Kei Tua o te Pae
Kei Tua o te Pae/Assessment for Learning: Early Childhood Exemplars is a best-practice guide that will help teachers continue to improve the quality of their teaching.
The exemplars are a series of books that will help teachers to understand and strengthen children's learning. It also shows how children, parents and whānau can contribute to this assessment and ongoing learning.
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A lens based on Te Whāriki – He tirohanga mai i Te Whāriki
Mathematics is woven throughout the strands in Te Whāriki. It is found specifically in the Communication/Mana Reo and the Exploration/Mana Aotūroa strands. The latter strand includes mathematical processes such as “setting and solving problems, looking for patterns, classifying things for a purpose, guessing, using trial and error, thinking logically and making comparisons”.13 This strand also includes spatial understandings.14 The Communication/Mana Reo strand includes “familiarity with numbers and their uses” and “skill in using the counting system and mathematical symbols and concepts, such as numbers, length, weight, volume, shape, and pattern”.15 This strand emphasises mathematics in referring to “activities that have meaning and purpose for children” and in the phrase “for meaningful and increasingly complex purposes”.16 As for the other domains of symbol systems and tools for making meaning and communicating, the principles in Te Whāriki mean that family “voices” will be sought and that “funds of knowledge” 17 from home and community will be acknowledged and included in the children’s portfolios.
The Te Whāriki perspective is that children will participate in the symbol systems and tools of mathematics for personal, social, and cultural purposes: for becoming confident and competent in culturally valued enterprises, expressing emotion, making connections across place and time, contributing their own abilities and viewpoints to the community, communicating with others (including appreciating the ways in which the available cultures communicate and represent), and making sense of their worlds.
At the same time, the possible pathways for learning that derive from the four principles of Te Whāriki (see Book 10) can help teachers to identify dimensions of strength as children become more interested in and involved with mathematics. Learning episodes associated with mathematical practices take on dimensions of strength as these episodes become:
- more strongly integrated into recognised patterns, regular events, and social practices over time. The exemplar “Jack explores space” includes a number of stories about Jack’s exploration of space and of his place in it. There are many everyday opportunities for him to explore his body in space (in boxes, in tunnels, and up and down steps) and to explore things in space (posting, stacking, rolling, and hiding). These opportunities provide increasing levels of challenge.
- distributed or stretched across a widening network of helpful people and enabling resources. In “Ezra explores height, balance, measurement, and number”, Ezra is exploring ways in which he can be taller by trying different units for measuring his height and trying a range of ways in which he can change his height.
- connected to a greater diversity of purposes, places, and social communities.
- more mindful (as children begin to take responsibility and make up their own minds).
These last two dimensions of strength are illustrated in “Playing with repeated patterns”. Jessica begins her interest during a visit to the Māori Gallery at the Auckland Museum (diversity and place). There she observes the patterns, including kōwhaiwhai, and draws them. She later constructs a complex pattern with its own personal purpose and meaning and its own unique rules and relationships (mindfulness).