Development and Validation of NUMBERQUEST for Grade 3 & 4 Learning Toolkit
DOI:
https://doi.org/10.55687/ste.v5i3.413Abstract
This study investigated the development and validation of the NumberQuest multi-grade learning toolkit to improve the division skills of Grade 3 and Grade 4 learners in selected multi-grade classrooms in the Schools Division of Apayao. It was anchored on the persistent problem of low numeracy performance, particularly in division with remainders, identified as the least learned competency. A developmental research design was used, involving Grade 3 and Grade 4 learners for the diagnostic assessment and limited try-out, and six (6) expert validators composed of mathematics teachers and education specialists. Instruments included a researcher-made diagnostic test, validation checklists, and usability evaluation tools. Results showed that learners performed satisfactorily in basic division, multi-digit division, and word problems but struggled with division with remainders. In response, the NumberQuest toolkit was developed, consisting of structured lessons, activity sheets, and contextualized tasks. Validation results revealed that the toolkit was highly valid in content, design, assessment, and usability. The study concludes that NumberQuest is an effective and context-responsive instructional material that improves learners’ division skills in multi-grade classrooms.
Keywords: division, multi-grade learners, instructional toolkit, numeracy, validation
References
Baroody, A. J., Clements, D. H., & Sarama, J. (2018). Teaching and learning mathematics through problem solving. Routledge.
Becker, G. S. (1993). Human capital: A theoretical and empirical analysis, with special reference to education (3rd ed.). University of Chicago Press.
Biggs, J., & Tang, C. (2011). Teaching for quality learning at university (4th ed.). Open University Press.
Bruner, J. S. (1960). The process of education. Harvard University Press.
Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.
Carpenter, T. P., Franke, M. L., & Levi, L. (2015). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.
Creswell, J. W. (2015). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (5th ed.). Pearson.
DeVellis, R. F. (2017). Scale development: Theory and applications (4th ed.). SAGE Publications.
Department of Education. (2023). MATATAG curriculum framework.
Department of Education. (2023). MATATAG curriculum guide: Mathematics.
Department of Education. (2023). National assessment results in elementary mathematics.
Department of Education – Cordillera Administrative Region. (2023). Regional education performance report.
Dick, W., Carey, L., & Carey, J. O. (2015). The systematic design of instruction (8th ed.). Pearson.
Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2019). How to design and evaluate research in education (9th ed.). McGraw-Hill.
Gustafson, K. L., & Branch, R. M. (2002). Survey of instructional development models (4th ed.). ERIC Clearinghouse on Information & Technology.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
Little, A. W. (2006). Education for all and multigrade teaching: Challenges and opportunities. Springer.
McMillan, J. H. (2018). Classroom assessment: Principles and practice for effective standards-based instruction (6th ed.). Pearson.
Molenda, M. (2003). In search of the elusive ADDIE model. AECT.
National Council of Teachers of Mathematics. (2020a). Principles to actions: Ensuring mathematical success for all. NCTM.
National Council of Teachers of Mathematics. (2020b). Catalyzing change in early childhood and elementary mathematics. NCTM.
Organisation for Economic Co-operation and Development. (2023a). PISA 2022 results (Volume I): Learning outcomes. OECD Publishing.
Organisation for Economic Co-operation and Development. (2023b). PISA 2022 country note: Philippines. OECD Publishing.
Partnership for 21st Century Skills. (2019). Framework for 21st century learning. P21.
Piaget, J. (1969). The psychology of the child. Basic Books.
Piaget, J. (1972). Intellectual evolution from adolescence to adulthood. Basic Books.
Plomp, T., & Nieveen, N. (2013). Educational design research. Netherlands Institute for Curriculum Development.
Pressman, J. L., & Wildavsky, A. (1984). Implementation (3rd ed.). University of California Press.
Reiser, R. A., & Dempsey, J. V. (2018). Trends and issues in instructional design and technology (4th ed.). Pearson.
Richey, R. C., & Klein, J. D. (2007). Design and development research: Methods, strategies, and issues. Lawrence Erlbaum Associates.
Second Congressional Commission on Education (EDCOM II). (2023). Miseducation: The failed system of Philippine education.
United Nations. (1989). Convention on the rights of the child.
United Nations Educational, Scientific and Cultural Organization. (2007). A human rights-based approach to education.
United Nations Educational, Scientific and Cultural Organization. (2017). Education for people and planet: Creating sustainable futures for all.
United Nations Educational, Scientific and Cultural Organization. (2024). Global education monitoring report 2024: Education at a crossroads.
World Bank. (2019). Ending learning poverty: What will it take?
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Studies in Technology and Education

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
License Terms
All articles published in Studies in Technology and Education (STE) are freely accessible under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
This license grants users the right to read, download, copy, distribute, and link to the full texts for non-commercial purposes, provided that appropriate credit is given and that the original work remains unaltered and unchanged.
This article is made available in accordance with the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.