
Grade R Numerosity Levels and Gaps: A Case of South African Learners in the Eastern Cape
Issue: Vol.5 No.6 Issue Article 5 pp.848 -859
DOI: https://doi.org/10.38159/ehass.2024565 | Published online 7th June, 2024
© 2024 The Author(s). This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).
Developing young learners’ knowledge in number sense is a priority if the aim is to build a rich mathematical foundation for successful learning and future innovative careers. Capturing students’ interests and motivation is crucial while mediating counting concepts. Literature directs practice on the important core concepts that are foundational in developing number sense. This paper therefore assessed how young South African children demonstrated number concepts before entering the reception class. The paper revealed the diverse knowledge attained by children in different settings before embarking on formal education. A qualitative analysis was employed using Clements and Sarama’s learning trajectories as an analytical tool for children’s counting progression. The findings indicated that children’s start mathematically is uneven with either fully or partially attained number concepts, for example, one-to-one correspondence, counting on, cardinality, and equality. Furthermore, the findings revealed that a lack of particular numerical skills such as keeping track while counting, reciter, and sequential verbal counting beyond 10 impede learners’ full realisation of understanding numerical concepts. The findings suggest pre-schooling stimulation that provides rich mathematical experiences and purposeful play towards the attainment of core foundational concepts. It was, therefore, recommended that Grade R Mathematics teachers intervene earlier during preschool to assist learners specifically from low socioeconomic backgrounds and mathematise learners’ play and activities to enhance their semi-attained numerical abilities. This paper informs the mathematics education community of the need for future interventions and a curriculum designed to improve these skills in young children. This could have a positive impact on long-term academic success and close the numeracy gap which is existing in mathematics achievement between high and low-income children.
Keywords: Numeracy, Trajectories, Innate Abilities, Counting, Grade R
Anobile, Giovanni, Roberto Arrighi, Elisa Castaldi, Eleonora Grassi, Lara Pedonese, Paula A. M. Moscoso, and David C. Burr. “Spatial but Not Temporal Numerosity Thresholds Correlate with Formal Math Skills in Children.” Developmental Psychology 54, no. 3 (March 2018): 458–73. https://doi.org/10.1037/dev0000448.
Aunio, Pirjo, and Pekka Räsänen. “Core Numerical Skills for Learning Mathematics in Children Aged Five to Eight Years – a Working Model for Educators.” European Early Childhood Education Research Journal 24, no. 5 (September 2, 2016): 684–704. https://doi.org/10.1080/1350293X.2014.996424.
Baroody, Arthur J. “Counting Ability of Moderately and Mildly Handicapped Children.” Education and Training of the Mentally Retarded, 1986, 289–300.
Baroody, Arthur J, and Mary R Gatzke. “The Estimation of Set Size by Potentially Gifted Kindergarten-Age Children.” Journal for Research in Mathematics Education 22, no. 1 (1991): 59–68.
Breive, S. “ Processes of Mathematical Inquiry in Kindergarten.” University of Agder, 2019.
Cheeseman, Jill, Christiane Benz, and Yianna Pullen. “Number Sense: The Impact of a Measurement-Focused Program on Young Children’s Number Learning.” Contemporary Research and Perspectives on Early Childhood Mathematics Education, 2018, 101–27.
Clements, D. H., and J. Sarama. Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge, 2009.
Clements, Douglas H. “Subitizing: What Is It? Why Teach It?” Teaching Children Mathematics 5, no. 7 (1999): 400–405.
———. “Supporting Young Children’s Logo Programming.” Computing Teacher 11, no. 5 (1984): 24–30.
Clements, Douglas H, and Julie Sarama. “Learning Trajectories in Early Mathematics–Sequences of Acquisition and Teaching.” Encyclopedia of Language and Literacy Development 7 (2009): 1–6.
Clements, Douglas H, Julie Sarama, and Candace Joswick. “Learning and Teaching Geometry in Early Childhood.” In Special Issues in Early Childhood Mathematics Education Research, 95–131. Brill, 2022.
Clements, Douglas H, Sudha Swaminathan, Mary Anne Zeitler Hannibal, and Julie Sarama. “Young Children’s Concepts of Shape.” Journal for Research in Mathematics Education, 1999, 192–212.
Creswell, John W. Educational Research: Planning, Conducting, and Evaluating. W. Ross MacDonald School Resource Services Library, 2013.
Delgado, Ana R, and Gerardo Prieto. “Cognitive Mediators and Sex-Related Differences in Mathematics.” Intelligence 32, no. 1 (2004): 25–32.
Feza, Nosisi N. “Teaching 5- and 6-Year-Olds to Count: Knowledge of South African Educators.” Early Childhood Education Journal 44, no. 5 (September 9, 2016): 483–89. https://doi.org/10.1007/s10643-015-0736-z.
Fuson, K. Children’s Counting and Concept of Number. New York, NY: Springer-Verlag, 1988.
Fuson, K. C. “Research on Whole Number Addition and Subtraction .” In Handbook of Research on Mathematics Teaching and Learning, edited by Douglas A. Grauws, 243–75. New York: Macmillan Publishing Co., 1992.
Gallistel, Charles R, and Rochel Gelman. “Non-Verbal Numerical Cognition: From Reals to Integers.” Trends in Cognitive Sciences 4, no. 2 (2000): 59–65.
Gilmore, Scott A. “Immunity Disorders: The Conflict of Foreign Official Immunity and Human Rights Litigation.” Geo. Wash. L. Rev. 80 (2011): 918.
Graven, Mellony Holm. “Poverty, Inequality and Mathematics Performance: The Case of South Africa’s Post-Apartheid Context.” Zdm 46 (2014): 1039–49.
Graven, Mellony, and Robyn Jorgensen. “Unexpected Outcomes of a Family Mathematics Story-Time Program.” Mathematics Education Research Group of Australasia, 2018.
Harrison, B., and D. Peterson. “Developing Math Skills in Early Childhood.” Mathematica Policy Research Issue Brief, 2017. http://files.eric.ed.gov.
Hawes, Zachary, Joan Moss, Beverly Caswell, Jisoo Seo, and Daniel Ansari. “Relations between Numerical, Spatial, and Executive Function Skills and Mathematics Achievement: A Latent-Variable Approach.” Cognitive Psychology 109 (2019): 68–90.
Hegarty, Mary, and Maria Kozhevnikov. “Types of Visual–Spatial Representations and Mathematical Problem Solving.” Journal of Educational Psychology 91, no. 4 (1999): 684.
Klar, Samara, and Thomas J Leeper. “Identities and Intersectionality: A Case for Purposive Sampling in Survey‐Experimental Research.” Experimental Methods in Survey Research: Techniques That Combine Random Sampling with Random Assignment, 2019, 419–33.
Koponen, Tuire, Kaisa Aunola, and Jari-Erik Nurmi. “Verbal Counting Skill Predicts Later Math Performance and Difficulties in Middle School.” Contemporary Educational Psychology 59 (2019): 101803.
Koponen, Tuire, Paula Salmi, Minna Torppa, Kenneth Eklund, Tuija Aro, Mikko Aro, Anna-Maija Poikkeus, Marja-Kristiina Lerkkanen, and Jari-Erik Nurmi. “Counting and Rapid Naming Predict the Fluency of Arithmetic and Reading Skills.” Contemporary Educational Psychology 44–45 (January 2016): 83–94. https://doi.org/10.1016/j.cedpsych.2016.02.004.
Kyttälä, Minna, and Juhani E Lehto. “Some Factors Underlying Mathematical Performance: The Role of Visuospatial Working Memory and Non-Verbal Intelligence.” European Journal of Psychology of Education 23 (2008): 77–94.
Lakoff, G., and R. E. Núñez. Where Mathematics Comes from: How the Embodied Mind Brings Mathematics into Being. New York, NY: Basic Books, 2000.
Mix, Kelly S. “Surface Similarity and Label Knowledge Impact Early Numerical Comparisons.” British Journal of Developmental Psychology 26, no. 1 (2008): 13–32.
Nes, Fenna Van, and Jan de Lange. “Mathematics Education and Neurosciences: Relating Spatial Structures to the Development of Spatial Sense and Number Sense.” The Mathematics Enthusiast 4, no. 2 (2007): 210–29.
Nikoloska, Ana. “Development of the Cardinality Principle in Macedonian Preschool Children.” Psihologija 42, no. 4 (2009): 459–75.
Piaget, J. The Child’s Conception of Number. London: Routledge & Kegan Paul, 1952.
Ramani, Geetha B, and Robert S Siegler. “Reducing the Gap in Numerical Knowledge between Low-and Middle-Income Preschoolers.” Journal of Applied Developmental Psychology 32, no. 3 (2011): 146–59.
Reddy, V., T. Zuze, M. Visser, L. Winnaar, A. Juan, C. Prinsloo, F. Arends, and S. Rogers. Beyond Benchmarks: What Twenty Years of TIMSS Data Tell Us About South African Education. Cape Town, South Africa: HSRC Press, 2015.
Reys, Robert, Mary Lindquist, Diana V Lambdin, and Nancy L Smith. Helping Children Learn Mathematics. John Wiley & Sons, 2014.
Sadler, Faith H. “Help! They Still Don’t Understand Counting.” Teaching Exceptional Children Plus 6, no. 1 (2009): n1.
Sophian, Catherine. “Early Developments in Children’s Understanding of Number: Inferences about Numerosity and One-to-One Correspondence.” Child Development, 1988, 1397–1414.
Thomas, B. “An Abstract of Kindergarten Teachers’ Elicitation and Utilization of Children’s Prior Knowledge in the Teaching of Shape Concepts.” New York: School of education, health, nursing, and arts professions, New York University, 1982.
Tolar, Tammy Daun, Amy R Lederberg, and Jack M Fletcher. “A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement.” Educational Psychology 29, no. 2 (2009): 239–66.
Viarouge, Arnaud, Edward M Hubbard, and Bruce D McCandliss. “The Cognitive Mechanisms of the SNARC Effect: An Individual Differences Approach.” PloS One 9, no. 4 (2014): e95756.
Wei, Wei, Hongbo Yuan, Chuansheng Chen, and Xinlin Zhou. “Cognitive Correlates of Performance in Advanced Mathematics.” British Journal of Educational Psychology 82, no. 1 (2012): 157–81.
Wynn, Karen. “Children’s Understanding of Counting.” Cognition 36, no. 2 (1990): 155–93.
Professor Nosisi Nellie Feza – University of Venda, South Africa.
Professor Shakespear Maliketi Chiphambo (Ph.D.,M.Ed., B.Ed Honours, B.Ed., PGDip. Ed., Dip.Ed) is a Mathematics Education Lecturer at Walter Sisulu University (WSU). He has over 30 research publications including research and book chapters in different peer-reviewed journals and edited books. Attended and presented at both international and national conferences. He has been serving as a research paper reviewer for the South African International Conference in Education (SAICEd), The 11th European Conference on Education, Eurasia Journal of Mathematics, Science and Technology Education (EJMSTE), National Research Foundation (NRF), Pythagoras journal, Walter Sisulu University, Journal of Education (Journal of the SA Education Research Association (SAERA)) and African Evaluation journal. He is interested in education research with a focus on teaching and learning of geometry and measurement, and early childhood education.
Feza, Nosisi Nellie & Shakespear Maliketi Chiphambo. “Grade R Numerosity Levels and Gaps: A Case of South African Learners in the Eastern Cape,” E-Journal of Humanities, Arts and Social Sciences 5, no.6 (2024): 848 -859. https://doi.org/10.38159/ehass.2024565
© 2024 The Author(s). Published and Maintained by Noyam Journals. This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).