"Kei hopu tōu ringa ki te aka tāepa, engari kia mau ki te aka matua."
Throughout time, all peoples have developed knowledge and understandings about how different aspects of their worlds relate to each other. This is the basis of pāngarau. Māori ancestors were extremely knowledgeable about the pāngarau evident in the various realms of the children of Rangi and Papa. This knowledge was of considerable importance in their everyday activities such as building, sailing and navigating on the open water, and gardening. With the advent of European settlement, our ancestors took a full part in new opportunities such as commerce. Pāngarau knowledge was important in their achieving success in these new endeavours. Over time, pāngarau has developed throughout the world, but has remained as an important body of knowledge in all aspects of our lives. Wherever one turns, pāngarau can be seen in our daily lives, in other areas of the school curriculum, and in most career pathways.
The content of the pāngarau curriculum is arranged into three strands: Number and Algebra; Measurement and Geometry; and Statistics, from Levels One to Six. These reduce to two strands at Levels Seven and Eight: Algebra and Calculus; and Statistics.
The achievement objectives are grouped under the key divisions of each strand.
There are three essential aspects of pāngarau which serve to integrate the three strands.
This is the basis of pāngarau, namely the exploration and use of the patterns and relationships seen in aspects of quantity, sets of data, space and time.
The Māori language has its own corpus to describe and explain essential pāngarau ideas. In addition to this, symbols and representations such as tables and graphs are used to communicate meaning. These constitute 'Pāngarau Literacy'. As the child grows, their pāngarau literacy develops and becomes essential to their understanding of pāngarau concepts, and to their communication in pāngarau, in order to achieve success in this learning area.
Pāngarau extends out to the other learning areas of the school, to the many contexts of family life, of sub-tribal and tribal endeavour, of community activity and of the Māori world in general, and is important in achieving our aspirations in all of these areas. It is important also that students gain a growing awareness and understanding of the many ways pāngarau can be used, and to become critical of the origin of the ideas, and the reasonableness of their use.
Pāngarau enhances the creativity, the critical thinking, the logical thinking, and the reasoning skills of students, as well as their ability to strategise, solve problems, evaluate and communicate.
Problems and activities in pāngarau should come from Māori contexts that the students are familiar with. In pāngarau, students will use relevant materials and apparatus, they will construct models, look for relationships, predict and justify outcomes, estimate, calculate with precision, explore patterns, and make generalisations.
It is important that pāngarau teaching is enjoyable and engaging for students, as well as cognitively challenging. The teacher will need to craft their discourse so that it is simple and clear, the questions and explanations are effective, and the students are settled in their learning.