A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years

Munirah Ghazali; Rosmawati Mohamed; Zainun Mustafa

doi:10.29333/ejmste/10871

Full Text (PDF)

Munirah Ghazali ¹ ² ^* , Rosmawati Mohamed ¹ , Zainun Mustafa ²

More Detail

¹ School of Educational Studies, Universiti Sains Malaysia, MALAYSIA² Regional Centre of Expertise for ESD, RCE Penang, Universiti Sains Malaysia, MALAYSIA^* Corresponding Author

Abstract

The definitions serve the purpose of communication and preservation of knowledge in scientific inquiry. However, it is quite often to perceive number sense concept without well-accepted definitions in the field of mathematics education research. Despite the mentioned issue, the current literature on children’s number sense provide a glean for introducing, implementing, and even measuring the number sense using the specific and contextualized indicators in early mathematics. Consequently, this phenomenon offers to bridge a gap in the literature concerning definitions of number sense and its indicators. This article systematically reviews on the indicators in measuring children’s number sense based on the past research guided by the PRISMA statements. The metadata were analysed using open-coding and were further re-coded through axial coding and selective coding to form a definition of number sense. This article discusses on limitations, implications, and the future research directions for studying children’s number sense in the primary schools’ mathematics.

Keywords

systematic review
number sense
numeracy
definition
mathematics education

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Literature Review

EURASIA J Math Sci Tech Ed, Volume 17, Issue 6, June 2021, Article No: em1968

https://doi.org/10.29333/ejmste/10871

Publication date: 01 May 2021

Article Views: 3185

Article Downloads: 2978

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Akçayır, G., & Akçayır, M. (2018). The flipped classroom: A review of its advantages and challenges. Computers & Education, 126, 334–345. https://doi.org/10.1016/j.compedu.2018.07.021
Alsawaie, O. N. (2012). Number sense-based strategies used by high-achieving sixth grade students who experienced reform textbooks. International Journal of Science and Mathematics Education, 10(5), 1071-1097. https://doi.org/10.1007/s10763-011-9315-y
Anobile, G., Burr, D. C., Iaia, M., Marinelli, C. V., Angelelli, P., & Turi, M. (2018). Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude. Scientific Reports, 8(1), 13571. https://doi.org/10.1038/s41598-018-31893-6
Baroody, A. J., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers' number sense. Early Education and Development, 20(1), 80-128. https://doi.org/10.1080/10409280802206619
Brankaer, C., Ghesquière, P., & De Smedt, B. (2017). Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test). Behavior research methods, 49(4), 1361-1373. https://doi.org/10.3758/
s13428-016-0792-3
Brereton, P., Kitchenham, B. A., Budgen, D., Turner, M., & Khalil, M. (2007). Lessons from applying the systematic literature review process within the software engineering domain. Journal of Systems and Software, 80(4), 571-583. https://doi.org/10.1016/j.jss.2006.07.009
Burnham, J. F. (2006). Scopus database: a review. Biomedical Digital Libraries, 3(1), 1. https://doi.org/10.1186/1742-5581-3-1
Carroll, W. M., Fuson, K. C., & Diamond, A. (2000). Use of student-constructed number stories in a reform-based curriculum. The Journal of Mathematical Behavior, 19(1), 49-62. https://doi.org/10.1016/S0732-3123(00)00038-9
Cheek, K. A. (2013). How geoscience novices reason about temporal duration: The role of spatial thinking and large numbers. Journal of Geoscience Education, 61(3), 334-348.
Chen, F., Yan, Y., & Xin, T. (2016). Developing a learning progression for number sense based on the rule space model in China. Educational Psychology, 37(2), 128-144. https://doi.org/10.1080/01443410.2016.1239817
Cheung, K. L., & Yang, D.-C. (2018). Examining the Differences of Hong Kong and Taiwan Students’ Performance on the Number Sense Three-tier Test. EURASIA Journal of Mathematics, Science and Technology Education, 14(7), 3329-3345. https://doi.org/10.29333/ejmste/91682
Chikiwa, S., Westaway, L., & Graven, M. (2019). What mathematics knowledge for teaching is used by a Grade 2 teacher when teaching counting. South African Journal of Childhood Education, 9(1), 1-9. https://doi.org/10.4102/sajce.v9i1.567
Chun Tie, Y., Birks, M., & Francis, K. (2019). Grounded theory research: A design framework for novice researchers. SAGE open medicine, 7, 2050312118822927.
Clarke, B., Baker, S., Smolkowski, K., Doabler, C., Strand Cary, M., & Fien, H. (2015). Investigating the efficacy of a core kindergarten mathematics curriculum to improve student mathematics learning outcomes. Journal of Research on Educational Effectiveness, 8(3), 303-324. https://doi.org/10.1080/19345747.2014.980021
Clarke, B., Shanley, L., Kosty, D., Baker, S. K., Cary, M. S., Fien, H., & Smolkowski, K. (2018). Investigating the incremental validity of cognitive variables in early mathematics screening. School Psychology Quarterly, 33(2), 264-271. https://doi.org/10.1037/spq0000214
Conant, L. L (1893). Primitive number systems. Smithsonian Institution: United States Congressional Serial Set, Volume 3131.
Courtney-Clarke, M., & Wessels, H. (2014). Number sense of final year pre-service primary school teachers. Pythagoras, 35(1), 1-9. https://doi.org/10.4102/pythagoras.v35i1.244
Crawley, E. S. (1897). Popular Science Monthly Volume 51 August 1897 — The Origin and Development of Number Systems 1897. Popular Science Monthly, 51.
Crawley, E., & Karpinski, L. (2019). Origin and Development of Number Systems. LM Publishers.
Creswell, J. W (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd Ed.). Sage publications.
de León, S. C., Jiménez, J. E., & Hernández-Cabrera, J. A. (2020). Confirmatory factor analysis of the indicators of basic early math skills. Current Psychology, 1-12.
Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics. OUP, USA.
Diezmann, C. M., & English, L. D. (2001). Developing young children's multidigit number sense. Roeper Review, 24(1), 11-13. https://doi.org/10.1080/02783190109554118
Dunphy, E. (2007). The primary mathematics curriculum: Enhancing its potential for developing young children's number sense in the early years at school. Irish Educational Studies, 26(1), 5-25. https://doi.org/10.1080/03323310601125088
Fuson, K. C., Caroll, W. M., & Drueck, J. V. (2000). Achievement results for second and third graders using the Standards-based curriculum Everyday Mathematics. Journal for Research in Mathematics Education, 31(3), 277-295. https://doi.org/10.2307/749808
Gavel, Y., & Iselid, L. (2008). Web of Science and Scopus: a journal title overlap study. Online information review, 32(1), 8-21. https://doi.org/10.1108/14684520810865958
Ghazali, M. (2004). An exploratory study into Malaysian children’s understanding of multiple representation strand on number sense. Jurnal Pendidik Dan Pendidikan, 33-46.
Gifford, S. (2014). A good foundation for number learning for five-year-olds? An evaluation of the English Early Learning ‘Numbers’ Goal in the light of research. Research in Mathematics Education, 16(3), 219-233. https://doi.org/10.1080/14794802.2014.895677
Gupta, A. (2019). Definitions, The Stanford Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (Ed.). https://plato.stanford.edu/archives/win2019/entries/definitions/
Guzmán, B., Rodríguez, C., Sepúlveda, F., & Ferreira, R. A. (2019). Number sense abilities, working memory and RAN: A longitudinal approximation of typical and atypical development in chilean children. Revista de Psicodidáctica (English ed.), 24(1), 62-70. https://doi.org/10.1016/j.psicoe.2018.11.003
Hornung, C., Schiltz, C., Brunner, M., & Martin, R. (2014). Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence. Frontiers in Psychology, 5. https://doi.org/10.3389/fpsyg.2014.00272
Howell, S. C., & Kemp, C. R. (2010). Assessing preschool number sense: Skills demonstrated by children prior to school entry. Educational Psychology, 30(4), 411-429. https://doi.org/10.1080/01443411003695410
Huijsmans, M. D. E., Kleemans, T., van der Ven, S. H. G., & Kroesbergen, E. H. (2020). The relevance of subtyping children with mathematical learning disabilities. Research in Developmental Disabilities, 104, 103704. https://doi.org/10.1016/j.ridd.2020.103704
Karsenty, R. (2014). Mathematical ability. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 579-582). Springer.
Keijzer, R., & Terwel, J. (2003). Learning for mathematical insight: A longitudinal comparative study on modelling. Learning and Instruction, 13(3), 285-304. https://doi.org/10.1016/S0959-4752(02)00003-8
Kermani, H. (2017). Computer Mathematics Games and Conditions for Enhancing Young Children's Learning of Number Sense. Malaysian Journal of Learning and Instruction, 14(2), 23-57.
Kerschen, K., Cooper, S., Shelton, R., & Scott, L. (2018). The impact of a summer mathematics academy on rising kindergartners’ understanding of early number concepts. Journal of Research in Childhood Education, 32(4), 419-434. https://doi.org/10.1080/02568543.2018.1497738
Kim, D., Shin, J., & Lee, K. (2013). Exploring latent class based on growth rates in number sense ability. Asia Pacific Education Review, 14(3), 445-453. https://doi.org/10.1007/s12564-013-9274-9
Kinzie, M. B., Whittaker, J. V., Williford, A. P., DeCoster, J., McGuire, P., Lee, Y., & Kilday, C. R. (2014). MyTeachingPartner-Math/Science pre-kindergarten curricula and teacher supports: Associations with children's mathematics and science learning. Early Childhood Research Quarterly, 29(4), 586-599. https://doi.org/10.1016/j.ecresq.2014.06.007
Kuhn, J.-T., & Holling, H. (2014). Number sense or working memory? The effect of two computer-based trainings on mathematical skills in elementary school. Advances in Cognitive Psychology, 10(2), 59–67. https://doi.org/10.5709/acp-0157-2
Kuldas, S., Sinnakaudan, S., Hashim, S., & Ghazali, M. (2017). Calling for the development of children's number sense in primary schools in Malaysia. Education 3-13, 45(5), 586-598. https://doi.org/10.1080/03004279.2016.1143521
Labinowicz, E. (1980). The Piaget Primer: Thinking, Learning, Teaching. Addison-Wesley Publishing Company, Inc.
Laurillard, D. (2016). Learning number sense through digital games with intrinsic feedback. Australasian Journal of Educational Technology, 32(6), 32-44. https://doi.org/10.14742/ajet.3116
Lee, Y. S., & Lembke, E. (2016). Developing and evaluating a kindergarten to third grade CBM mathematics assessment. ZDM, 48(7), 1019-1030. https://doi.org/10.1007/s11858-016-0788-6
Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, e164. https://doi.org/10.1017/S0140525X16000960
Linder, S. M., Powers-Costello, B., & Stegelin, D. A. (2011). Mathematics in early childhood: Research-based rationale and practical strategies. Early Childhood Education Journal, 39(1), 29-37. https://doi.org/10.1007/s10643-010-0437-6
Lyublinskaya, I. (2009). Developing Number Sense with Technology-Based Science Experiments: Reflections on Classroom Practice in Primary Grades and Pre-service Education. Mathematics Teaching-Research Journal Online, 3(2), 1-14.
Mejias, S., Muller, C., & Schiltz, C. (2019). Assessing Mathematical School Readiness. Frontiers in Psychology, 10, 1173. https://doi.org/10.3389/fpsyg.2019.01173
Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & Prisma Group. (2009). Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. PLoS medicine, 6(7), e1000097.
NCTM (National Council of Teachers of Mathematics) (2000). Principles and Standards for School Mathematics. NCTM.
Okoli, C., & Schabram, K. (2010). A Guide to Conducting a Systematic Literature Review of Information Systems Research. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1954824
Ottmar, E. R., Konold, T. R., Berry, R. Q., Grissmer, D. W., & Cameron, C. E. (2014). Evaluating the structure of the Mathematics Teacher Questionnaire: A measure of exposure to mathematics instructional practices and content. Learning Environments Research, 17(1), 127-138. https://doi.org/10.1007/s10984-013-9147-5
Pitta-Pantazi, D. (2014). Mathematical ability. In: S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 470-474). Springer.
Planas, N., & Schütte, M. (2018). Research frameworks for the study of language in mathematics education. ZDM, 50(6), 965-974. https://doi.org/10.1007/s11858-018-0997-2
Rendell, G. (2008). Learning fraction sense: Applying Piaget's operative theory of meaning in a multi agent system to overcome the learning paradox. International Journal of Learning, 15(2).
Reynvoet, B., Smets, K., & Sasanguie, D. (2016). “Number Sense”: What’s in a Name and Why Should We Bother? In Continuous Issues in Numerical Cognition (pp. 195-214). Elsevier. https://doi.org/10.1016/B978-0-12-801637-4.00009-3
Riess, A. (1943). Numerical quantification vs. number sense. The Journal of Psychology, 15(1), 99-108.
São José, J. M. S., Amado, C. A. F., Ilinca, S., Buttigieg, S. C., & Taghizadeh Larsson, A. (2019). Ageism in health care: a systematic review of operational definitions and inductive conceptualizations. The Gerontologist, 59(2), e98-e108.
Sarama, J., Clements, D. H., Swaminathan, S., McMillen, S., & Gonzalez Gomez, R. M. (2003). Development of mathematical concepts of two-dimensional space in grid environments: An exploratory study. Cognition and Instruction, 21(3), 285-324. https://doi.org/10.1207/S1532690XCI2103_03
Sasanguie, D., Göbel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418-431. https://doi.org/10.1016/j.jecp.2012.10.012
Schacter, J., & Jo, B. (2017). Improving preschoolers’ mathematics achievement with tablets: a randomized controlled trial. Mathematics Education Research Journal, 29(3), 313-327. https://doi.org/10.1007/s13394-017-0203-9
Schacter, J., Shih, J., Allen, C. M., DeVaul, L., Adkins, A. B., Ito, T., & Jo, B. (2016). Math shelf: A randomized trial of a prekindergarten tablet number sense curriculum. Early Education and Development, 27(1), 74-88. https://doi.org/10.1080/10409289.2015.1057462
Sengul, S. (2013). Identification of Number Sense Strategies used by Pre-service Elementary Teachers. Educational Sciences: Theory and Practice, 13(3), 1965-1974. https://doi.org/10.12738/estp.2013.3.1365
Shaffril, H. A. M., Krauss, S. E., & Samsuddin, S. F. (2018). A systematic review on Asian's farmers' adaptation practices towards climate change. Science of the Total Environment, 644, 683-695.
Shoemaker, P. J., Tankard Jr, J. W., & Lasorsa, D. L. (2003). How to build social science theories. Sage publications.
Sierra-Correa, P. C., & Kintz, J. R. C. (2015). Ecosystem-based adaptation for improving coastal planning for sea-level rise: A systematic review for mangrove coasts. Marine Policy, 51, 385-393.
Sterner, G., Wolff, U., & Helenius, O. (2020). Reasoning about Representations: Effects of an Early Math Intervention. Scandinavian Journal of Educational Research, 64(5), 782-800. https://doi.org/10.1080/00313831.2019.1600579
Szűcs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2014). Cognitive components of a mathematical processing network in 9‐year‐old children. Developmental Science, 17(4), 506–524. https://doi.org/10.1111/desc.12144
Timasheff, N. S. (1947). Definitions in the social sciences. American Journal of Sociology, 53(3), 201-209.
Tsvetkov, V. Y. (2014). Dichotomous Systemic Analysis. Life Science Journal, 11, 586-590.
Vaismoradi, M., Jones, J., Turunen, H., & Snelgrove, S. (2016). Theme development in qualitative content analysis and thematic analysis. Journal of Nursing Education and Practice, 6(5), 100-110. https://doi.org/10.5430/jnep.v6n5p100
Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2017). Number sense in the transition from natural to rational numbers. British Journal of Educational Psychology, 87(1), 43-56. https://doi.org/10.1111/bjep.12134
Verschaffel, L., Greer, B., & Torbeyns, J. (2006). Numerical thinking. In A. Gutie´rrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present and future (pp. 51-82). Sense Publishers.
Verschaffel, L., Greer, B., and De Corte, E. (2017). Whole number concepts and operations. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). IAP.
Voronin, I. A., Ovcharova, O. N., Bezrukova, E. M., & Kovas, Y. (2018). Cognitive and non-cognitive predictors of the unified state exam performance of students from schools with regular and advanced mathematical curricula. Psychology in Russia: State of the art, 11(4), 177-199. https://doi.org/10.11621/pir.2018.0412
Wright, B. (1994). Mathematics in the lower primary years: A research-based perspective on curricula and teaching practice. Mathematics Education Research Journal, 6(1), 23-36. https://doi.org/10.1007/BF03217260
Xinkui, L. (2016). From" Evolution of Literature" to" Bias of Perspective": Imposed Interpretation and the Definition of Literary Theory. Journal of Graduate School of Chinese Academy of Social Sciences, 01.
Yang, D. C., & Hsu, C. J. (2009). Teaching number sense for 6th graders in Taiwan. International Electronic Journal of Mathematics Education, 4(2), 92-109.
Yang, D. C., Li, M. N., & Lin, C. I. (2008). A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics. International Journal of Science and Mathematics Education, 6(4), 789-807. https://doi.org/10.1007/s10763-007-9100-0
Yilmaz, Z. (2017). Young children’s number sense development: Age related complexity across cases of three children. International Electronic Journal of Elementary Education, 9(4), 891-902.
Zanzali, N. A. A., & Ghazali, M. (1997). Assessment of school children’s number sense. Proceedings of the International Conference on Mathematics Education into the 21st Century: Societal Changes: Issues and Approaches.

How to cite this article

APA

Ghazali, M., Mohamed, R., & Mustafa, Z. (2021). A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), em1968. https://doi.org/10.29333/ejmste/10871

Vancouver

Ghazali M, Mohamed R, Mustafa Z. A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years. EURASIA J Math Sci Tech Ed. 2021;17(6):em1968. https://doi.org/10.29333/ejmste/10871

AMA

Ghazali M, Mohamed R, Mustafa Z. A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years. EURASIA J Math Sci Tech Ed. 2021;17(6), em1968. https://doi.org/10.29333/ejmste/10871

Chicago

Ghazali, Munirah, Rosmawati Mohamed, and Zainun Mustafa. "A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 6 (2021): em1968. https://doi.org/10.29333/ejmste/10871

Harvard

Ghazali, M., Mohamed, R., and Mustafa, Z. (2021). A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), em1968. https://doi.org/10.29333/ejmste/10871

MLA

Ghazali, Munirah et al. "A Systematic Review on The Definition of Children’s Number Sense in the Primary School Years". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 6, 2021, em1968. https://doi.org/10.29333/ejmste/10871