Investigating Solutions to Non-Routine Mathematics Problems in a Collaborative Setting
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Abstract
The study investigated Grade 9 students’ solutions to non-routine mathematics problems (NRPs) in a collaborative learning setting. The implementation aimed to enhance learners’ problem-solving proficiency and collaborative engagement through structured NRPs aligned with the Most Essential Learning Competencies (MELCs) prescribed by the Department of Education (DepEd), Philippines for the first quarter, particularly on solving quadratic equations using methods such as completing the square and applying the quadratic formula. Specifically, the study sought to (1) develop non-routine problems and (2) examine students’ strategies in solving algebraic problems. A mixed-methods design was employed involving twenty-five (25) Grade 9 learners from TNHS, a public school in Lanao del Sur. Findings consistently aligned with the study’s objectives. First, in developing NRPs suited to Grade 9 learners, teachers’ evaluation confirmed their validity and instructional relevance, with all five problems rated Excellent (overall mean = 3.47). These ratings highlighted strong content validity, clarity of presentation, and appropriateness to learners’ cognitive readiness. Second, in examining learners’ strategies and proficiency, group outputs showed steady progress from Beginning in NRP 1 (x̄ = 2.45) to Proficient in NRP 5 (x̄ = 3.80), with an overall mean of 3.42 (Approaching Proficiency). Classroom observations reinforced this trajectory, rising from Apprentice in NRP 1 (x̄ = 3.27) to Proficient in NRP 5 (x̄ = 4.87), though some groups continued to struggle with generalizing solutions and systematically recording procedures. Qualitative insights further confirmed that learners demonstrated flexible reasoning, increased confidence in non-routine problem solving, and stronger engagement during collaborative work. Overall, the integration of contextualized NRPs aligned with MELCs on quadratic equations effectively enhanced students’ mathematical proficiency, problem-solving confidence, and collaborative participation, thereby achieving both research objectives and demonstrating the pedagogical value of non-routine problems in fostering higher-order thinking among Grade 9 learners.
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References
Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages, and innovative teaching. Jossey-Bass.
Department of Education. (2012). DO 73, s. 2012: Guidelines on the assessment and rating of learning outcomes under the K to 12 Basic Education Curriculum. https://www.deped.gov.ph/2012/09/05/do-73-s-2012-guidelines-on-the-assessment-and-rating-of-learning-outcomes-under-the-k-to-12-basic-education-curriculum/
Felmer, P. (2023). Collaborative problem-solving in mathematics. Current Opinion in Behavioral Sciences, 52, Article 101296. https://doi.org/10.1016/j.cobeha.2023.101296
Johnson, D. W., & Johnson, R. T. (2014). Collaborative learning in the classroom: The power of group work. In The handbook of educational psychology (pp. 199–227). Routledge.
Junaid, A. (2025). Enhancing problem-solving skills in secondary mathematics education through collaborative learning. Journal of Interdisciplinary Perspectives, 3(9), 95–107. https://doi.org/10.69569/jip.2025.230
Keleş, T., & Yazgan, Y. (2025). The link between non-routine problem-solving success levels and strategic flexibility of gifted fourth-grade students. Frontiers in Psychology, 16, Article 1614829. https://doi.org/10.3389/fpsyg.2025.1614829
Nguyen, H. A., Guo, Y., Stamper, J., & McLaren, B. M. (2020). Improving students’ problem-solving flexibility in non-routine mathematics. Artificial Intelligence in Education, 12164, 409–413. https://doi.org/10.1007/978-3-030-52240-7_74
Yazgan, Y. (2025). Strategic flexibility and persistence among gifted and non-gifted students in non-routine problem solving. International Journal of Mathematical Education in Science and Technology, 56(5), 877–895.
