A Conceptual Framework for Teaching Addition, Subtraction, and Multiplication in Kindergarten Using Grid-Counting Approach
DOI:
https://doi.org/10.58955/jecer.163270Keywords:
mathematical grid table, counting, arithmetic operations, manipulativesAbstract
This paper presents a conceptual framework for teaching basic arithmetic operations – addition, subtraction, and multiplication – at the kindergarten level using the Hundred Chart. Based on developmental learning theories and supported by a comprehensive literature review, the proposed approach bridges the gap between concrete manipulatives and abstract mathematical reasoning. While not reporting empirical findings, this framework lays the groundwork for future experimental research into developmentally appropriate numeracy strategies in early childhood education. We contend that this visual and structured method, when incorporated in the early grade curriculum, will foster counting fluency, number sense, and operational understanding in a way that is accessible and engaging for young learners. Researchers and teacher educators looking for developmentally appropriate methods, as well as classroom practitioners and curriculum developers hoping to make maths education more tangible and interesting for younger students, can all benefit from this framework.
References
Abdul, G. S. A., & Subeini, A. (2021). Teachers’ Use of Manipulatives in Teaching Numeracy at Early Childhood Centres in the Nkoranza North District [University of Education Winneba (UEW)]. http://ir.uew.edu.gh
Anghileri, J. (2006). Teaching Number Sense (2nd ed.). Bloomsbury Publishing.
Anthony, G., & Walshaw, M. (2009). Mathematics Education in the Early Years: Building Bridges. Contemporary Issues in Early Childhood, 10(2), 107–121. https://doi.org/10.2304/ciec.2009.10.2.107
Arcavi, A. (2003). The Role of Visual Representations in the Learning of Mathematics. Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/A:1024312321077
Bahadıri, E. (2017). Teaching Multiplication and Multiplication Tables by the Application of Finger Multiplication. European Journal of Education Studies. https://zenodo.org/records/345417
Bakos, S., & Sinclair, N. (2019). Pips (times) Pods: Dancing towards multiplicative thinking. Proceedings of CERME11, 2209–2216. https://www.researchgate.net/publication/340540826
Baroody, A., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. Washington DC: National Association for the Education of Young Children.
Björklund, C., & Runesson Kempe, U. (2019). Framework for analysing children’s ways of experiencing numbers. Eleventh Congress of the European Society for Research in Mathematics Education (CERME11). https://hal.science/hal-02414843v1
Björklund, C., van den Heuvel-Panhuizen, M., & Kullberg, A. (2020). Research on Early Childhood Mathematics Teaching and Learning. ZDM - Mathematics Education, 52(4), 607–619. https://link.springer.com/article/10.1007/s11858-020-01177-3
Bjørnebye, M. (2019). Pre-schoolers’ ability to synchronise multiple representations of numerosity in embodiment of a counting-on-strategy. Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), Utrecht University. https://hal.science/hal-02414850v1
Campbell, J. I. D., & Xue, Q. (2001). Cognitive Arithmetic Across Cultures. Journal of Experimental Psychology: General, 130(2), 299–315. https://doi.org/10.1037/0096-3445.130.2.299
Carlsen, M., Erfjord, I., & Hundeland, P. S. (2020). Mathematics Education in the Early Years. Results from the POEM4 Conference, 2018. https://link.springer.com/book/10.1007/978-3-030-34776-5
Carpenter, T. P., & Moser, J. M. (1984). The Acquisition of Addition and Subtraction Concepts in Grades One through Three. Journal for Research in Mathematics Education, 15(3), 179–202.
Charlesworth, R. (2016). Math and Science for Young children (8th ed.). Cengage Learning.
Chesney, M. (2013). Mental Computation Strategies for Addition. Australian Primary Mathematics Classroom - 18.
Claessens, A., & Engel, M. (2013). How Important is Where you Start? Early Mathematics Knowledge and Later School Success. Teachers College Record, 115(6), 1–29. https://doi.org/https://doi.org/10.1177/016146811311500603
Clements, D. H., & Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach. Routledge.
Clements, D. H., & Sarama, J. (2023). Learning Trajectories in Early Mathematics - Sequences of Acquisition and Teaching. Encyclopedia on Early Childhood Development.
Common Core State Standards. (2016). Deconstructed for Classroom Impact. The Common Core Institute.
Cox, L. S. (1975). Systematic Errors in the Four Vertical Algorithms in Normal and Handicapped Populations. Journal for Research in Mathematics Education, 6(4), 202. https://doi.org/10.2307/748696
Cross, C. T., Woods, T. A., & Schweingruber, H. A. (2009). Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. National Academies Press. https://doi.org/10.17226/12519
Ebby, C. B., Hulbert, E. T., & Broadhead, R. M. (2020). A Focus on Addition and Subtraction: Bringing Mathematics Education Research to the Classroom (1st ed.). Routledge. https://doi.org/10.4324/9781003038337
Elofsson, Jessica. (2017). Children’s Early Mathematics Learning and Development: Number Game Interventions and Number Line Estimations. [Doctoral dissertation, Linköping University].
Freudenthal, H. (2002). Revisiting Mathematics Education: China Lectures. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47202-3
Geist, E. (2009). Children Are Born Mathematicians: Promoting the Construction of Early Mathematical Concepts in Children Under Five. Upper Saddle River, NJ: Pearson. https://www.researchgate.net/publication/234636880
Ginsburg, H. P. (2002). Little Children, Big Mathematics: Learning and Teaching in the Pre-School. Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education.
Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics Education for Young Children: What It is and How to Promote It. Social Policy Report, 22(1), 1–24. https://doi.org/10.1002/j.2379-3988.2008.tb00054.x
Guo, D., McTigue, E. M., Matthews, S. D., & Zimmer, W. (2020). The Impact of Visual Displays on Learning Across the Disciplines: A Systematic Review. In Educational Psychology Review (Vol. 32, Issue 3, pp. 627–656). Springer. https://doi.org/10.1007/s10648-020-09523-3
Haskell, S. H. (2000). The Determinants of Arithmetic Skills in Young Children: Some Observations. European Child & Adolescent Psychiatry, 9. https://doi.org/10.1007/s007870070011
Hatano, G., & Inagaki, K. (1984). Two Courses of Expertise. Hokkaido University Collection of Scholarly and Academic Papers. http://hdl.handle.net/2115/25206
Henry, V. J., & Brown, R. S. (2008). First-Grade Basic Facts: An Investigation into Teaching and Learning of an Accelerated, High-Demand Memorization Standard. Journal for Research in Mathematics Education, 39(2), 153–183.
Hulbert, E. T., Petit, M. M., Ebby, C. B., Cunningham, E. P., & Laird, R. E. (2024). A Focus on Multiplication and Division: Bringing Mathematics Education Research to the Classroom (2nd ed.). Routledge. https://doi.org/10.4324/9781003185529
Hunting, R. P. (2003). Part-Whole Number Knowledge in Preschool Children. The Journal of Mathematical Behavior, 22(3), 217–235. https://doi.org/10.1016/S0732-3123(03)00021-X
Istomina, A., & Arsalidou, M. (2024). Add, Subtract and Multiply: Meta-Analyses of Brain Correlates of Arithmetic Operations in Children and Adults. Developmental Cognitive Neuroscience, 69. https://doi.org/10.1016/j.dcn.2024.101419
Kame’enui, E. J., & Simmons, D. C. (1999). Toward Successful Inclusion of Students with Disabilities: The Architecture of Instruction. Volume 1: An Overview of Material Adaptations. The Council for Exceptional Children.
Kullberg, A., Björklund, C., Brkovic, I., & Runesson Kempe, U. (2020). Effects of Learning Addition and Subtraction in Preschool by Making the First Ten Numbers and their Relations Visible with Finger Patterns. Educational Studies in Mathematics, 103(2), 157–172. https://doi.org/10.1007/s10649-019-09927-1
Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication. Journal of Experimental Psychology: General, 124(1), 83–97. https://doi.org/10.1037/0096-3445.124.1.83
Martins‐Mourão, A. (2000). Children’s Understanding of Number in the Primary School Years: A Unifying View from Early Counting to Knowledge of Place Value. [Doctoral dissertation, University of London].
Mercader, J., Miranda, A., Presentación, M. J., Siegenthaler, R., & Rosel, J. F. (2018). Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study. Frontiers in Psychology, 8. https://doi.org/10.3389/fpsyg.2017.02375
Mitchell, D. (2015). Inclusive Education is a Multi-Faceted Concept. CEPS Journal, 5. https://doi.org/10.25656/01:10611
Mutlu, Y., Akgün, L., & Akkuşci, Y. E. (2017). What Do Teachers Think About Finger-Counting? International Journal of Curriculum and Instruction, 12(1), 268–288.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Library of Congress Cataloguing-in-Publication.
National Council of Teachers of Mathematics (NCTM). (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.
National Mathematics Advisory Panel. (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel.
Nunes, Terezinha., & Bryant, Peter. (1996). Children Doing Mathematics. Oxford: Blackwell Publishers. https://www.wiley.com/en-us/Children+Doing+Mathematics-p-9780631184720
Öçal, T. (2021). ‘I remembered this mathematics course because … ’: How Unforgettable Mathematics Experiences of Pre-service Early Childhood Teachers are Related to Their Beliefs. International Journal of Mathematical Education in Science and Technology, 52(2), 282–298. https://doi.org/10.1080/0020739X.2020.1861349
Oers, van B. (2013). The Roots of Mathematising in Young Children’s Play. Early Mathematics Learning. https://doi.org/10.1007/978-1-4614-4678-1_8
Orhun, N. (2007). An Investigation into the Mathematics Achievement and Attitude Towards Mathematics with Respect to Learning Style According to Gender. International Journal of Mathematical Education in Science and Technology, 38(3), 321–333. https://doi.org/10.1080/00207390601116060
Papandreou, M., & Tsiouli, M. (2022). Noticing and understanding children’s everyday mathematics during play in early childhood classrooms. International Journal of Early Years Education, 30(4), 730–747. https://doi.org/10.1080/09669760.2020.1742673
Piaget, J., & Inhelder, B. (1969). The Psychology of the Child. Basic Books.
Pushparatnam, A., Ding, E., Lee, K., Rolla, A., & Wilinski, B. (2020). Effective Teaching Practices in Early Childhood Education (ECE): The Evidence Base for the Teach ECE Classroom Observation Tool.
Resnick, L. B. (1984). A Developmental Theory of Number Understanding. Learning Research and Development Center, University of Pittsburgh.
Rusdawati. (2020). The Early Childhood Mathematics Learning. Proceedings of the International Conference of Early Childhood Education (ICECE 2019). https://doi.org/10.2991/assehr.k.200715.021
Schoenherr, J., Strohmaier, A. R., & Schukajlow, S. (2024). Learning with Visualizations Helps: A Meta-Analysis of Visualization Interventions in Mathematics Education. Educational Research Review, 45, 100639. https://doi.org/10.1016/j.edurev.2024.100639
Siegler, R. S. (2005). Children’s Learning. American Psychologist, 60(8), 769–778. https://doi.org/https://doi.org/10.1037/0003-066X.60.8.769
Sokpe, B. Y., Osiakwan, J. K., & Appiah, J. (2022). Module for Bachelor of Education Programme (Primary): Psychological Basis of Teaching and Learning Mathematics. Institute of Education, University of Cape Coast.
Soylu, F., Lester, F. K., & Newman, S. D. (2018). You can count on your fingers: The Role of Fingers in Early Mathematical Development. Journal of Numerical Cognition, 4(1), 107–135. https://doi.org/10.5964/jnc.v4i1.85
Thompson, I. (1999). Mental Calculation Strategies for Addition and Subtraction. Part 1. The Mathematical Association, 28(5), 2–4. https://doi.org/https://www.jstor.org/stable/30215422
Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2004). Efficiency and Adaptiveness of Multiple School-Taught Strategies in the Domain of Simple Addition. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 4, 321–328.
Tudge, J. R. H., & Doucet, F. (2004). Early mathematical experiences: observing young Black and White children’s everyday activities. Early Childhood Research Quarterly, 19(1), 21–39. https://doi.org/10.1016/j.ecresq.2004.01.007
Walla, M., & Palmér, H. (2024). Discourses on mathematics education in the context of early assessment. 29th International Mathematical Views Conference 2023 – Selected Papers, 12(4). https://journals.helsinki.fi/lumatb/article/view/2452/1968
World Bank Group. (2021). Teach ECE: Helping Countries Track and Improve Teaching Quality in Early Childhood Education. World Bank Group Education. www.worldbank.org/teachece
Xu, F., Spelke, E. S., & Goddard, S. (2005). Number Sense in Human Infants. Developmental Science, 8(1), 88–101. https://doi.org/10.1111/j.1467-7687.2005.00395.x
Young-Loveridge, J. (2002). Early Childhood Numeracy: Building an Understanding of Part-Whole Relationships. Australasian Journal of Early Childhood. https://doi.org/10.1177/183693910202700408
Zhou, Z., & Peverly, S. T. (2005). Teaching Addition and Subtraction to First Graders: A Chinese Perspective. Psychology in the Schools, 42(3), 259–272. https://doi.org/10.1002/pits.20077
Zimmermann, W., & Cunningham, S. (1991). Editors’ Introduction: What Is Mathematical Visualization? Washington DC: The Mathematical Association of America.
