Volume 12 Issue 2 (2023)

Misconceptions about Numbers and Operations–A Case Study of Preschoolers

pp. 57-74  |  Published Online: May 2023  |  DOI: 10.22521/edupij.2023.122.4 (registering DOI)

Artemis Eleftheriadi, Konstantinos Lavidas, Gerasimos Koustourakis, Stamatis Papadakis


Background/purpose – Investigation into the misconceptions of preschool students in mathematics and their differences between the ages 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been carried out on preschoolers’ previous knowledge and misconceptions about mathematics, no corresponding research has been found in Greece. This study aims to investigate preschoolers’ misconceptions about numbers and operations and to reveal differences between preschoolers aged 4-5 and 5-6 years.

Materials/methods – Data was collected through semi-structured interviews and analyzed using the content analysis method.

Results – The results showed that 5-6 years old preschoolers perform better than the 4-5 years old ones. Most misconceptions of the latter group appeared to be related to reverse counting, identifying arithmetic symbols and their matching quantities, adding and removing numbers without using auxiliary objects and multiplication. On the contrary, some preschoolers aged 5-6 needed help adding or subtracting two-digit numbers without using auxiliary objects. There were also a few cases where cardinality, division and multiplication were observed.

Conclusion – The distribution of students in kindergarten is mostly mixed aged groups, these findings will enable teachers to offer and personalize teaching support to these two aged groups.

Keywords: Maths, preschool education, numbers, operations, knowledge skills, misconceptions


AlAjmi, M. K. (2022). The impact of digital leadership on teachers’ technology integration during the COVID-19 pandemic in Kuwait. International Journal of Educational Research, 112, 101928. https://doi.org/10.1016/j.ijer.2022.101928

Alkhadim, S.G., Cimmeta, D. A., Marx, W.R., Gutshaw, A.C., Yaden, B.D. (2021). Validating the research-based early math assessment (REMA) among rural children in southwest United States. Studies in Educational Evaluation, 68. doi: https://doi.org/10.1016/j.stueduc.2020.100944

Aubrey, C. (1993). An investigation of the mathematical knowledge and competencies which young children bring into school. British Educational Research Journal, 19, 27–41. doi: https://doi.org/10.1080/0141192930190103

Babark, H.Z., Mohamedamin, P., Kakamad, K. (2019). Piaget’s cognitive developmental theory: critical review. Education Quarterly Reviews, 2, 517-524. doi: https://doi.org/10.31014/aior.1993.02.03.84

Bernstein, B. (2000). Pedagogy, Symbolic control and identity. Theory, Research, Critique. (Revised edition). N.Y.: Rowman & Littlefield

Bryman, A. (2016). Social research methods. Oxford University Press

Charlesworth, R., Leali, A.S. (2012). Using problem solving to assess young children’s mathematics knowledge. Early Childhood Education Journal, 39, 373–382. doi: https://doi.org/10.1007/s10643-011-0480-y

Claessens, A., Duncan, G., Engel, M. (2009). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28, 415-427. doi: https://doi.org/10.1016/j.econedurev.2008.09.003

Clements, H.D., Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the “Building Blocks” project. Journal for Research in Mathematics Education, 38, 136-163. doi: https://doi.org/10.2307/30034954

Copley, J.V. (2009). The young child and mathematics (2nd ed.).Washington DC: National Association of Education for Young Children

Dafermou, C., Koulouri, P., Mpasagianni, E. (2006). Kindergarten Teachers’ Guide. Athens: OEDB (in Greek)

Eleftheriadi, A., Lavidas, K., Komis, V. (2021). Teaching Mathematics in Early Childhood Education with ICT: The Views of Two Contrasting Teachers’ Groups. Journal of Digital Educational Technology, 1. doi: https://doi.org/10.21601/jdet/11117  

Engel, M., Claessens, A., Finch, A.M. (2013). Teaching students what they already know? The (Mis)Alignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis, 35, 157-178. doi: https://doi.org/10.3102/0162373712461850 

[European Education and Culture Executive Agency] (n.d.). https://national-policies.eacea.ec.europa.eu/

Hurst, M., Anderson U., Cordes, S. (2016). Mapping among number words, numerals, and nonsymbolic quantities in preschoolers. Journal of Cognition and Development, 18, 41–62. doi: https://doi.org/10.1080/15248372.2016.1228653

Koustourakis, G. (2007). The new educational policy for the reform of the curriculum and the change of school knowledge in the case of Greek compulsory education. International Studies in Sociology of Education, 17, 131-146. doi: https://doi.org/10.1080/09620210701433878

Koustourakis, G. (2013). A Sociological Approach to the Official Discourse on Space in the case of Greek Kindergarten Classrooms. The International Journal of Early Childhood Learning, 19, 1-13. doi: https://doi.org/10.18848/2327-7939/CGP/v19i03/48399

Koustourakis, G. (2014). A Sociological Approach to Painting Teaching according to the Contemporary Greek Kindergarten Curriculum. The International Journal of Early Childhood Learning, 20, 23-37. doi: https://doi.org/10.18848/2327-7939/CGP/v20i01/48408

Koustourakis, G. (2018). Classroom space and kindergarten curriculum: a sociological approach to teachers' discourse on the status of space and its use in teaching. European Journal of Alternative Education Studies, 3, 47-65. doi: https://doi.org/10.5281/zenodo.1422864

Koustourakis, G., Zacharos, K. (2011). Changes in School Mathematics Knowledge in Greece: a Bernsteinian Analysis. British Journal of Sociology of Education, 32, 369-387. doi: https://doi.org/10.1080/01425692.2011.559339

Lavidas, K., Skopeliti, I., Zacharos, K., & Panagiotounakos, E. (2023). Preservice preschool teachers’ mathematics experience and math anxiety on their beliefs about and attitudes toward teaching mathematics, Journal of Early Childhood Teacher Education. https://doi.org/10.1080/10901027.2023.2196943

Lavidas, K., Apostolou, Z., Papadakis, S. (2022). Challenges and Opportunities of Mathematics in Digital Times: Preschool Teachers’ Views. Education Sciences, 12, 459. MDPI AG. doi: http://dx.doi.org/10.3390/educsci12070459

Lee, J. (2014). Is children’s informal knowledge of mathematics important? Rethinking assessment of children’s knowledge of mathematics. Contemporary Issues in Early Childhood, 15, 293–294. doi: https://doi.org/10.2304/ciec.2014.15.3.293

Lee, J., Md-Yunus, S. (2016). Investigating children’s abilities to count and make quantitative comparisons. Early Childhood Education Journal, 44, 255-262. doi: https://doi.org/10.1007/s10643-015-0707-4

Litkowski, C.E., Duncan, J.R., Logan, A.R.J., Purpura, D.J. (2020). When do preschoolers learn specific mathematics skills? Mapping the development of early numeracy knowledge. Journal of Experimental Child Psychology, 195, 105-114. doi: https://doi.org/10.1016/j.jecp.2020.104846

McDonald, A.J., Merkley, R., Mickle, J., Collimore, L., Hawes, Z., Ansari, D. (2021). Exploring the implementation of early math assessments in kindergarten classrooms: A research-practice collaboration. Mind Brain and Education, 15, 311–321. doi: https://doi.org/10.1111/mbe.12293

McDonald, A., Murphy, S. (2019). Mathematics education for children under four years of age: a systematic review of the literature. Early Years, 41, 522–539. doi: https://doi.org/10.1080/09575146.2019.1624507

McGuire, P., Kinzie, B.M., Berch, B.D. (2011). Developing number sense in Pre-K with five-frames. Early Childhood Educational Journal, 40, 213–222. doi: https://doi.org/10.1007/s10643-011-0479-4

Ministry of Education Curriculum for kindergarten [New school. School of 21st century. New Curriculum]. (2014). Greece: Athens, YPEPTH/P.I. [in Greek]

Muthukrishnan, P., Kee, M.S., Sidhu, G.K. (2019). Addition Error Patterns Among the Preschool Children. International Journal of Instruction, 12, 115–132. doi: https://doi.org/10.29333/iji.2019.1228a 

National Council of Teachers of Mathematics. (2001). Principles and standards for school mathematics. Reston VA: National Council of Teachers of Mathematics

Nguyen, H.N., Laski, V.E., Thomson, L.D., Bronson, B.M., Casey, M.B. (2017). More Than Counting: Learning to Label Quantities in Preschool. YC Young Children, 72, 22–29. doi: https://www.jstor.org/stable/90013678

Ohio Department of Education. (2004). Early learning content standards. Columbus, OH: Author

Piaget, J. (1952). The origin of intelligence in children. New York: International University Press

Piaget, J., Gruber, H.E., Vonèche, J.J. (1995). The essential Piaget: an interpretive reference and guide. Northvale, N.J.: Jason Aronson Inc

Pogiatzi, M., Bardoutsou, I., Lavidas, K., Komis, V. (2022). Interviewing preschool children in Greece about their usage of mobile devices at home. SN Social Sciences, 2, 215. doi: https://doi.org/10.1007/s43545-022-00522-5

Sarama, J., Clements, H.D. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge

Shiakalli, M. A., Zacharos, K., Lavidas, K. (2017). Preparing preschool teachers for teaching probability. Review of Science, Mathematics and ICT Education, 11, 93-117. doi: https://doi.org/10.26220/rev.2810

Watts, W.T., Duncan, J.G., Siegler, S.R., Davis-Kean, E.P. (2014). What is past is prologue: Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43, 352–360. doi: https://doi.org/10.3102/0013189 × 14553660

Zacharos, K., Koustourakis, G., Papadimitriou, K. (2014). Analyzing the implemented curriculum of Mathematics in Preschool Education. Mathematics Education Research Journal, 26, 151–167. doi: https://doi.org/10.1007/s13394-013-0086-3



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