A playful approach to exploring 4- to 6-year old children's thinking about and with numbers

NORA SCHEUER; FLAVIA IRENE SANTAMARIA; MÓNICA HAYDÉE ECHENIQUE

Hong Kong

Conferencia; Quality Childhood Conference International (QCCI); 2015

The Hong Kong Institute of Education y University of Cambridge, Faculty of Education

According to the view that teaching is based on teachers? notions of the nature of the learner?s mind (Olson & Bruner, 1996), attempts to improve the Quality of Childhood Education in the field of mathematics would benefit from a better understanding of the plasticity and diversity of children's numerical thinking. We understand children's numerical thinking as production that evolves by adapting cultural numerical functions (such as quantification, numerical comparison, etc.) and forms (such as oral and notational numeration systems) in order to accomplish goals in contexts of activity (Saxe, 2012) and reflection. In this process, in addition to applying certain well-established procedures and ideas, children explore others with which they are slightly familiar, and even attempt innovations.Studies conducted on clinical interviews, dialogical classrooms and everyday practices (Brizuela, 2004; Hughes, 1986; Micalco-Méndez, in press; Santamaria, in press; Scheuer et al., 2000; Teubal & Guberman, 2014) have shown that when children are asked to represent quantities within open, relevant tasks, they display and explore very different resources, making use of material, interactional and representational affordances of the situation. Thus, in order to investigate, interpret and promote children?s numerical thinking, it is necessary to confront them with meaningful situations involving a variety of ?cognitive zones?, ranging from zones where the child feels comfortable and knowledgeable to spaces he/she has seldom gone through, yet is willing to explore. A playful approach, encouraging children to think of alternatives that make sense even if they are not conventional solutions, is particularly suitable to this end. Based on this framework, we present a study of the ways in which children attending the first years of compulsory schooling in Argentina represent different numerical magnitudes. Our aims are to describe and explain: a) the resources children display, explore and transform in relation to a range of numerical tasks, and b) the articulation of such resources at an individual level, in terms of cognitive trajectories showing the tension between using what is known and exploring novelties in order to convey numerical meanings. Based on the Zone of Proximal Development as an indicator of the child?s potential of scaffolded learning (Vygotsky, 1978; Wood, Bruner & Ross, 1978), we are interested in identifying a ?zone of cognitive comfort? and a zone of potential development, within which we distinguish a proximal zone and a distant zone. We interviewed 60 children aged 4, 5 and 6 years in Kindergarten and Grade 1 at two schools in the same district with a contrasting population in socioeconomic terms.The introductory tasks consisted of a short conversation about child?s number practices; displaying number series as far as possible both orally and on paper; quantifying sets of plastic chips, and noting down such quantities on paper. The main tasks were thinking of increasing and decreasing quantities (a very big number of.../ less, even less, none) in relation to three imaginary references (chips, ages in a lifetime, stars seen in the sky at night). Children were asked to note down those quantities ?with your ideas? and reread them. The interviews were audio-taped and transcribed. Qualitative analyses focused on the resources children used in each task, and on their trajectories over the series of tasks. After providing a general overview of results, we select three case studies of children who engaged in the playful numerical situations by articulating consolidated, emergent, innovative procedures and ideas in very different ways.We close the presentation by reflecting on how these findings offer a rich potential for interventions on the part of teaching professionals. We underscore the need for educational researchers, policy makers and professionals to pay special attention to the tension between consolidated and emergent knowledge in children?s numerical thinking, as well as to socio-cultural and cognitive diversity operating within learning communities.