Background

In this blog, I anticipate discussing some of the pertinent issues about young children´s mathematics learning in early childhood institutions such as preschools and kindergartens. This issue raises many issues to do with childhood and the best way to support teaching and learning.

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There are many reasons why this interest is receiving so much attention now. An analysis by Greg Duncan and colleagues of six longitudinal studies suggested that early mathematics knowledge is the most powerful predictor of later learning including the learning of reading (Duncan et al., 2007). This and concerns, such as that preschools are inhibiting children from learning the deep mathematics of which they were capable (Clements & Sarama, 2007), has resulted in preschool mathematics education becoming a focus in recent years (Barber, 2009; Perry, Young-Loveridge, Dockett, & Doig, 2008). Many countries, such as New Zealand (Haynes, 2000), are faced with a dilemma of wanting to ensure that children begin school with stronger mathematical understandings, while also wanting to adhere to the philosophy that preschool children should learn through play. This is a dilemma that some see as irreconcilable (Lee & Ginsburg, 2009; Carr & May, 1996).

The role of the teacher is one of the issues that is raised. Some believe that preschool teachers should not interfere with children´s play and that children will learn simply from being engaged in different situations. However, in her research, Björklund (2008) showed that adults were important in setting the parameters for children’s opportunities to engage with mathematical ideas. When adult support is not available, then concerns have been raised about whether children are able to explicitly explore mathematical ideas while playing:

Children do indeed learn some mathematics on their own from free play. However, it does not afford the extensive and explicit examination of mathematical ideas that can be provided only with adult guidance. … Early mathematics is broad in scope and there is no guarantee that much of it will emerge in free play. In addition, free play does not usually help children to mathematise; to interpret their experiences in explicitly mathematical forms and understand the relations between the two. (Lee & Ginsburg, 2009, p. 6)

It is the adult’s role which is crucial in preschool learning. In Sweden, concern was expressed about preschool teachers’ ability to use resources such as those designed by Fröbel, the German pedagogue who was instrumental in setting up preschools in the nineteenth century. Doverborg (2006) cited a study by Leeb-Lundberg (1972) which found that deep mathematical understanding was required for teachers to support students to use some of Fröbel’s equipment. When this was not provided in their teacher education, it was impossible for teachers to support children in developing mathematical understanding.

A consequence of these concerns, especially in English-speaking countries, has been the implementation of a number of mathematics teaching programs in preschools. An American project, Big Math for Little Kids, was founded on the view that children needed to be presented with activities in a cohesive manner, but that these activities should be joyful and contribute to developing children’s curiosity about mathematics (Greenes, Ginsburg, & Balfanz, 2004). Repetition of the activities provided opportunities for an extension of the mathematical ideas that were being introduced. For Greenes et al. (2004), the development of mathematical language was a key to helping children reflect on their learning.

Preschool mathematics programs of this type are generally sequenced with an expectation that children will move along a number of development progressions. For example, in another American project, Building Blocks, a set of activities were provided, based on learning trajectories for children (Sarama & Clements, 2004). Teachers who understood the learning trajectories were better able to provide “informal, incidental mathematics at an appropriate and deep level” (p. 188). Papic, Mulligan and Mitchelmore (2011) implemented an intervention program on repeating and spatial patterning in one preschool over a six month period. Children were grouped according to how they performed on an initial diagnostic interview and then provided with tasks for their level. A combination of individual and group time was provided. Children progressed to the next level if they showed competency in their current level. Papic et al. (2011) found that, after one year at school, the children performed better on a general numeracy assessment than children from a control group.

Although these programs support children to develop specific mathematical understandings, there are concerns about how formal instruction in early childhood settings could lead to “learned helplessness and a feeling of failure” (Farquhar, 2003, p. 21). Many preschool and early school programs, such as those described by Papic et al. (2011) and Clarke, Clarke and Cheeseman (2006), include assessing children before, or as, they enter school on their mathematical knowledge. Such assessments risk children being labelled as “behind” or “at-risk” at a much earlier age. Although designed to support teachers to target their teaching to the children’s levels, this has the potential to lower teachers’ expectations about children’s capabilities. As well, it may affect children’s perception of themselves as learners of mathematics. When combined with stories about the value of mathematics in their adult lives, being marked out as needing extra support to learn mathematics could limit their willingness to persevere because there is too much risk of accepting themselves as failures if they persist and still do poorly (Lange, 2008).

Another concern in whether a formal approach to mathematics teaching in preschool actually has a lasting impact on children’s academic performances. In a study of children from 3 preschools with different pedagogical approaches, Marcon (2002) found that at different ages, children showed different academic performance. At the last stage of the study when children moved into their sixth year of school, children who had attended a preschool that was academically focused showed the least progress. “Grades of children from academically directed preschool classrooms declined in all but one subject area (handwriting) following the Year 6 transition” (Marcon, 2002, p. 20).

Although a correlation may exist between mathematics knowledge on entering school and later learning, the circumstances of children’s lives will have contributed to the knowledge that they showed at all ages. In reporting on a longitudinal project, in New Zealand, that followed about 500 children till they were 10 years old Wylie (2001) found that:

children who started school with low literacy and mathematics scores were much more likely to improve their scores if their parents were highly educated, or if their family had a high income. Good quality early childhood education and experiences at home, or later out-of-school activities using language, symbols, and mathematics, also made improvement more likely. (p. 11)

The circumstances that meant that young children did not have “good quality childcare” may be the same circumstances that did not provide them with rich out-of-school activities. As Marcon (2002) warned there are many variables that affect children’s later school achievement, not just their preschool programs.

Regardless of the uncertainty about whether a more formal approach to the teaching of mathematics in preschool has an impact of children’s later academic performance, it is unlikely that the lid of this Pandora’s Box can be closed. Consequently, discussion around how young children should engage in mathematics in preschools will continue .

References

Barber, P. (2009). Introduction. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, 28th January to 1st February 2009, Lyon (France), (pp. 2535-2536). Institut National de Recherche Pèdagogique. Retrieved from http://www.inrp.fr/editions/editions-electroniques/cerme6/working-group-14

Björklund, C. (2008). Toddlers’ opportunities to learn mathematics. International Journal of Early Childhood, 40(1), 81-95.

Carr, M. & May, H. (1996). The politics and processes of the implementation of Te Whaariki, the New Zealand national early childhood curriculum 1993-6. In M. Carr & H. May (Eds.), Implementing Te Whaariki (pp. 1-13). Wellington: Institute for Early Childhood Studies.

Clarke, B., Clarke, D. M., & Cheeseman, J. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18(1), 78-102

Clements, D. H. & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester (Ed.), Second handbook of research in mathematics teaching and learning (pp. 461-555). Charlotte, NC: Information Age.

Doverborg, E. (2006). Svensk förskola [Swedish pre-school]. In E. Doverborg & G. Emanuelsson (Eds.), Små barns matematik [Small children’s mathematics] (pp. 1-10). Göteborg: NCM Göteborgs Universitet.

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanow, P. et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446.

Farquhar, S.-E. (2003). Quality teaching early foundations: Best evidence synthesis iteration. Wellington: New Zealand Ministry of Education. Retrieved from http://www.educationcounts.govt.nz/publications/series/2515/5963

Greenes, C., Ginsburg, H. P., & Balfanz, R. (2004). Big math for little kids. Early Childhood Research Quarterly, 19(1), 159-166.

Haynes, M. (2000). Mathematics education for early childhood: A partnership of two curriculums. Mathematics Teacher Education & Development, 2, 93-104.

Lange, T. (2008). A child’s perspective on being in difficulty in mathematics. The Philosophy of Mathematics Education Journal, 23. Retrieved from: http://people.exeter.ac.uk/PErnest/pome23/index.htm

Lee, J. S. & Ginsburg, H. P. (2009). Early childhood teachers’ misconceptions about mathematics education for young children in the United States. Australasian Journal of Early Childhood, 34(4), 37-45. Retrieved from: http://www.earlychildhoodaustralia.org.au/australian_journal_of_early_childhood/ajec_index_abstracts/ajec_vol_34_no_4_december_2009.html

Marcon, R. A. (2002). Moving up the grades: Relationship between preschool model and later school success. Early Childhood Research and Practice, 4(1). Retrieved from: http://ecrp.uiuc.edu/v4n1/index.html

Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237-268

Perry, B., Young-Loveridge, J., Dockett, S., & Doig, B. (2008). The development of young children’s mathematical understanding. In H. Forgasz, A. Barkatsas, A. J. Bishop, B. Clarke, S. Keast, W. T. Seah, & P. Sullivan (Eds.), Research in mathematics education in Australasia 2004-2007 (pp. 17-40). Rotterdam: Sense Publishers.

Sarama, J. & Clements, D. H. (2004). Building Blocks for early childhood mathematics. Early Childhood Research Quarterly, 19(1), 181-189.

Wylie, C. (2001). Ten years old & competent: The fourth stage of the competent children’s project – a summary of the main findings. Wellington: New Zealand Council for Educational Research. Retrieved from http://www.nzcer.org.nz/research/publications/ten-years-old-and-competent-fourth-stage-competent-children-project-summary-ma

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