Tikanga pangarau - Mathematics

Mathematics (maths) education in the context of these unit plans is about exploring patterns, quantities, symbols and statistics relating to Moriori, as well as growing our awareness of the connectivity with nature that mathematics can have.


Learning, in its many forms, can and should be engaging, informative, useful and should create more questions than answers.


Akonga should be given real-world problems to solve, and the ability to harness their own natural skills in order to make sense of the world of numbers and patterns around them.mathematics-education,learning,unit-plant-templates

Tikanga pangarau was important to Moriori, as the kaitiaki of Rekohu, they needed to manage the natural resources carefully to ensure their own survival.

No more seal were taken or killed than was necessary to survive. No more hopo (albatross) were taken than were needed, for to take more would have meant there would be nothing the following year.
Trees were circumspectly cut for shelters and firewood, but none were ever allowed to perish unneccessarily.
An awareness of numbers led to the ritual of castration, which was used as a way of keeping the population to a sustainable level.

Moriori had an awareness of number and their ability to predict volume and calculate capacity was historically recorded. Otten their calculations involved a spiritual dimension as well as the practical and physical components. For example, before the killing of a whale, or the hopo, prayers were offered, as thanks and apology and also to ask that there be more next year. This shows an awareness of managing resources, rather than a simple request to the gods to keep supplying foodstocks.


Why learn about mathematics?

Tikanga pangarau is essential learning for akonga if they are to be successful in the world they will eventually graduate into.  They will need to be able to decode patterns and numbers across a wide range of scenarios and settings, from their own wages, to their shopping trolley contents.

According to the New Zealand Curriculum document, Mathematics Education is about:

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.
Mathematicians and statisticians use symbols, graphs, and diagrams to help them find and communicate patterns and relationships, and they create models to represent both real-life and hypothetical situations. These situations are drawn from a wide range of social, cultural, scientific, technological, health, environmental, and economic contexts.

How is the learning area structured?

Mathematics in the New Zealand curriculum learning area is broken down into strands, (see below), but we believe that a more holistic approach better serves our akonga. There may well be times where individual strategies and skills need to be micro-managed and/or micro-taught, but the general inclination in our unit plans is to use an inquiry model for learning that allows learners to acquire the skills that they need, in order to be able to then learn themselves whatever content it is that they might need, whenever they might need it.


It is obvious to us that younger learners benefit from rote-learning the basic facts. We make no apology for this statement. It may seem inconsistent with other learning styles and pedagogies found within this site, but it is based on experience and observation and an awareness that statistically, New Zealand school students are plummeting down a steep slope of non-achievement in mathematics.

Learners need to have rote basic facts to 10 before they finish year 2. They need to have learned the times tables (up to 12) before the end of year 6. With those skills on board, students should have success in mathematics at the appropriate level right through from Year 7- Year 13.

With those skills on board, students then just need to be shown how to learn whatever it is that they need to learn.

There is too much knowledge in the world today to expect akonga to absorb it all. Far better that we equip them on how to learn, rather than on what to learn.

Mathematics learning should be integrated across all curriculum learning and across all learning opportunities. It is in those forward-thinking inquiry-based classrooms where students will learn contextual mathematics. This is the type of learning that students absorb and retain.

Tell me and I forget. Teach me and I may remember. Involve me and I will learn!

Tapeke akoranga is involved and inclusive learning, where we are all in together and our learning is based on the real world and the problems we see and experience. It is not abstract mathematics where artificial teaching happens, and incidental learning is the best possible outcome. Involved learning requires the maths to be real, tangible and concrete. Numbers in a book can be used to represent the problems, but the problems must be genuine and cross-strands.



The New Zealand Curriculum Document:

The achievement objectives are presented in three strands. It is important that students can see and make sense of the many connections within and across these strands.

  • Number and algebra 

Number involves calculating and estimating, using appropriate mental, written, or machine calculation methods in flexible ways. It also involves knowing when it is appropriate to use estimation and being able to discern whether results are reasonable. Algebra involves generalising and representing the patterns and relationships found in numbers, shapes, and measures.

  • Geometry and measurement 

Geometry involves recognising and using the properties and symmetries of shapes and describing position and movement. Measurement involves quantifying the attributes of objects, using appropriate units and instruments. It also involves predicting and calculating rates of change.

  • Statistics

Statistics involves identifying problems that can be explored by the use of appropriate data, designing investigations, collecting data, exploring and using patterns and relationships in data, solving problems, and communicating findings. Statistics also involves interpreting statistical information, evaluating data-based arguments, and dealing with uncertainty and variation.



FREE Mathematics Unit Plan Templates are here >>>>>>>

 Do you have a unit plan that you would like to share with us for inclusion on this site?

There are a number of ways in which you can submit your unit plans to us. We accept unit-plans and lesson-plans via email (thats the easiest way) but you can "share them with us" on Google, send them to us via dropbox (yours) or even physically post them to us (that last one is probably the least reliable method).

 If you want to emails them to us:
  1. Make a note of where your unit-plan is stord on your computer
  2. Click on the button to the righteducation-resources unit plan submissions
  3.  Type "Unit Plan Attached" in the subject line
  4. Enter your message into the message area
  5. Click on the attachment button and find the Unit-plan
  6. Click send.




If you want to share your Unit Plans or Lesson Plans with us via Google Docs:

  1. Open the Unit Plan or Lesson Plan in Google Docs
  2. Click on the SHARE button  (The upper right hand corner.... Its the blue one with "Share" written on it)
  3. Type in support@education-resources.co.nz
  4. Click on send. (When the warning about 'no account' pops up, click on OK)

To share your unit plans or lesson plans with us via Dropbox. You copy, move or save your unit plan to your dropbox and then "invite" us (support@education-resources.co.nz) to access it.