Mathematics
Pāngarau

Introduction

The exemplars in this book should be considered in conjunction with the discussion in Book 16. A definition of mathematics and statistics in The New Zealand Curriculum includes the statement:

Mathematics is the exploration and use of patterns and relationships in quantities, space, and time. Statistics is the exploration and use of patterns and relationships in data. These two disciplines are related but different ways of thinking and of solving problems. Both equip students with effective means for investigating, interpreting, explaining, and making sense of the world in which they live.1

The National Numeracy Strategy uses this definition:

To be numerate is to have the ability and inclination to use mathematics effectively in our lives – at home, at work, and in the community.2

The exemplars in this book record children participating in mathematical practices – exploring relationships and using patterns in quantities, space, and time – for a range of purposes.

James Greeno has called this “situated knowing in a conceptual domain”, and he used the workshop or the kitchen as a metaphor (see Book 16). Alan Bishop, a leading writer and researcher in mathematics education, has emphasised a cultural perspective on mathematics education that is consistent with the approach to education taken in Te Whāriki. He sets out six activities: counting, measuring, locating, designing, playing, and explaining.3 He adds:

All these activities are motivated by, and in their turn help to motivate, some environmental need. All of them stimulate, and are stimulated by, various cognitive processes, and I shall argue that all of them are significant, both separately and in interaction, for the development of mathematical ideas in any culture. Moreover all of them involve special kinds of language and representation. They all help to develop the symbolic technology which we call “mathematics”.4

Discussing the importance of play to cultural life, Bishop comments, quoting Vygotsky, that “the influence of play on a child’s development is enormous”5 because it provides opportunities for abstract thinking. Barbara Rogoff also suggests that children supporting each other and learning together, a key feature of play, makes a powerful contribution to mathematical learning.6 Bishop emphasises the playing of games. He notes that playing is “indeed a most serious business”7 as well as a significant adult activity. Games model reality, and “it is not too difficult to imagine how the rule-governed criteria of mathematics have developed from the pleasures and satisfactions of rule-governed behaviour in games”.8 Bishop also elaborates on the activity he calls “explaining”, the purpose of which is to expose relationships between phenomena. He emphasises the explanatory relationships of meaning making: finding similarity, and connections and classifications, to explain events or experiences. He notes that the diversity of languages brings culturally diverse explanatory classifications and ways of explaining.

Similarly, within the context of Aotearoa New Zealand, an early childhood mathematics working group set up in 2003 by the Ministry of Education developed “te kākano”, a metaphor for describing the range of purposeful activities for developing mathematical tools and symbol systems in a bicultural environment.9 The metaphor represents the child as te kākano (the seed), embedded in a context. The range of mathematical purposes and tools that develop is influenced by the “fertiliser” or “soil” that surrounds te kākano. These influences include teacher pedagogy, teacher content knowledge, family/whānau knowledge, and resources, all of which interact with the child’s interests to privilege particular mathematical domains. The metaphor highlights the value of identifying the range of cultural purposes for mathematics within a setting.

The strands in the Te Kākano diagram [GIF; 63kb] cross and interweave in different activities. For example, in one exemplar, calculating and counting, measuring, and designing might all overlap. In another, estimating and predicting might overlap with “pattern sniffing”. Therefore, the names on the seed strands indicate the sorts of strategies and dispositions a teacher might notice. Each of these strands includes possibilities for increasing mathematical complexity.

A lens can be placed at any point in the diagram to look in more depth at what is happening for a particular child or group of children. Within the lens, we can see the authentic context in which an activity takes place and the specific detail of the strategies, the dispositions happening there, and the mathematical complexity involved.

Effective Pedagogy in Mathematics/Pāngarau: Best Evidence Synthesis Iteration [BES] includes a chapter on mathematics in the early years, which is consistent with the approach taken here. It draws attention to the value of play and of everyday activities as meaningful contexts for mathematics learning, and it highlights aspects of the factors that nurture te kākano (teacher content and pedagogical knowledge, appropriate resources, and family/whānau mathematics).10

The mathematics exemplars in this book are viewed through one or more of the three lenses outlined in Book 16: a lens that focuses on assessment practices, referring to the definition of assessment as “noticing, recognising, and responding”, from Book 1 of Kei Tua o te Pae;

  • Te Whāriki lens;
  • a lens that focuses on the symbol systems and tools described as “mathematics”.

In this section


Last updated: 26 June 2014