Mathematics through play: The influence of adult intervention on young children’s shifts between play and mathematical discourses

Marie Therese Farrugia


Presently, a typical school day in a kindergarten (ages 3-5 years) in Malta tends to include periods of‘free play’ interspersed with structured adult-guided activities (Sollars, 2013). By free play, I refer to play of the child’s choice within the parameters of the physical environment and the resources available. Generally, the free play is carried out on small tables using tabletop toys, blocks, puzzles, and other items. The children might also play in the ‘home corner’ and other such areas. The play area/items might be suggested by the teacher or chosen by the children themselves. During periods of free play, the children will tend to play on their own, that is, without adult intervention. On the other hand, the school day also includes activities that are adult-guided. These include listening to stories, making crafts, singing, physical exercise, and learning letters and numbers. The latter often includes completing simple worksheets. Anecdotal evidence indicates that the structured approach to letter recognition and writing is given due importance as a ‘preparation for school’. However, the National Curriculum (Ministry for Education and Employment, 2012) and the related Learning Outcomes Framework (Directorate for Quality and Standards in Education, 2015), have set a new direction for early childhood education. These policy documents stipulate the pedagogy to be used for young children should be distinguished from the more structured pedagogy' used in the later years of primary schooling (ages 8-11). As a result, subject syllabi have been eliminated and the various disciplines, including mathematics, are expected to be targeted indirectly or in relation to ongoing projects.The teacher is expected to take the role of a ‘responsive’ adult, even during play, during which observation and continuous assessment of children are crucial. As Stacey (2009, p. 14) recommends: “Join the children in play and engage in authentic conversations with them”.

Given this new direction, I wished to explore what it might mean to ‘learn mathematics through play’. I wished to first explore if, and how, young children engage ‘spontaneously’ with mathematics during play, and then to reflect on how an adult might be instrumental to encourage children to give numerical/quantitative interpretations to their play items. In order to support my reflections, I drew on the theoretical construct of discourses. In this chapter, I distinguish between ‘play discourse’ and ‘mathematical discourse’ and consider learning mathematics as a shift from the former to the latter. In particular, I draw on the classic works by Vygotsky (1967) and Walkerdine (1988) and on the more recent elaboration of mathematical discourse by Sfard (2008).

Play and mathematics

White (2014) presents behavioural and dispositional criteria that characterise play. She states that an activity can be described as ‘play’ if it is: pleasurable, intrinsically motivated, process-oriented, freely chosen and non-literal (that is, it involves make- believe). Tucker (2010) notes that play is a feature of etfective early years pedagogy and, indeed, writing within the context of mathematics education, Bjorklund (2016) conjectures that there is hardly any early childhood educator or researcher who would not argue for the value of children’s play. However, Helenius, Johansson, Lange, Meaney and Wernberg (2016) explain that the acknowledgement of the importance of the educator in early childhood education has led to questions about the kind of learning that children gain when “left to their own devices’” (p. 7) and, indeed, Tucker (2010, p. 7) states, that “all play needs quality adult involvement at some level”. For the present discussion, I find it helpful to refer to involvement as ‘intervention’, using the definition for intervention offered by Duncan and Lockwood (2008): all things adults do to support and extend children’s learning. This not only includes sensitive interaction as children play, but also has implications for the very resources provided for play so that, as aptly put by Novakowski (2015), one can open possibilities by limiting choices depending on items provided.

Several studies on mathematics have been carried out in early childhood settings wherein adult guidance is involved in what one might refer to as ‘playful’ activities. One example is that given by Sayers, Andrews and Bjorklund Boistrup (2016), who describe how one teacher asked her children to use dominoes to use numbers to represent six, and another teacher who instructed children to split six pebbles into two groups in any way they liked. Another example is explained by Brandt (2013); in her study, kindergarten teachers set up pattern-related tasks, setting some rules for completion, and guiding the children through them. On the other hand, it is less common to find studies on mathematics in the context of‘free’ play. One notable exception is Helenius, Johansson, Lange, Meaney, Riesbeck and Wernberg (2016), who use free play situations (four 6-year-old children playing with Lego™ blocks), to theorize what renders play ‘mathematical’.These authors suggest that play is rendered mathematical if it is creative, participator)' and if it includes rule negotiation, and they distinguish their method of analysis from a more common approach to associate the mathematics of young children with school topics such as number, geometry, pattern, measurement, etc. However, I have decided to take the latter approach - in particular, focusing on the curricular strand of Number - since this aspect of mathematics is given importance in our local kindergartens. Furthermore, keeping the new direction of our Early Years Curriculum, I wished to explore how learning about number might be integrated into play rather than structured activities.

I was drawn to a particular type of play, namely, play with ‘loose parts’. These are sets of items such as pebbles, acorns, shells, tree slices, corks, ice-cream sticks and blocks. My interest in focusing on play with loose parts derives from the fact that these items lend themselves to creativity and imaginative play. Indeed, as stated by Daly and Beloglovsky (2015), children can combine, redesign, line up, take apart, and put loose parts backs together in almost endless ways, since they come with no directions. Children can turn them into whatever they desire: a stone can become a character in a story, and an acorn an ingredient in an imaginary soup. Furthermore, these objects invite conversations and interactions and encourage collaboration and cooperation (Daly & Beloglovsky, 2015).

With specific regard to mathematics, Tucker (2010) suggests that loose parts offer opportunities for counting, sorting, pattern making, operations, investigations into weight and length, and problem solving. I am aware of only one project that (in part) focused on mathematics and loose parts. This was carried out by Novakowski (2015), who worked with teachers to provide children with provocations or invitations inspired by the ‘Reggio Approach’ (see, for example, Edwards, Gandini, & Forman, 1998). However, most of the activities in the Novakowski project were set up with an intention in mind. For example, a pattern with gems is displayed, prompting the children to explore patterns of their own, or a challenge is set up whereby the children are invited to stack five pebbles. On the other hand, I wished to focus my attention on child-initiated play, due to the importance this is afforded in contemporary perspectives on early childhood education (Duncan & Lockwood, 2008; Wood & Attfield, 2005).

My first research question was whether children would spontaneously engage in a discourse that might be recognised as mathematical. Second, I asked if, and how, the discourse would be influenced when sets of numerals were added to the sets of items available to play with; third, I wished to investigate if, and how, an adult’s intervention might encourage a shift between play and mathematical discourses. In order to address these questions, I decided to take on the role of teacher-researcher with a small group of kindergarten children, and to set up a play context similar to one that I might expect to find in a typical kindergarten classroom.

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