Background

The importance of early mathematics

Children's early experiences of mathematics form the foundation for their future mathematics learning and success. Mathematics enables children to think logically, strategically, creatively and critically. Mathematical knowledge and skills provide building blocks for success in many areas of life and work.1

New Zealand and international research on children's learning in the early years confirms the importance of early experiences in mathematics for future educational success.2 New Zealand's Competent Children study has tracked the development of a group of learners from early childhood education, through school and into adulthood. It shows that at age 10, the quality of early childhood education still influences children's competencies that lead to a successful adulthood, and that mathematical ability is one of the most influential factors. The study shows that most children acquire basic mathematical knowledge and skills before the age of eight years. Duncan and Murnane suggest that early mathematics skills are highly predictive of later academic achievement.3

Creating a disposition for mathematical learning

New Zealand's early childhood curriculum,Te Whāriki, focuses on supporting children's learning dispositions and broad competencies that can be readily transferred to new situations (such as starting school). The attitudes and expectations that are formed at an early age continue to influence a child's learning throughout life.4 The ECE Taskforce report, An Agenda for Amazing Children, in 2011 highlighted the importance of learning dispositions, such as curiosity and perseverance, to later educational success.5 These are critical dispositions for children's early learning experiences of mathematics.

The concept of Te Kākano - the seed - has been used to describe teaching and learning of mathematics in early childhood. See Figure 1. Peters and Rameka, in an article about Te Kākano, explain that dispositions influence how people tend to invest their capabilities. They state that motivation is crucial to the development of children's early mathematical concepts and it is important that the disposition to explore these concepts is not lost. "Pedagogical approaches play a key role in ensuring that the inclination to use mathematics is fostered and teachers' own positive dispositions towards mathematics are likely to be central to this process." Peters and Rameka argue that inappropriate teaching practice, such as rote learning in isolation of any meaningful contexts, may result in children developing negative attitudes to mathematics.

Figure 1: Te Kākano

this graph shows the links between Te Whariki and strengthening Te Kakano, from infants and toddlers nurturing the seed and the transition to school.

Source: Te Aho Tukutuku

Image credit: Ministry of Education © Crown 2016

Mathematics in Te Whāriki

Mathematics is woven throughout the strands of Te Whāriki, specifically in Mana Reo - Communication and Mana Aotūroa - Exploration. However, there is potential for mathematics in all strands.

Mana Reo - Communication

Mathematical learning outcomes relating to the goals of communication include:

  • familiarity with numbers and their uses
  • skill in using the counting system and mathematical symbols and concepts such as numbers, length, weight, volume, shape and pattern.

Mana Aotūroa - Exploration

Mathematical learning outcomes relating to the goals of exploration include:

  • setting and solving problems
  • looking for patterns
  • classifying things for a purpose
  • guessing
  • using trial and error
  • thinking logically and making comparisons.7 

Te Aho Tukutuku/Early Mathematics

Te Aho Tukutuku is a Ministry of Education (the Ministry) resource designed to support and strengthen the teaching and learning of mathematics in early childhood education.

The Ministry intended the material to spark mathematical discussions and investigations, provide information and examples to support 'noticing, recognising and responding' to children's mathematical learning, and be a useful resource for teachers and leaders to explore.

The resource is grounded in Te Whāriki and the Te Kakano framework in Kei Tua o te Pae/ Assessment for Learning: Early Childhood Exemplars Book 18: Mathematics Pangarau.8 It includes short papers as well as information about mathematical learning and examples of young children putting mathematical ideas into action.

Te Aho Tukutuku uses the Te Kakano framework as a metaphor for growing rich mathematics.

It recognises the movement and unfolding from "te kore, ki te po, ki te ao marama” (from nothingness, to the night, to the world of light) and the dynamic, integrated lifelong nature of mathematical learning.

Nurturing the seed

Many things nurture the seed: teacher pedagogy, teacher content knowledge, family/whānau knowledge, and resources. The Te Aho Tukutuku resource provides information on the importance of these aspects, and offers a way to strengthen and enrich, foster and develop mathematics teaching and learning.

Strands of early mathematics

Te Aho Tukutuku outlines six strands of early mathematics:

  • Pattern - the process of exploring, making and using patterns.
  • Measuring - answering the question "How big is it?”
  • Sorting - separating objects into groups with similar characteristics.
  • Locating - exploring space or finding or 'locating' something, such as a place (location), or an item in space.
  • Counting and grouping - the process for working out the answer to a question about "How many?” Grouping involves putting things together.
  • Shape - naming shapes and identifying the unique specific properties or features of shapes.

Summary of Effective Pedagogy in Mathematics/Pangarau Best Evidence Synthesis Iteration (BES)9 

Key findings: The early years 

Young children are powerful mathematics learners. Research has consistently demonstrated how a wide range of children's everyday activities, play and interests can be used to engage, challenge and extend children's mathematical knowledge and skills. There is now strong evidence that the most effective settings for young learners provide a balance between opportunities for children to benefit from teacher-initiated group work and freely chosen, yet potentially instructive play activities. Teachers in early childhood settings need a sound understanding of mathematics to effectively capture the learning opportunities within the child's environment and make available a range of appropriate resources and purposeful and challenging activities. Using this knowledge, effective teachers provide scaffolding that extends the child's mathematical thinking while simultaneously valuing the child's contribution.

Key ideas: The early years

  • All children can be powerful mathematics learners.
  • Children have their own purpose for activities.
  • Children's involvement in mathematical learning experiences depends on interest.
  • Mathematics learning experiences should be both planned and informal/spontaneous.
  • Everyday activities and play situations provide a wealth of mathematical experiences.
  • Teachers can extend the child-initiated activities by scaffolding, thematic instruction, or instruction.
  • Teachers need to cater for children's interests and mathematical abilities and to engage children in challenging learning experiences.
  • Content matter is important.

Issues identified in early mathematics teaching

Low levels of content knowledge and the resulting lack of confidence limits the ability of teachers to engage children in the mathematics learning opportunities present in existing activities. This low-level knowledge also limits the ability of teachers to introduce more focused, interventional activities designed to cater for diverse learners. Other issues identified included teachers:

  • being unaware of the need to cater for children's interests and mathematical abilities, and to engage children in challenging learning experiences
  • missing many opportunities for sustained, shared cognitive engagement
  • seeing mathematics as numeracy only
  • being unaware of home mathematical experiences, expectations and aspirations
  • not following their planning for mathematics teaching and learning.