Conceptual Mathematics Teaching and Learner Reasoning Support of Key Stage 2 Teachers in Ambaguio, Nueva Vizcaya
DOI:
https://doi.org/10.65339/ijsis.V1.I3.148Keywords:
Classroom Mathematical Discourse Facilitation, Conceptual Error Analysis, Conceptual Mathematics Teaching, Instructional Enhancement Framework, Key Stage 2, Learner Reasoning Support, Mathematical Language, Mathematics Education, Teacher Professional DevelopmentAbstract
This study examined conceptual mathematics teaching practices, learner reasoning support, and classroom mathematical discourse facilitation among Key Stage 2 teachers in Ambaguio, Nueva Vizcaya, and developed an instructional enhancement framework based on the findings. Anchored in constructivist learning theory, social constructivist learning theory, mathematical proficiency theory, pedagogical content knowledge, and teacher noticing, the study employed a quantitative explanatory pathway design with predictive mediation modeling. Sixty-four Grades 4–6 teachers were selected through simple random sampling and surveyed using a researcher-made questionnaire with an overall Content Validity Index of 0.94 and Cronbach’s alpha of 0.95. Conceptual mathematics teaching, learner reasoning support, and classroom mathematical discourse facilitation were generally practiced to a great extent. However, learner-generated representations, structured error analysis, strategy comparison, peer mathematical discussion, misconception reconstruction, and reasoning-extending feedback required strengthening. Conceptual mathematics teaching was strongly and positively related to learner reasoning support (r = .671, p < .001). The final regression model explained 55.2% of the variance in reasoning support, with conceptual error analysis (β = .35, p = .001) and concept connection and progression (β = .27, p = .010) emerging as significant predictors. Classroom mathematical discourse partially mediated the relationship, with a significant indirect effect of .33, 95% CI [.18, .49]. The study recommends strengthening learner-centered reasoning and discourse practices through the proposed instructional enhancement framework and school-based professional learning. The study aligns with SDG 4—Quality Education by supporting responsive, conceptually grounded mathematics instruction and teacher professional development. Its sustainability impact is primarily educational, socio-cultural, and institutional, supporting durable mathematical understanding and locally informed improvement of teaching practice.
References
Abdelrahim, S., Jiménez-Silva, M., Restani, R., Martin, R., & Albano, T. (2025). Leveraging children’s multicultural literature to support students’ math identity and problem solving. Teaching for Excellence and Equity in Mathematics, 16(1). https://doi.org/10.63966/teem.v16i1.2010 DOI: https://doi.org/10.63966/teem.v16i1.2010
Aderinoye-Rabiu, R. A., Bello, A. B., Usman, A. A., Falebita, O. T., & Oloyede, G. O. (2025). Assessing the influence of primary mathematics educators’ content knowledge and pedagogical content knowledge on teaching effectiveness. Pedagogical Research, 10(3), Article em0240. https://doi.org/10.29333/pr/16665 DOI: https://doi.org/10.29333/pr/16665
Aziz, T. A., Makmuri, & Hakim, L. (2024). The conceptual validity aspect of pre-service mathematics teachers’ reasoning on linear algebra. AIP Conference Proceedings. https://doi.org/10.1063/5.0183415 DOI: https://doi.org/10.1063/5.0183415
Bogota, A. (2024). A teacher and her language minoritized students in a translanguaging mathematics classroom: Activating and suppressing our full linguistic repertoires for increased mathematical reasoning and sense-making. https://doi.org/10.70013/z6vl8pn7 DOI: https://doi.org/10.70013/z6vl8pn7
Bohara, P. S. (2024). Supporting teachers in implementing project-based learning in teaching secondary mathematics: An action research. Advances in Mobile Learning Educational Research. https://doi.org/10.25082/amler.2024.02.007 DOI: https://doi.org/10.25082/AMLER.2024.02.007
CAST. (2024). Universal Design for Learning guidelines version 3.0 [Graphic organizer]. CAST. https://udlguidelines.cast.org
Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 109, 205–236. https://doi.org/10.1007/s10649-021-10104-6 DOI: https://doi.org/10.1007/s10649-021-10104-6
Copur-Gencturk, Y. (2022). Mathematics teaching expertise: A study of the dimensionality of content knowledge, pedagogical content knowledge, and content-specific noticing skills. Teaching and Teacher Education, 114, Article 103696. https://doi.org/10.1016/j.tate.2022.103696 DOI: https://doi.org/10.1016/j.tate.2022.103696
Davidson, A., Keate, L. A., & Clark, J. C. (2025). Reasoning Champions: Exploring the practice of teachers leading professional learning. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-025-00534-3 DOI: https://doi.org/10.1007/s13394-025-00534-3
Department of Education. (2023a). MATATAG curriculum: Mathematics curriculum guide, Grades 1, 4, and 7. Department of Education.
Department of Education. (2023b). General shaping paper: MATATAG curriculum. Department of Education.
Gunawan, W., & Hadi, S. (2024). The effect of a Realistic Mathematics Education (RME) approach and reasoning ability on students’ conceptual and procedural understanding. Contemporary Educational Researches Journal, 14(2). https://doi.org/10.18844/cerj.v14i2.9318 DOI: https://doi.org/10.18844/cerj.v14i2.9318
Jacobs, V. R., Empson, S. B., Jessup, N. A., Dunning, A., Pynes, D., Krause, G., & Franke, T. M. (2024). Profiles of teachers’ expertise in professional noticing of children’s mathematical thinking. Journal of Mathematics Teacher Education, 27, 295–324. https://doi.org/10.1007/s10857-022-09558-z DOI: https://doi.org/10.1007/s10857-022-09558-z
Jiménez-Silva, M., Martin, R., Restani, R., Abdelrahim, S., & Albano, T. (2025). Supporting multilingual students’ mathematical discourse through teacher professional development grounded in design-based research: A conceptual framework. Education Sciences, 15(6), 778. https://doi.org/10.3390/educsci15060778 DOI: https://doi.org/10.3390/educsci15060778
Kanandjebo, L. N. (2024). Pedagogical responsiveness of mathematics instruction at inclusive secondary schools: A particularistic case study. Interdisciplinary Journal of Sociality Studies, 4(S1). https://doi.org/10.38140/ijss-2024.vol4.s1.04 DOI: https://doi.org/10.38140/ijss-2024.vol4.s1.04
Lee, Y.-J. (2025). The effects of functional moves in teacher questioning on students’ contextualization of mathematical word problem solving. Journal of Mathematics Teacher Education, 28, 73–101. https://doi.org/10.1007/s10857-023-09616-0 DOI: https://doi.org/10.1007/s10857-023-09616-0
Lit, S., Kool, M., & Drijvers, P. (2026). Teacher knowledge and skills for mathematical problem solving: A systematic literature review. Journal of Mathematics Teacher Education. Advance online publication. https://doi.org/10.1007/s10857-025-09737-8 DOI: https://doi.org/10.1007/s10857-025-09737-8
Lo, H. (2024). Reform-based mathematics teaching practices for teacher candidates’ professional development. Proceedings of the International Academic Conference on Teaching, Learning and Education. https://doi.org/10.33422/tleconf.v1i1.325 DOI: https://doi.org/10.33422/tleconf.v1i1.325
Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/ijemst.1111 DOI: https://doi.org/10.46328/ijemst.1111
Mangwende, E. (2026). Social constructivism: Principles and implications to mathematics learning. International Journal of Review in Mathematics Education, 1(1), 70–79. DOI: https://doi.org/10.23917/ijrime.15221
Maroba, M., & Mphunyane, M. (2025). Experiences of teaching mathematics to Grade 10 learners with hearing-impairment at an inclusive secondary school in Lesotho. Universal Journal of Educational Research. https://doi.org/10.64637/632863 DOI: https://doi.org/10.64637/632863
Mayer, R. E. (2021). Multimedia learning (3rd ed.). Cambridge University Press. https://doi.org/10.1017/9781316941355 DOI: https://doi.org/10.1017/9781316941355
Moremi, K. C. (2025). Mathematics teachers’ professional noticing of learners’ mathematical thinking and their subsequent instructional decisions: A case of lesson study. International Journal for Lesson and Learning Studies. Advance online publication. https://doi.org/10.1108/IJLLS-05-2025-0125 DOI: https://doi.org/10.1108/IJLLS-03-2025-0074
Moreno, M., Llinares, S., & Santonja, P. (2024). Prospective secondary mathematics teachers’ use of inquiry-based teaching principles as conceptual tools when modifying mathematical tasks. Journal on Mathematics Education, 15(4), 1131–1152. https://doi.org/10.22342/jme.v15i4.pp1131-1152 DOI: https://doi.org/10.22342/jme.v15i4.pp1131-1152
Mutia, I. (2025). Exploring students’ challenges in understanding mathematical concepts. Psychology and Education: A Multidisciplinary Journal. https://doi.org/10.70838/pemj.421006 DOI: https://doi.org/10.70838/pemj.421006
Ncube, M., & Luneta, K. (2025). Concept-based instruction: Improving learner performance in mathematics through conceptual understanding. Pythagoras, 46(1). https://doi.org/10.4102/pythagoras.v46i1.815 DOI: https://doi.org/10.4102/pythagoras.v46i1.815
Organisation for Economic Co-operation and Development. (2023a). PISA 2022 assessment and analytical framework. OECD Publishing. https://doi.org/10.1787/dfe0bf9c-en DOI: https://doi.org/10.1787/dfe0bf9c-en
Organisation for Economic Co-operation and Development. (2023b). PISA 2022 results: Factsheets: Philippines. OECD Publishing.
Öz, T., & Işık, A. (2024). The opportunities for mathematical reasoning skills that teachers provide for their students in the learning environment. Participatory Educational Research, 11(3). https://doi.org/10.17275/per.24.31.11.3 DOI: https://doi.org/10.17275/per.24.31.11.3
Padilla, M. O., Velasco, N., & Ortiz, S. A. (2025). Analysis of pedagogical content knowledge for teaching mathematics in early childhood education. Journal of Infrastructure, Policy and Development. https://doi.org/10.24294/jipd10135 DOI: https://doi.org/10.24294/jipd10135
Planas, N., & Pimm, D. (2023). Mathematics education research on language and on communication including some distinctions: Where are we now? ZDM–Mathematics Education, 55, 853–866. https://doi.org/10.1007/s11858-023-01497-0 DOI: https://doi.org/10.1007/s11858-023-01497-0
Priyanda, R., Herman, T., Amalia, R., & Ihsan, I. R. (2025). Exploring teachers’ pedagogical reasoning in mathematics education using the TPACK framework. Frontiers in Education. https://doi.org/10.3389/feduc.2025.1552760 DOI: https://doi.org/10.3389/feduc.2025.1552760
Rahman, Z. G. (2023). Pre-service mathematics teachers’ experience with productive struggle. The Educational Forum, 87(2), 112–130. https://doi.org/10.1080/00131725.2022.2072033 DOI: https://doi.org/10.1080/00131725.2022.2072033
Sharma, S., & Sharma, S. (2023). Successful teaching practices for English language learners in multilingual mathematics classrooms: A meta-analysis. Mathematics Education Research Journal, 35, 821–848. https://doi.org/10.1007/s13394-022-00414-0 DOI: https://doi.org/10.1007/s13394-022-00414-0
Shimizu, Y., & Kang, H. (2025). Research on classroom practice and students’ errors in mathematics education: A scoping review of recent developments for 2018–2023. ZDM–Mathematics Education, 57, 695–710. https://doi.org/10.1007/s11858-025-01704-0 DOI: https://doi.org/10.1007/s11858-025-01704-0
Sjöblom, M., Valero, P., & Olander, C. (2023). Teachers’ noticing to promote students’ mathematical dialogue in group work. Journal of Mathematics Teacher Education, 26, 509–531. https://doi.org/10.1007/s10857-022-09540-9 DOI: https://doi.org/10.1007/s10857-022-09540-9
Söderström, S., & Palm, T. (2024). Feedback in mathematics education research: A systematic literature review. Research in Mathematics Education. Advance online publication. https://doi.org/10.1080/14794802.2024.2401488 DOI: https://doi.org/10.1080/14794802.2024.2401488
Stylianides, G. J., Stylianides, A. J., & Moutsios-Rentzos, A. (2024). Proof and proving in school and university mathematics education research: A systematic review. ZDM–Mathematics Education, 56, 47–59. https://doi.org/10.1007/s11858-023-01518-y DOI: https://doi.org/10.1007/s11858-023-01518-y
Suryanti, S., & Yanti, L. P. (2025). Pre-service mathematics teacher perception of teaching fraction. International Journal of Mathematics and Computer Research, 13(6). https://doi.org/10.47191/ijmcr/v13i6.11 DOI: https://doi.org/10.47191/ijmcr/v13i6.11
Teng, Y., & Yang, Z. (2024). Articulating the problems encountered of pre-service mathematics teachers in conceptual teaching training. Asian Journal of Education and Social Studies, 50(9). https://doi.org/10.9734/ajess/2024/v50i91571 DOI: https://doi.org/10.9734/ajess/2024/v50i91571
Vistro-Yu, C. P., Hao, L. C., & Helton Sua, M. (2025). The struggle is real: Finding opportunities for problem posing in the Philippine school mathematics curriculum. Asian Journal for Mathematics Education, 4(2), 280–294. https://doi.org/10.1177/27527263251340036 DOI: https://doi.org/10.1177/27527263251340036
Wei, Y., Zhang, Q., & Guo, J. (2022). Can mathematical modelling be taught and learned in primary mathematics classrooms: A systematic review of empirical studies. Education Sciences, 12(12), Article 923. https://doi.org/10.3390/educsci12120923 DOI: https://doi.org/10.3390/educsci12120923
Weingarden, M., & Buchbinder, O. (2023). Teacher learning to teach mathematics via reasoning and proving: A discursive analysis of lesson plans modifications. Frontiers in Education. https://doi.org/10.3389/feduc.2023.1154531 DOI: https://doi.org/10.3389/feduc.2023.1154531
Weyers, J., König, J., Scheiner, T., Santagata, R., & Kaiser, G. (2024). Teacher noticing in mathematics education: A review of recent developments. ZDM–Mathematics Education, 56, 249–264. https://doi.org/10.1007/s11858-023-01527-x DOI: https://doi.org/10.1007/s11858-023-01527-x
Zentgraf, K., & Prediger, S. (2024). Demands and scaffolds for explaining the connection of multiple representations: Revisiting the bottle-filling task. The Journal of Mathematical Behavior, 73, Article 101118. https://doi.org/10.1016/j.jmathb.2023.101118 DOI: https://doi.org/10.1016/j.jmathb.2023.101118
Zhang, W., Li, L., & Disney, L. (2025). “Asking questions is the key”: Chinese kindergarten teachers support children’s mathematics concept learning and spatial reasoning through a Conceptual PlayWorld approach. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-025-00530-7 DOI: https://doi.org/10.1007/s13394-025-00530-7
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