Teaching Practices in Mathematics and Learners’ Learned Competencies

Authors

DOI:

https://doi.org/10.54536/ajahs.v5i4.8770

Keywords:

Learned Competency, Teaching Practices In Mathematics

Abstract

Teaching practices in Mathematics play a crucial role in shaping learners’ understanding of mathematical concepts. In today’s 21st-century classroom, there is an increasing demand for learners who can not think critically. The study aimed to determine the level of teachers’ teaching practices in Mathematics and learners’ learned competencies. Particularly, this study sought to identify the level of teachers’ teaching practices in Mathematics; find out the level of learners’ learned competencies; and determine the significant relationship between teacher-respondents’ assessment of their teaching practices in Mathematics and learners’ learned competencies. The study involved one hundred fifty-two (152) Grade 5 teachers and three hundred six (306) Grade 5 learners selected as respondents and used a descriptive-correlational research design. The universal sampling technique was employed in this study. The instruments were patterned and modified, and the statistical treatments used were the mean, standard deviation, and Pearson Correlation. Findings revealed that the majority of the teacher-respondents assessed the teaching practices, which resulted in a level of highly practiced. The learners’ learned competency is at the level of very satisfactory. The correlation between teachers’ teaching practices and learners’ learned competency was significant; it was linear and directly proportional. The study concludes that problem-based learning and order of operations have contributed positively to students’ understanding and performance in applying the correct order of operations. It recommends that teachers should strengthen the use of concrete, representational abstract and conduct more activities on factors and multiples to further improve learners’ learned competency.

Downloads

Download data is not yet available.

References

Abdul-Karim, H., Kasimu, O., Rahaman, A. A., Kanimam, Y. S., Imoro, M., & Dokurugu, M. E. (2023). Assessing the impact of algebra tiles as visual and manipulative aids on students’ algebraic understanding. American Journal of Educational Research, 11(10), 705–711. https://doi.org/10.12691/education-11-10-9

Agrawal, J., & Morin, L. L. (2020). Evidence-based practices: Applications of concrete representational abstract framework across math concepts for students with mathematics disabilities. Learning Disabilities Research & Practice, 31(1), 34–44. https://doi.org/10.1111/ldrp.12093

Ahmad, J., & Siller, R. (2024). Concrete-pictorial-abstract instruction: Enhancing students’ learning motivation and achievement in mathematics. Cogent Education.

Ali, S. (2022). Enhancing student performance in mathematics through concrete-representational-abstract (CRA) approach. International Journal of Science and Research Archive, 14(3), 1732–1738.

Banerjee, S. (2021). Models, analysis and application. Indian Institute of Technology Roorkee.

Bautista, M. C., & Ramos, J. L. (2023). Effectiveness of structured practice and reinforcement in Grade 5 learners’ mastery of operations with fractions. Philippine Journal of Basic Education Research, 5(4), 55–70.

Bautista, R. G., & Cruz, A. L. (2023). Effectiveness of visual aids in teaching Grade 5 mathematics competencies in the Philippines. Philippine Journal of Educational Research, 12(2), 112–129.

Bimenyimana, K., & Uworwabayeho, K. (2022). Concrete-pictorial-abstract instruction: Enhancing students’ learning motivation and achievement in mathematics. Cogent Education.

Black, P., & Wiliam, D. (2021). Assessment for learning and classroom practice: Impact on student achievement and equity. Assessment in Education: Principles, Policy & Practice, 28(1), 1–17.

Blum, W., & Borromeo Ferri, R. (2020). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45–58.

Boaler, J., & Staples, M. (2022). Building conceptual understanding of algebraic procedures: The role of practice and worked examples in mastering order of operations. Journal for Research in Mathematics Education, 53(3), 189–207.

Booth, J. L., McGinn, K. M., & Barbieri, C. (2021). Common misconceptions in the order of operations: Diagnosing and addressing student errors. Mathematical Thinking and Learning, 23(4), 297–314.

Borromeo Ferri, R. (2020). Theoretical and empirical differentiations of phases in the modeling process. ZDM, 38(2), 86–95. https://doi.org/10.1007/BF02655883

Bouck, E. C., Park, J., & Nickell, B. (2021). Using virtual and concrete manipulatives to teach mathematical concepts to elementary students. Intervention in School and Clinic, 57(2), 73–81.

Bouck, E. C., Satsangi, R., & Park, J. (2020). The concrete–representational–abstract approach for students with learning disabilities: An evidence-based practice synthesis. Remedial and Special Education, 39(4), 211–228. https://doi.org/10.1177/0741932517721712

Bron, J. F., & Prudente, M. S. (2024). Examining the effect of problem-based learning approach on learners’ mathematical creativity: A meta-analysis. International Journal of Research in Education and Science, 10(3), 653–668. https://doi.org/10.46328/ijres.3456

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2020). 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

Carbonneau, K. J., Marley, S. C., & Selman, R. L. (2022). The efficacy of using visual representations to support mathematics learning: A meta-analysis. Journal of Educational Psychology, 114(4), 567–588.

Clark, F. B., & Kamii, C. (2022). Interventions for students struggling with multiplicative concepts: Factors and multiples. Journal of Mathematical Behavior, 66, 100943.

Dela Cruz, A. R., & Villanueva, T. G. (2023). Remediation strategies for Grade 5 learners with low performance in factors and multiples. Philippine Journal of Education, 102(2), 145–160.

Dela Cruz, M. J., & Felipe, J. M. (2021). Divisibility rules for 2, 5 and 10 and divisibility rules for 3, 6, and 9. Division of Tarlac City.

Dela Rosa, D. M. (2023–2024). Localized competencies for Grade 5 mathematics. Tapinac Elementary School.

Department of Education. (2022). Most essential learning competencies: Mathematics Grade 5. Department of Education.

Department of Education. (2025). Learning exemplar module 5: Solving real-life problems with GCF and LCM. DepEd Learning Portal.

Doerr, H. M., Ärlebäck, J. B., & Costello Staniec, A. (2020). Design and effectiveness of modeling-based mathematics in a summer bridge program. Journal of Engineering Education. https://doi.org/10.1002/jee.20037

Durandt, R., Blum, W., & Lindl, A. (2022). Fostering mathematical modelling competency of South African engineering students: Which influence does the teaching design have? Educational Studies in Mathematics, 109, 361–381. https://doi.org/10.1007/s10649-021-10068-7

Ebner, S., MacDonald, M. K., Grekov, P., & Aspiranti, K. B. (2025). A meta-analytic review of the concrete-representational-abstract math approach. Learning Disabilities Research & Practice, 40(1), 31–42. https://doi.org/10.1177/09388982241292299

Fuchs, D., Fuchs, L. S., & Malone, A. S. (2021). Response to intervention and differentiated mathematics instruction for students with varying achievement levels. Exceptional Children, 87(4), 423–440.

Fuchs, L. S., Powell, S. R., & Schumacher, R. F. (2021). Supporting students with mathematics difficulties: Evidence-based interventions for multiplicative reasoning. Learning Disabilities Research & Practice, 36(3), 187–200.

Gallo-Toong, N. (2020). Enhancing student performance in mathematics through concrete-representational-abstract (CRA) approach. International Journal of Science and Research Archive, 14(3), 1732–1738.

Garcia, R. D., & Santos, P. V. (2023). Addressing varying levels of competency in Grade 5 fraction operations through differentiated instruction. Philippine Journal of Basic Education Research, 5(2), 112–127.

Gersten, R., Jordan, N. C., & Flojo, J. R. (2021). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 54(5), 323–336.

Hattie, J., & Clarke, S. (2020). Visible learning: Feedback. Routledge.

Hattie, J., & Clarke, S. (2022). Visible learning: Feedback and the role of assessment for learning in mathematics. Educational Psychology Review, 34(2), 567–589.

Hidayat, R., Mohd Ayub, A. F., Abd Hamid, H. S., & Nasir, N. (2025). Difficulties in instructing mathematical modeling: Case study in Malaysia. International Electronic Journal of Mathematics Education, 20(2), Article em0811. https://doi.org/10.29333/iejme/15815

Hidayat, R., Mohd Ayub, A. F., Setambah, M. A. B., & Mazlan, N. H. (2025). A systematic review of the best practices for teaching mathematical modelling in education context. European Journal of Science and Mathematics Education, 13(4), 255–272. https://doi.org/10.30935/scimath/17155

Hung, W., Dolmans, D. H. J. M., & van Merriënboer, J. J. G. (2021). A new approach to problem-based learning: An overview and implications for instructional design. Educational Psychology Review, 33, 1125–1140.

International Journal of Advanced Multidisciplinary Studies. (2024). Primary competencies of Grade 5 learners in mathematics: Basis for a proposed intervention program, 5(5).

Kilic, S., & Cakiroglu, E. (2022). The impact of concrete and representational activities on students’ understanding of divisibility rules. International Journal of Mathematical Education in Science and Technology, 53(7), 1682–1698.

Luzano, J. F. P. (2025). Redefining quality learning practices in mathematics education: A scoping review of contemporary trends and educational innovations. International Journal of Education in Mathematics, Science, and Technology.

Magana, A. J., & Coutinho, S. (2023). Learner-centered approaches in mathematics education: Effects on engagement and conceptual understanding. International Journal of Mathematical Education in Science and Technology, 54(6), 891–908.

Makondo, J. (2020). Enhancing student performance in mathematics through concrete-representational-abstract (CRA) approach. International Journal of Science and Research Archive, 14(3), 1732–1738.

Medes, A. (2023). Real-life mathematics. Abiva Publishing House, Inc.

Mendoza, K. P., & Lopez, F. S. (2023). Effectiveness of demonstration and drill activities on Grade 5 learners’ mastery of order of operations. Philippine Journal of Basic Education Research, 5(1), 33–48.

Mendoza, L. K., & Torres, R. S. (2023). Utilization of concrete manipulatives in teaching number sense among Grade 5 pupils. Asia Pacific Journal of Education, Arts and Sciences, 10(1), 45–58.

Morin, L. L., Watson, S. M., & Hester, P. (2021). A systematic literature review of the concrete-representational-abstract instructional approach in mathematics and literacy. Learning Disabilities Research & Practice, 36(3), 185–194.

Nguyen, T. H., & Le, M. P. (2024). Visual representations in the CRA framework: Bridging concrete manipulatives to abstract mathematical thinking. Mathematics Education Research Journal, 36(1), 45–62.

Nierves, M. J. G. (2022, September 19–20). Grade 5 math lesson on factors & multiples. Legarda Elementary School.

Nivera, G., & Marcelino, D. (2024). Math for all. Don Bosco Press.

Nunes, T., & Bryant, P. (2021). Children’s understanding of number properties: The role of instruction and practice. ZDM–Mathematics Education, 53(5), 987–1000.

Nunes, T., Bryant, P., & Barros, R. (2021). The development of multiplicative reasoning and understanding of factors and multiples. ZDM–Mathematics Education, 53(5), 1001–1014.

PHINMA Cagayan de Oro College. (2023). College of Management and Accountancy. https://coc.phinma.edu.ph/college-of-management-and-accountancy/

Reyes, L. B., & Manaloto, R. S. (2022). Addressing learning gaps in Grade 5 Mathematics through remedial instruction. Philippine Journal of Education, 101(3), 112–128.

Reyes, L. M., & Cruz, A. B. (2023). Overall academic performance and consistency of Grade 5 learners in mathematics competency. Philippine Journal of Education, 102(4), 201–215.

Rittle-Johnson, B., Schneider, M., & Star, J. R. (2021). Not a one-way street: How comparing procedures can improve students’ understanding of order of operations. Educational Psychology Review, 33(1), 1–24.

Rittle-Johnson, B., Schneider, M., & Star, J. R. (2022). The role of practice and feedback in mastering arithmetic procedures. Contemporary Educational Psychology, 68, 101998.

Santos, M. L., & Rivera, D. E. (2023). Effectiveness of activity-based instruction on Grade 5 pupils’ mastery of factors and multiples. Philippine Journal of Basic Education Research, 5(3), 78–92.

Sarama, J., & Clements, D. H. (2022). The role of manipulatives in early mathematics: Pattern blocks and place value understanding. Journal for Research in Mathematics Education, 53(4), 278–295.

Savin-Baden, M., & MacKenzie, A. (2022). Finding and creating spaces of innovation. Postdigital Science and Education, 4(2), 540–556. https://doi.org/10.1007/s42438-021-00266-0

Siegler, R. S., Fazio, L. K., & Pyke, A. A. (2022). Strategies for supporting students’ learning of fraction arithmetic. Educational Psychology Review, 34(4), 2147–2168.

Spooner, K. (2024a). Using mathematical modelling to provide students with a contextual learning experience of differential equations. International Journal of Mathematical Education in Science and Technology, 55(2), 565–573. https://doi.org/10.1080/0020739X.2023.2244472

Spooner, K. (2024b). What does mathematical modelling have to offer mathematics education? Insights from students’ perspectives on mathematical modelling. International Journal of Mathematical Education in Science and Technology, 55(3), 615–627. https://doi.org/10.1080/0020739X.2021.2009052

Taite, G., & DiNapoli, J. (2025). Perspectives on mathematical modeling education: Conceptions and research. MDPI Encyclopedia.

Tañola, M. D., & Lomibao, L. S. (2024). Understanding how students learn mathematics: A systematic literature review of contemporary learning strategies in mathematics education post-2020.

Tomlinson, C. A., & Imbeau, M. B. (2020). Leading and managing a differentiated classroom. ASCD.

Tomlinson, C. A., & Imbeau, M. B. (2022). Differentiated instruction for diverse learners in mathematics classrooms. Educational Leadership, 79(5), 28–34.

Torres, J. R., & Dela Peña, M. A. (2023). Effectiveness of activity-based learning on Grade 5 pupils’ mastery of divisibility rules. Philippine Journal of Basic Education Research, 5(2), 45–61.

Van Hoof, J., Degrande, T., Ceulemans, A., Verschaffel, L., & Van Dooren, W. (2021). Towards a better understanding of fraction difficulties: The role of instruction and practice. ZDM–Mathematics Education, 53(5), 1029–1043.

Verschaffel, L., Depaepe, F., & Van Dooren, W. (2022). Procedural knowledge and conceptual understanding in multiplicative concepts: The case of factors and multiples. Educational Studies in Mathematics, 109(2), 301–318.

Villas, C. D. (2024a). Grade 5 math lesson on divisibility rules. Kapitbahayan Elementary School.

Villas, C. D. (2024b). Grade 5 math lesson on factors and multiples. Kapitbahayan Elementary School.

Witzel, B. S., & Allsopp, D. H. (2022). The accessible mathematics classroom: Using the CRA framework to support all learners (2nd ed.). Brookes Publishing.

Witzel, B. S., & Riccomini, P. J. (2020). Optimizing math curriculum to meet the learning needs of students. Preventing School Failure: Alternative Education for Children and Youth, 52(1), 13–18. https://doi.org/10.3200/PSFL.52.1.13-18

Witzel, B. S., Riccomini, P. J., & Schneider, E. (2020). Implementing CRA with secondary students with learning disabilities in mathematics. Intervention in School and Clinic, 43(5), 270–276. https://doi.org/10.1177/1053451208314734

Yew, E. H. J., & Goh, K. (2016). Problem-based learning: An overview of its process and impact on learning. Health Professions Education, 2(2), 75–79. https://doi.org/10.1016/j.hpe.2016.01.004

Yıldırım, & Karabulut. (2023). Enhancing pupils’ performance in mathematics through the use of concrete-pictorial-abstract approach. International Journal of Research and Innovation in Social Science.

Zhang, S., Yu, S., Xiao, J., Liu, Y., & Jiang, T. (2022). The effects of concrete-representational-abstract sequence instruction on fractions for Chinese elementary students with mathematics learning disabilities. International Journal of Science and Mathematics Education, 20, 1481–1498. https://doi.org/10.1007/s10763-021-10215-9

Downloads

Published

2026-10-20

How to Cite

Billones, E. B. ., Pontillas, P. V. ., Corpuz, G. G. ., & Comon, J. D. . (2026). Teaching Practices in Mathematics and Learners’ Learned Competencies. American Journal of Arts and Human Science, 5(4), 58-74. https://doi.org/10.54536/ajahs.v5i4.8770

Similar Articles

11-20 of 63

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)

1 2 > >>