Note: The countries listed in purple following each reference, 

indicate where the author/s reside.

Apologies: We are aware that there are number of other

articles and chapters that relate to Children's Mathematical

Graphics, however, we regret that unless they are published

in English, we are unable to include them. Since we are unable to provide access for you to read the content of books we have included

just a few, key texts.

Our publications: Carruthers, E., & Worthington, M. [England]

Mathematics: 

Anantharajan, M. (2020). Teacher noticing of mathematical thinking in young children’s representations of counting. Journal for Research in Mathematics Education, 51(3),268-300. [The Netherlands]

Aubrey, C. (1994). An investigation of children’s knowledge of mathematics school entry and the knowledge their teachers hold about teaching and learning mathematics, about young learners and mathematical subject knowledge, British Educational Research Journal, 20(1), pp. 105-120. [England]   

Barnes, C. (2005). Too much teaching? Mathematics Teaching 190, pp. 23-25. March 2005. [England]   

Berciano, A., Jiménez-Gestal, C., & Salgado, M. (2017). Kindergartners’ use of symbols in the semiotic representation of 3-Dimensional changes. International Electronic Journal of Mathematics Education, 11(3), 311-331. [Spain]

                                                      Brizuela, B. (2004). Mathematical development in young children:

                                                             Exploring notations. Teachers College Press. [USA]

Butcher, E. (2017). Mathematics in the Early Years can be pressure-free and everywhere for everyone. ATM. [England]

Cartwright, K. (2023). Interpreting young children’s multiplicative strategies through their drawn representations. Mathematics Education Research Journal. [Australia]

Clarke, D. M. (2015). Written algorithms in the primary years: Undoing the ‘good work’? Making mathematics vital. Proceedings of the twelfth biennial conference of the Australian Association of Mathematics Teachers, 93-98. [Australia]

Cook, D. (2001). ‘You can't have a cake unless it's written down’: Semiotic activity and authentic learning in play as a potential tool for analysis. Early Child Development and Care, 168(1), 49-62. [England]

Cook, D. (2006). Mathematical sense making and role play in the nursery. Early Childhood Development and Care, 121(1), 55-66. [England]

Culverhouse, H. (2017). An investigation into indoor and outdoor mathematical play. Association of Teachers of mathematics (ATM). May, 2017. [England]

Davies, E. (2017). How can we develop children’s mark making and independence to encourage their use of mathematical graphics? Bristol Early Years Research. [England]

Disney, L., Li, L. (2022). Above, below, or equal? Exploring teachers’ pedagogical positioning in a playworld context to teach mathematical concepts to preschool children. Teaching and Teacher Education, 114. [Australia]

Dooley, T., Dunphy, E., & Shiel, G. (2014). Mathematics in early childhood and primary education (3 – 8 years): Definitions, theories, development and progression. Research report no. 17. National Council for Curriculum and assessment. [Ireland]

Downton, A., & Maffia, A.(2023). Preschool children's representation of division word problems through drawings. Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education. Haifa, Israel, July 16-21, 2023. [Australia & Italy]

Edo, M., Planas, N., & Badillo, E. (2009). Mathematical learning in a context of play. European Early Childhood Education Research Journal, 17(3), 325–341. [Spain]

Ewers-Rogers, J., & Cowan, R. (1996). Children as apprentices to number. Early Child Development and Care 125, 15-25. [England]

Figueiredo, M. P., Gomes, H., & Rodrigues, C. (2018). Mathematical pedagogical content knowledge in Early Childhood Education: tales from the ‘great unknown’ in teacher education in Portugal. European Early Childhood Education Research Journal, 26(4), 535–546.  [Portugal]

Finesilver, C. (2022). Beyond categories: Dynamic qualitative analysis of visuospatial representation in arithmetic. Educational Studies in Mathematics, 110, 271-290. [England]

Fragkiadaki, G. (2020). Young children’s representations and ideas about the mathematical signs of plus and minus. European Journal of Alternative Education Studies, 5(1), 108-119. [Greece]

Glasgow Counts: A framework for mathematics. (2021). [Scotland]

Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning.1 (2), 155-177. [The Netherlands]

Hazily Alkan. S., & Sahin, I. (2023). Addressing language diversity in early years mathematics: Proposed classroom practices through a live brief assessment.  Edu.Sci. 13(10), 1025. [England / Hungary]

Hofslundsengen, H.,  Magnusson, M.,  Svensson, A-K.,  Jusslin, S., Mellgren, E., Hagtvet, B. E., & Heilä-Ylikallio, R. (2020). The literacy environment of preschool classrooms in three Nordic countries: Challenges in a multilingual and digital society, Early Child Development and Care, 190(3), 414-427. [Norway/Sweden/Finland]

Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Basil Blackwell. [England]

Jacoby, S. (2005). Thoughts on emergent maths. Mathematics Teaching, 193. [England]

Kaartinen, S., & Kumpulainen, K. (2012). The emergence of mathematizing as a culture of participation in the early childhood classroom. European Early Childhood Education Research Journal, 20 (2), 263-281.[Finland]

Konstantinidou, Z., Brentas, F., & Stamatoglou, M. (2024). The connections children develop between science and mathematics: An example of temperature measurement in the kindergarten. Contemporary Mathematics and Science Education, 5(1), ep24004. [Greece]

Leavy, A, M., & Hourigan, M. (2018). Inscriptional capacities of young children engaged in statistical investigations. In A.M. Leavy, M. Melitiou-Mavrotheris & E. Paparistodemou, (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking. Singer. [Ireland] 

Luciano, D., Trespoli, P., & Re, A-M. (2012). Path to numbers writing: A longitudinal study with children from 3.5 to 5.5 years old. Journal of Educational and Developmental Psychology, 2(2), 20-31. [Italy]

Mackay, K., Stephenson, N., Thomas, B., & McChesney, J. (2022). Recognising young children as mathematicians Connecting mathematical concepts to practices, pedagogy, and play. Early Childhood Folio, 26(1). [New Zealand]

MacDonald, A. (2012). Young children’s photographs of measurement in the home. Early Years, 32(1), 71-85. [Australia]    

MacDonald, A. (2013). Using children’s representations to investigate meaning-making in mathematics.Australasian Journal of Early Childhood, 38(2), 65–73. [Australia]

Moffett, P. (2019). Bring calculations to life with meaningful contexts. Early Years Education, (EYE). 20(9), 18-20. [Northern Ireland]

Moffett, P., & Eaton, P. (2018). The impact of the Promoting Early Number Talk project on the development of abstract representation in mathematics. European Early Childhood Education Research Journal, 26(4), 547-561. [Northern Ireland]

Munn, P. (1997). Writing and number. In I Thompson (ed.). Teaching and Learning Early Number. Open University Press.  [Scotland]

Munn, P. (1998). Number symbols and symbolic function in preschoolers. In C. Donlan (ed.). The development of mathematical skills. Psychology Press. [Scotland]

Munn, P. & Schaffer, R. (1993). Literacy and numeracy events in social interactive contexts. International Journal of Early Years Education, 1(3), 61-80.  [Scotland]

Nelson, E. (2014). Using students' pictorial representations to promote mathematical thinking. Yale-NewHaven Teachers Institute. Yale, USA. [USA]

Nikiforidou, Z. (2017). Risk literacy: Concepts and pedagogical implications for early childhood education.  Contemporary Issues in Early Childhood 18(3) 322–33. [Greece]H

Ott, B.  (2017). Children’s drawings for word problems-design of a theory and an analysis tool. CERME 10, Feb 2017, Dublin, Ireland. [Switzerland]

Ott, B.  (2020). Learner-generated graphic representations for word problems: an intervention and evaluation study in grade 3. Educational Studies in Mathemaitcs 105 (1), 91-113. [Switzerland]

Oughton, R., Nichols, K., Bolden, D. S., Dixon-Jones, S., Fearn, S., Darwin, S., … Townsend, A. (2022). Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematicians. Mathematical Thinking and Learning, 1–20. [England]

Palmér, H., & and van Bommel, J. (2020). The role and connection between systemization and representation when young children work on a combinatorial task. In O. Thiel & B. Perry (Eds.). Innovative Approaches in Early Childhood Mathematics. Routledge. [Sweden]

Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation(s) in developing mathematical understanding, Theory Into Practice, 40 (2), 118-127. [USA]

Papandreou, M. (2019). Young children's representational practices in the context of self-initiated data investigations. Early Years, 42(3), 371-387. [Greece]

Papandreou, M., & & Konstantinidou. (2020). 'We make stories one meter long": Children's participation and meaningful mathematical learning in early childhood classrooms. Review of Science, Mathematics & ICT Education,14(2), 43-64. [Greece]

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. [Greece]

Parviainen, P., Eklund, K., Koivula, M., Liinamaa, T., & Rutanen, R. (2023). Teaching early

mathematical skills to 3‐ to 7‐year‐old children — Differences related to mathematical skill category, children’s age group and teachers’ characteristics. International Journal of Science and Mathematics Education, 21, 1961–1983. [Finland]

Perry, B., & Dockett, S. (2008). Young children's access to powerful mathematical ideas. In L. D. English (Ed.), Handbook of international research in mathematics education, pp. 81-112. Routledge. [Australia]

Petersson,J., Sayers, J., Rosenqvist, E., &  Andrews, P. (2022). Parent-initiated activities in support of Swedish year-one children’s learning of mathematics: Age-appropriate complements to school? International Journal of Early Years Education, 30 (4), 831-846. [Sweden / UK / Denmark]

Poland, M., & van Oers, B. (2007). Effects of schematising on mathematical development. European Early Childhood Education Research Journal, 15(2), 269–293. [The Netherlands]

Poland, M., van Oers, H. J. M., & Terwel, J. (2009). Schematising activities in early childhood education. Educational Research and Evaluation, 15(3), 305-321. [The Netherlands]

Pollitt, R., Cohrssen, C., & Wright, S. (2015). Thirty-one is a lot!: Assessing four-year-old children's number knowledge during an open-ended activity. Australasian Journal of Early Childhood, 40(1), 13-22. [Australia]

Pound, L. (2012). EYFS best practice: Be specific ... mathematics. Nursery World (7th December). [England]

Read, M.J. (2022). Capstone project : Zometool: From 0 to the 4th dimension: from 0 to the 4th dimension. California State University. Masters Thesis. [USA]

Reikerås, E. (2020). Relations between play skills and mathematical skills in toddlers. ZDM, 52(4), 703-716. [Norway]

Rose, J., & Gilbert, L. (2017). Learning, development and the curriculum. Chapter 5, BERA – TACTYC Early Childhood Research Review 2003 – 2017. [England]

Salomonsen, T. (2020). What does the research tell us about how children best learn mathematics? Early Child Development and Care, 190(13), 2150–2158. [Norway]

Schäfer, J. (2010).  An investigation of how visual arts can be used to teach mathematical concepts of space and shape in grade R. MA, Rhodes University. [South Africa]

Svensson, C. (2022). Discerning preschool teacher’s experiences to enhance children’s participation in mathematical play activities. Springer Nature Social Sciences, 2, 157. [Sweden]

Schäfer, J. (2010).  An investigation of how visual arts can be used to teach mathematical concepts of space and shape in grade R. MA, Rhodes University. [South Africa]

Svensson, C. (2022). Discerning preschool teacher’s experiences to enhance children’s participation in mathematical play activities. Springer  Nature Social Sciences, 2, 157. [Sweden]

Terwel, J., van Oers, B., van Dijk, I., & van den Eeden, P. (2009). Are representations to be provided or generated in primary mathematics education? Educational Research and Evaluation, 15(1), 25-44. 

Thompson, I. (2008). What do young children's mathematical graphics tell us about the teaching written calculatlions? In I .Thompson (Ed.). Teaching and learning early number. 2nd ed. Open University Press. [England]

Tolchinsky, L. (2003). The cradle of culture and what children know about writing and numbers before being taught. Lawrence Erlbaum. [USA]

Tomasello, M. (2003). Constructing a language: A usage-based theory of language acquisition. Harvard University Press. [Germany]

Vandersteen, G. (2002). Children's own methods of recording number: "I will do two writings" Mathematics in School, 31(5), 2-8. [England]

Van Dijk, I. M. A. W., van Oers, B., & Terwel, J. (2003). Providing or designing? Constructing models in primary maths education. Learning and Instruction, 13, 53-72. [The Netherlands]

van Dijk, I. M. A. W. , van Oers, B. , Terwel, J. and Eeden, P. van den. (2003). Strategic learning in primary mathematics education: Effects of an experimental program in modelling, Educational Research and Evaluation, 9(2), 161 — 187.  [The Netherlands]

van Dijk, E.F., van Oers, B., & Terwel, J. (2004): Schematising in early childhood mathematics education: Why, when and how? European Early Childhood Education Research Journal, 12(1), 71-83. [The Netherlands]

Vanegas, Y., Prat, M., & Edo, M. (2022). Mathematical representations of 5 and 6-year-old children when solving an open-ended problem. Alteridad: Revista de Educación, 17 (2), 180. [Spain]

van Oers, B. (2000). The appropriation of mathematical symbols: A psychosemiotic approach to mathematical learning. In P. Cobb., E. Yackel., & K. McClain. (eds.). Symbolizing and communicating in mathematics classrooms. In Lawrence Earlbaum Associates. [The Netherlands]

van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in

Mathematics, 74(1), 23-37. [The Netherlands]

van Oers, B. (2013). Communicating about number: Fostering young children's mathematical orientation in the world. In L. English & J. Mulligan (eds.). Reconceptualising Early Mathematics Learning: Advances in Mathematics Education. Springer. [The Netherlands]

van Oers, B. (2023). The development of mathematical thinking in young children’s play: The role of communicative tools. In: Palmér, H., Björklund, C., Reikerås, E., Elofsson, J. (eds).Teaching Mathematics as to be Meaningful – Foregrounding Play and Children’s Perspectives. Springer, Cham. [The Netherlands]

Voutsina, C., Stott, D. (2023). Preschool children’s conceptions of the meanings and use of written numerals in everyday life: a phenomenographic study of the nature and structure of qualitative variation. Educational Studies in Mathematics. [England]

Wilmot, D., & Schafer, J. (2015). Visual arts and the teaching of the mathematical concepts of shape and space In Grade R classrooms. South African Journal of Childhood Education, 5(1), 62-84. [South Africa]

Zhang, W., Li, L., & Disney, L. (2023). Chinese early childhood teachers’ perspectives on mathematics education in play-based contexts. Early Years. [Australia]