Home⇛DAVAO RESEARCH JOURNAL⇛vol. 15 no. 3 (2024)

Utilizing the lattice method to enhance multiplication automaticity in Grade 4 Pupils

Crezel Jane G. Moreno | Bryan L. Susada

Discipline: Education

 

Abstract:

This study introduced a new method to help students who struggle with multiplying multiple digits. This study examined the effect of the lattice approach on multiplication automaticity among Grade 4 students at Cateel Central Elementary School during the school year 2023-2024. Utilizing a quasi-experimental methodology, the study compared two intact groups: a control group with 22 respondents taught using traditional multiplication methods, and an experimental group with 21 respondents taught using the lattice method. Pre-test results indicated that neither the control nor the experimental group met the expectations set by the K to 12 grading system, with grade percentages of 65.68 and 67.22, respectively. Statistical analysis showed no significant difference between the pre-test scores of the two groups, suggesting a similar initial level of multiplication proficiency. Post-test results, however, revealed a significant improvement in the experimental group’s performance, with a grade percentage of 84.77 compared to the control group’s 74.70. The statistical analysis confirmed this difference as significant, with a t-value of -3.383 and a p-value of 0.002. The findings demonstrate the superior efficacy of the lattice method over traditional teaching methods in enhancing multiplication skills among Grade 4 students.



References:

  1. Arguel, A., Lockyer, L., Lipp, O. V., Lodge, J. M., and Kennedy, G. (2017). Inside out: Detecting learners’ confusion to improve interactive digital learning environments. Journal of Educational Computing Research, 55(4), 526–551. https://doi.org/10.1177/0735633116674732
  2. Baker, A. T., and Cuevas, J. (2018). The importance of automaticity development in mathematics. Georgia Educational Researcher, 14(2), 13–23. https://doi.org/10.20429/ger.2018.140202
  3. Balancio, J. (2023, December 5). No improvement in learning? 2022 PISA results show Filipino learners still lagging behind in math, reading, science. ABS-CBN News. https://news.abs-cbn.com/news/12/05/23/no-improvement-in-learning-ph-pisa-results
  4. Banaszak, B. (2022). Lattice method of multiplication: Overview and examples. Study.com.
  5.  Boaler, J. (2015a). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.
  6. Boaler, J. (2015b, January 28). Fluency without fear: Research evidence on the best ways to learn math facts. Schudio. https://www.youcubed.org/evidence/fluency-without-fear/
  7. Cardino, J. M., and Ortega-Dela Cruz, R. A. (2020). Understanding of learning styles and teaching strategies towards improving the teaching and learning of mathematics. LUMAT International Journal on Math Science and Technology Education, 8(1). https://doi.org/10.31129/LUMAT.8.1.1348
  8. Chevalier, J. M., and Buckles, D. J. (2019). Participatory action research: Theory and methods for engaged inquiry. Routledge. https://doi.org/10.4324/9781351033268
  9. Del Carmen Chamorro, M. (2021). Can we explain students’ failure in learning multiplication? In Teaching multiplication with lesson study (pp. 265–289). Springer International Publishing. https://doi.org/10.1007/978-3-030-28561-6_11
  10. Donovan, M. M. O. (2021, July 19). An overview of Bruner and Piaget—Cognitive constructivists. Pure. https://pure.au.dk/portal/en/publications/an-overview-of-bruner-and-piagetcognitive-constructivists
  11. Dotan, D., and Zviran-Ginat, S. (2022). Elementary math in elementary school: The effect of interference on learning the multiplication table. Cognitive Research: Principles and Implications, 7(1). https://doi.org/10.1186/s41235-022-00451-0
  12. Gardiner, T. (2016). Teaching mathematics at secondary level. Open Book Publishers. https://doi.org/10.11647/OBP.0071
  13. Goos, M., Vale, C., Stillman, G., Makar, K., Herbert, S., and Geiger, V. (2020). Teaching secondary school mathematics: Research and practice for the 21st century. Routledge. https://doi.org/10.4324/9781003117810
  14. Ines, J. (2023). PH still among lowest in math, science, reading in global student assessment. Rappler. https://www.rappler.com/philippines/for-second-time-ph-ranks-among-lowest-pisa-2022/
  15. International Commission on Mathematical Instruction (ICMI). (2023). The role of mathematics in the overall curriculum. Math Union. https://doi.org/10.1007/978-3-031-13548-4
  16. Javornik, I., and Lipovec, A. (2020). Do alternative algorithms for two-digit multiplication really help students to be more efficient? Academia.
  17. Larsson, K. (2016). Students’ understandings of multiplication. Diva Portal. URN (urn:nbn:se:su:diva-134772)
  18. Leighton, L. (2020). What is the lattice method of multiplication? ResearchGate. https://www.researchgate.net/publication/…
  19. Lewis, C. (2016). How does lesson study improve mathematics instruction? ZDM: The International Journal on Mathematics Education, 48(4), 571–580. https://doi.org/10.1007/s11858-016-0792-x
  20. Lopez, L. A. (2020). Improving teachers’ conceptual knowledge of fractions through online subject-specific professional development. Journal of Mathematics Teacher Education.
  21. Milton, J. H., Flores, M. M., Moore, A. J., Taylor, J. J., and Burton, M. E. (2019). Using the concrete–representational–abstract sequence to teach conceptual understanding of basic multiplication and division. Learning Disability Quarterly: Journal of the Division for Children with Learning Disabilities, 42(1), 32–45. https://doi.org/10.1177/0731948718790089
  22. Moussa-Inaty, J., Causapin, M., and Groombridge, T. (2020). Does language really matter when solving mathematical word problems in a second language? A cognitive load perspective. Educational Studies, 46(1), 18–38. https://doi.org/10.1080/03055698.2018.1516629
  23. Mulwa, E. C. (2015). Difficulties encountered by students in the learning and usage of mathematical terminology: A critical literature review. ERIC. https://eric.ed.gov/?id=EJ1080447
  24. Newton, N., Record, A. E., and Mello, A. J. (2024). Fluency doesn’t just happen in multiplication and division: Strategies and models for teaching the basic facts. Taylor & Francis. ISBN 9781032557007 https://doi.org/10.4324/9781032614229
  25. Obongen, A. V., Allauigan, L. M., Carpo, D. N., and Pablo, M. N. (2020). The effect of introducing the box/lattice method to the competency of Grade 9 students of Holy Spirit National High School in multiplying polynomials. Neliti.com. https://www.scholarzest.com
  26. Organisation for Economic Co-operation and Development. (2023). PISA 2022 results: Factsheets Philippines. https://doi.org/10.1787/471ae22e-en
  27. Ozdem-Yilmaz, Y., and Bilican, K. (2020). Discovery learning—Jerome Bruner. In Springer texts in education (pp. 177–190). Springer International Publishing. https://doi.org/10.1007/978-3-030-43620-9_13
  28. Özenç, M., Dursun, H., and Şahin, S. (2020). The effect of activities developed with web 2.0 tools based on the 5E learning cycle model on the multiplication achievement of 4th graders. Participatory Educational Research, 7(3), 105–123. https://doi.org/10.17275/per.20.37.7.3
  29. Qetrani, S., Ouailal, S., and Achtaich, N. (2021). Enhancing students’ conceptual and procedural knowledge using a new teaching approach of linear equations based on the equivalence concept. Eurasia Journal of Mathematics Science and Technology Education, 17(7), em1978. https://doi.org/10.29333/ejmste/10938
  30. Rannikmäe, M., Holbrook, J., and Soobard, R. (2020). Social constructivism—Jerome Bruner. In Springer texts in education (pp. 259–275). Springer International Publishing. https://doi.org/10.1007/978-3-030-43620-9_18
  31. Rebekawati, A. (2017, January). The effect of using the lattice method on multiplication achievement among elementary students. ResearchGate. https://doi.org/10.2991/aisteel-17.2017.94
  32. Richey, J. E., Andres-Bray, J. M. L., Mogessie, M., Scruggs, R., Andres, J. M. A. L., Star, J. R., Baker, R. S., and McLaren, B. M. (2019). More confusion and frustration, better learning: The impact of erroneous examples. Computers & Education, 139, 173–190. https://doi.org/10.1016/j.compedu.2019.05.012
  33. Rineck, L. M. (2020). A holistic approach to developmental mathematics. University of Wisconsin Milwaukee. https://dc.uwm.edu/etd/2587
  34. Rizzo, A. (2023). The golden ratio theorem: A framework for interchangeability and self-similarity in complex systems. Advances in Pure Mathematics, 13(09), 559–596. https://doi.org/10.4236/apm.2023.139038
  35. Santos, C. (2023). Filipino students still lagging behind in science, reading, math - PISA. RepublicAsia Media, Inc. https://republicasiamedia.com/news/filipino-students-still-lagging-behind-other-countries-in-science-reading-math-pisa/
  36. Sarkingobir, Y., Egbebi, L. F., and Awofala, A. O. A. (2023). Bibliometric analysis of the thinking styles in math and its implications on science learning. International Journal of Essential Competencies in Education, 2(1), 75–87. https://doi.org/10.36312/ijece.v2i1.1391
  37. Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., and Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 123–140. https://doi.org/10.1007/s10857-014-9279-2
  38. Thomas, L. (2020, July 31). Quasi-experimental design. Scribbr. https://www.scribbr.com/methodology/quasi-experimental-design/
  39. Van der Ven, S. H. G., Straatemeier, M., Jansen, B. R. J., Klinkenberg, S., and van der Maas, H. L. J. (2015). Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems. Learning and Individual Differences, 43, 48–62. https://doi.org/10.1016/j.lindif.2015.08.013
  40. Yayuk, E., Purwanto, As’ari, A. R., and Subanji. (2020). Primary school students’ creative thinking skills in mathematics problem solving. European Journal of Educational Research, 9(3), 1281–1295. https://doi.org/10.12973/eu-jer.9.3.1281

Tools


Copyright © 2025  KITE Digital Educational Solutions |  Exclusively distributed by CE-Logic