Editorial

The original rationale for this special issue on early childhood mathematics education was to make visible the wealth of research in this area which, we argue, has been under-valued in recent times. Arguably, this is a consequence of increased attention on school achievement and the need to develop methodological paradigms which focus on “what works” in raising attainment, which contrasts with earlier exploratory studies of how and why young children learn. However, this under-valuation is perplexing given the widespread belief that children’s early experiences with mathematics (aged 0 to eight years) have a lasting impact on their progress, attainment and disposition to study mathematics later in their educational career. In light of this, the articles in this special issue are selected in order to represent the diversity of research in this area. They draw on various theoretical perspectives and methodologies to critically explore the foundations of young children’s competencies and relationships with mathematics and the forms of pedagogy deemed appropriate to teaching mathematics in early childhood. They also span a number of national contexts, education systems and learning environments (the family home, kindergarten, early school) and consequently utilise a number of different terms to refer to “early childhood” including: preschool, early years and pre-primary. For the sake of clarity, we have defined early childhood mathematics education as that which involves children aged 0 to eight years. This may include a variety of educational settings: kindergarten, private day nurseries, preschool and the early years of formal schooling depending on the country/education system in which it is situated.

The special issue consists of five research articles which we have loosely grouped together to reflect two key themes: (1) recognising the mathematical competencies of young children and the importance of their beliefs about learning mathematics; and (2) conceptualisations of pedagogy in early childhood mathematics education policy and practice. At the heart of these two themes lies an overarching focus on the child as an agent in the learning process. In relation to the first theme, agency can be seen in the recognition of the child as a subject/actor engaged with others (carers, teachers, researchers) in mathematising in the world through which they develop a mathematical perspective and also an awareness of themselves as mathematics learners. The second theme seeks to question how the agency of the child is located within conceptualisations of pedagogy for early childhood, with a distinction drawn between approaches that are led by the child and those led by the teacher. Typically, it is the former approach which emphasises the child’s agency, with the adult facilitating opportunities for spontaneous mathematising rather than teaching a mathematics curriculum. This contrasts with some versions of a teacher-led approach whereby the child may be given less access to mathematising if the teacher must adhere to a prescriptive, fast paced curriculum with rigid learning objectives in order to prepare children for the formal school mathematics curriculum. Crucial to this distinction is the question of how we understand the purpose of early childhood mathematics education and early childhood education more broadly. From a social pedagogy perspective, this purpose is typically focused on building the whole child to enable their independence in the outside world. Whereas, a school readiness approach in its most stringent form, might typically be designed purely to raise attainment later in the school career.

Theme 1: Mathematical competencies and beliefs in early childhood mathematics

Historically, much of the literature on mathematics in early childhood has focused on young children’s understandings of key mathematical concepts and principles such as the cardinality and ordinality of number (e.g. Gelman & Gallistel, 1978), the use of symbolic number systems (Mundy & Gilmore, 2009) and the emergence of mathematical thinking through dialogue in the home (Hughes, 1981, 1986; Melhuish, Phan et al., 2008) and play (van Oers, 2010). In this body of literature, an important aim has been to challenge deficit assumptions regarding young children’s mathematical competencies (see earlier work by Hughes, 1986; and Gelman, 1972) and to demonstrate that they are capable of engaging in more complex mathematics much earlier than previously thought (e.g. number, algebra or modelling). In this respect, the “social turn” in mathematics education (Lerman, 2000) has been significant in shifting attention to the social practices, conceptual tools, and semiotic and material resources needed for adults to co-construct such competences with the learner.

The article offered by Pessia Tsamir, Dina Tirosh, Ruthi Barkai, and Esther Levenson adds to this body of literature by focusing on children’s competencies and engagement with repeated pattern tasks. Drawing on Fischbein’s concept of intuitive cognition, they present evidence regarding young children’s intuitive/non-intuitive engagement with repeated pattern structures (e.g. AB, ABB, ABC, ABA) as they solve puzzles on a tablet app. Through close analysis of three children’s physical gestures and verbalisations, they argue that some pattern structures (notably the ABA unit of repeat) appear to be non-intuitive to young children whereas other pattern structures such as AB, ABC are intuitively recognised which facilitates engagement with the task. As such, this article draws our attention to the balance between intuition and coercion which children negotiate as they engage with pattern structures and the unit of repeat. In making this argument, this article recognises the child as an agent, making their own decisions as they engage with the tablet app. It recognises the behaviour derived from these decisions (verbal and non-verbal) as evidence of intuition, coercion and non-intuitive thinking. Clearly this article has much to offer not only to the research field of early mathematics education but also to teachers and early childhood educators regarding children’s intuitive/non-intuitive engagement, which can be used in practice to facilitate children’s engagement with repeated pattern tasks.

In a similar vein, the article presented by Einav Keisar and Irit Peled illustrates the potential of enabling young children to develop mathematical competencies through modelling tasks. Although there is much written about mathematical modelling tasks/ problems in the later stages of schooling, there is to date only very limited research on young children learning through such tasks (English 2010, 2012; Leavy & Hourigan, 2018). This article analyses young children’s engagement with a series of group modelling tasks and uses a timeline representation of the modelling cycle to identify how they shift their approach to problem-solving as the tasks progress. A key argument in this article is that modelling tasks such as those it describes require a change in the didactical contract between teacher and child – for example, the socio-mathematical norms of the classroom (Yackel & Cobb, 1996) – and, consequently, the establishment of new curricular goals. The analysis offered here highlights how modelling tasks, such as those described in the article, place the child at the centre of the learning activity, whereby they must act as problem-solvers (with peers) engaged in meaningful tasks or problems. A key finding is that such modelling tasks can encourage young children’s spontaneous use of mathematical concepts. As noted elsewhere in the literature on modelling (Vos, 2011), this recognises the importance of task authenticity and thus addresses the problem of how to utilise young children’s “everyday” or embedded mathematical concepts in teaching formal school mathematics.

Next, the article by Jo Towers, Miwa Takeuchi and Lyndon Martin focuses on young children’s emotional relationships with mathematics and their beliefs about their own mathematical competencies and those of others. As such, this article takes a critical stance on the social and discursive construction of what it means to be mathematically competent and the cultural norms, values and beliefs children draw on in constructing beliefs about their own competencies. They particularly focus on parents’ voices and the cultural norms associated with classroom practices demonstrating how they are evident in young children’s images of, and emotional relationships with, mathematics. This article makes an important contribution to the field, given the lack of literature on young children’s developing emotional relationships with mathematics (with the exception of work on mathematics anxiety – Sorvo et al., 2017 and Cargnelutti, Tomasetto & Passolunghi, 2016). In doing so, they highlight how beliefs and feelings which are frequently described in the literature on adolescent attitudes towards mathematics (such as “maths is a hard subject”) are also present in the mathematical autobiographies of young children. The child’s voice is clearly foregrounded in the autobiographical method since it positions them as a research collaborator, whereby they are given agency to express their own beliefs. However, this article also explains how the beliefs expressed through such autobiographies are mediated by the voice of others (e.g. parents) who may or may not be directly present.

Theme 2: Conceptualising pedagogy in early childhood education policy and practice

The notion of teaching mathematics in early childhood to prepare children for the school curriculum and thereby improve later attainment has received support in some sections of the research community (Clements & Sarama, 2009; Melhuish, Sylva et al., 2008; Sylva, Melhuish, Sammons, Siraj-Blatchford, & Taggart, 2011). However, this special issue presents two articles that offer critical analysis of this argument by investigating how pedagogies for early mathematics education are represented in policy and are understood in practice. Both seek to evaluate the tensions, conflicts and connections between a “school readiness” approach (i.e. teaching mathematics to prepare the way for the formal school mathematics curriculum) and social “play-based” pedagogies. As we note above, this debate dominates the early childhood education sector internationally – as captured in the Starting Strong II report by OECD (2006) referred to in the article by Fosse et al. For instance, whilst the Nordic countries have a strong social pedagogy tradition, in England, the Early Years Foundation Stage (EYFS) has introduced goals for early mathematics learning (Gifford, 2014) which are intended to prepare children for the school mathematics curriculum. Arguably, this has made pupil (whether child, toddler or infant) assessment highly visible whereby mathematical competencies are measured in relation to a normative developmental trajectory culminating in “readiness” for the school curriculum at age five. Such assessment is then also used to measure the quality of provision in early childhood settings so that the child becomes an output of the teaching process rather than an agent of their own learning. There has been much criticism and resistance to the “school readiness” approach internationally (see for example the More than a Score campaign in England resisting the introduction of Baseline Assessment at age five: www.morethanascore.org.uk).

In relation to this debate, the article by Trude Fosse, Troels Lange, Magni Hope Lossius and Tamsin Meaney presents a critical analysis of how a pedagogy for “school readiness” is gradually seeping into early childhood education policy in Norway, particularly in relation to mathematics. The article’s location in the Norwegian context is significant, given recent resistance amongst early childhood educators to the notion of using kindergarten to “prepare children for school” – viewed as a marker of the schoolification of early childhood education. Using Critical Discourse Analysis (CDA) of both Norwegian and OECD policy documents, the authors highlight how words such as “teaching” and “learning” are connected more strongly to mathematics (and its synonyms) than words such as “playing”, which are associated with the social pedagogy tradition. They also highlight how such documents connect “playing” to social skills and a discourse regarding “care”, which reduces the function of the social pedagogy and consequently, positions the “school readiness” approach as a necessary requirement for developing children’s mathematical competencies. They argue, therefore, that mathematics can be viewed as “a Trojan horse” in this context, shifting early childhood policy towards “teaching” and away from “playing” by stealth. Of course, a shift such as this may result in a reduction in agency for both the teacher and the child if teaching and learning becomes a commodity of the school system serving its needs rather than those of the child, teacher, parents, and community.

The article by Ola Helenius offers a different stance in this debate. Rather than critiquing the encroachment of the “school readiness” agenda into early mathematics education, he instead provokes us to think about what counts as pedagogy in this context. Using Sweden as an example, his starting point is to note the tensions in how “teaching” is conceptualised in a context where a traditional play-based pedagogy is already hybridised with a formal “school orientated” pedagogy. The latter inevitably results in the need for increased formalisation of teaching as a means to evaluate the quality of preschool provision. To address this need, Helenius presents a framework for conceptualising the teaching of mathematics in early childhood in order to make “pedagogy” more visible in this context, but also to recognise the broad and diverse range of activities which teachers have responsibility for. The core dimensions of this framework rest on the participation of the teacher, the extent to which the activity is planned and the pedagogic goal of the activity – all of which may vary in any one activity. They also enact different power relations between the teacher and child which necessarily implicates different degrees of agency for both teacher and child in mathematical activity. He argues that such a framework is necessary to help manage the relationship between teachers and policymakers and resolve some of the tensions which arise in a system (like Sweden) whereby play-based preschool practices (which require informal teaching) are viewed as being “at risk” due to increased pressures to formalise teaching.

Conclusion

To conclude, whilst categorising the articles which comprise this special issue in terms of the above two themes was not planned in advance, the fact that it is possible to do so is testament to their theoretical and conceptual contribution to early childhood mathematics education literature. Many have called for more theorised studies of curriculum, pedagogy, play and assessment in early childhood education. By connecting the five articles to these two themes, our intention has been to draw attention to the concepts, frameworks and analyses they collectively offer, thus addressing this call. Finally, by focusing on young children’s emerging mathematical competencies and beliefs and by critically examining the forms of pedagogy that may support the development of such competencies/beliefs, we hope to provide a resource which will engage teachers, parents, practitioners and policymakers interested in these issues.