan, A., & Leong, E. (2017). The flipped classroom strategy: The effects of implementation at the elementary school level mathematics lessons. In S. De Silva (Ed.), Proceedings of the 3rd International Conference on Education 2017 (Vol. 3, pp. 186-197). The International Institute of Knowledge Management.
  43. Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555-570.
  44. Whitacre, I., Bishop, J. P., Lamb, L. L., Philipp, R. A., Schappelle, B. P., & Lewis, M. (2015). Integers: History, textbook approaches, and children’s productive mathematical intuitions. In Proceedings of the 33rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 913-920).