__Mathematics in New Zealand Curriculum__

In 1992 the Ministry of Education revised the mathematics curriculum. The curriculum is divided into five learning areas, (Geometry, Algebra, Measurement, Statistics and Number) and 3 processes (Problem Solving, Developing Logic and Reasoning and Communicating Mathematical Ideas). The ENP and ANP programmes focus on Number as being the key to all other strands.

A *Number Framework *has been established to help teachers, parents, and students to understand the requirements of the Number strand from *Mathematics in the New Zealand Curriculum. *There are two main sections to the framework, the distinction is made between strategy and knowledge. The *Strategy *section describes the mental processes students use to estimate answers and solve operational problems with numbers. The *Knowledge *section describes the key items of knowledge that students need to learn.

It’s important that students make progress in both sections of the framework. Strong knowledge is essential for students to broaden their strategies across a full range of numbers, and knowledge is often an essential prerequisite for the development of more advanced strategies.

Strategy →creates new knowledge through use→ Knowledge

←provides the foundation for strategies←

__An overview of the Strategy Stages__

For the descriptions of the strategies that students use at each stage, please refer to the submenus.

__An Overview of the Knowledge Section of the Framework__

The knowledge section of the framework outlines the important items of knowledge that students should learn as they progress through the strategy stages. This knowledge plays a critical role in students applying their available strategies with proficiency and fluency across all the numbers and problem types that they may encounter.In the framework, knowledge is categorised under four content domains: Number Identification, Number Sequence and Order, Grouping/Place Value, Basic Facts, and Written Recording.

**Students should not be exposed to standard written****algorithms (working form) until they use part-whole mental strategies. **Premature exposure to working formsrestricts students’ ability and desire to use mental strategies. This inhibits their development of number sense. However, in time, written methods must become part of student’s calculation repertoire.

Basic fact knowledge is critical. The Number Framework emphasises that the process of deriving number facts using mental strategies is important in coming to know and apply these facts. It also demands that students come to know a broader range of facts than previously, including groupings of numbers, and that they have knowledge of factors of numbers and decimal and fraction conversions at the higher stages.

__ ____How can I help my child?____ __

There are lots of things you can do to help and support your child with their numeracy education. These include:

**Discussing what everyday numbers mean.**

For example: When numbers ‘pop’ up in conversations, use these as opportunities to talk about the numbers……”The goal shoot for the Silver Ferns is 1.97m tall.” ”Is that taller than you Dad?”……..”It says here that a kiwi’s egg weighs about ¼ the weight of the mother”. Is that the same for a hen Mum?”

**Play mathematical games together.**

Snakes and Ladders and games that require counting or adding using a dice or two are a great way to practice using numbers (and do something as a family). Ask your children to teach you a game they play at school. Most games don’t require special equipment and with a couple of dice and a few counters, you can play a vast array of games.

**Work together on problems around the house.**

Ask questions about everyday things you are doing. For example: “We have 7 eggs in this tray and 9 in this tray. How many do we have altogether?” ………” This recipe makes enough for 4 people, but we will have 10 people for dinner tonight. What should we do?”

**Take an interest in how your child figures things out.**

Ask how they got their answers and __DON’T__ accept the ‘I don’t know’ response. Really listen to how they got their answers and get them to explain it so you understand. For example: “How did you get that answer?” “To work out 45 + 28, I go 45+30=75 and take 2 off.”…….. “I took longer to work the answer out than you. How did you do it?” “To do 27 x 3, I third and treble. I did 27 ÷ 3 = 9 and 3 x 3 = 9, so 9 x 9 = 81. I could also have done 30 x 3 = 90 and then take off 3x3 =9. 90 – 9 = 81. The chainsaw method would also work. 20 x 3 = 60 and 7 x 3 = 21. 60 + 21 = 81”

**Help your child manage time and money.**

Time and money management not only help with your child’s ability to use numbers, but will be important skills later in life. For example: “It’s now 5.45pm and Nana comes at 7pm. Do you think we have time for a family bike ride?” ………”I’ve got $20 to buy presents for 8 people.” “How much will you spend on each gift?”

**Take an interest in what your child does at school.**

Ask them what they are currently learning? What is their favourite activity or game at the moment? What are the things they are having trouble with? etc. Remember to really listen to your children. By showing interest, it gives the clear message that you care and that what they are learning, and education in general, are important.

**Explore numeracy websites together**.

The NZ Maths website (www.nzmaths.co.nz) has information, games and activities for parents and students to assist with their education. There are lots of other sites that also have fun numeracy activities and games.

__A few Q & A’s__ __At what age / Year level should each child be at each stage?__

There is no set strategy stage a child should be ‘at’ and the stages are NOT equal in length or requirements. A child may spend several years working on a stage or may quickly progress through the early stages. All people learn at different rates. We do not ‘push’ students through the stages as they need to secure their understanding at each level before progressing. Surveys have shown that most of our population (90% +) operate at Strategy Stage 5 or below. Last year we had most of our Year 8 students leaving at Stage 6 or above (after only one year of teaching the new programme). The focus has gone from ‘What answer did you get?’ to ‘How did you get that answer?’.

__Can children be between stages?__When under stress or just tiredness, everyone, including adults, sometimes slip backwards from their best way of thinking about a problem, and may appear to be between stages. For example even a person who is very good at maths may find the number of days between 3rd July and 9th July by counting on their fingers rather than reasoning the answer is 9 - 3 then take away 1. We encourage the students to operate at their highest stage of thinking while acknowledging that occasional slippage is natural and not a concern.

__Why not teach students to solve problems only by the written form____?__Students can be taught the written forms with sufficient practice. But this does not require thinking or process. To be numerate a student needs to be able to check any written answer by mental checking. These require thinking rather than following a set procedure. For example, if a student works out 48 x 52 is 246 that student should use estimation processes to see the answer is about 50 x50, and so the answer must be near 2500. So the thinking skills are not an optional extra even if the student is practised at using written methods.

__What about basic facts?__Children need to know, almost without thinking, what the result is when they add or multiply any pair of numbers between 1 and 10. They should learn these basic facts as soon as they understand how addition and multiplication work (there is no point learning times tables if they do not understand multiplication). Their confidence and success with maths depends on sound basic facts knowledge.

__Should they use calculators?__Children should do most calculations in their heads. They should only use calculators or pencil and paper when the numbers are hard.

__What are the benefits of the ENP & ANP programmes?__

Ø Students enjoy working with numbers through the use of equipment and demonstrate a positive attitude towards problem solving.

Ø Students get to solve problems with others and by themselves, sharing ideas and strategies.

Ø Students are able to discuss **HOW** they solve problems rather than simply what answer they get with other students, their teacher and you!

Ø Students are able to calculate in their heads without need for pencil & paper and calculators.

Ø Students are given improved feedback on what learning step they need to take next and this leads to improved student performance.

Ø Students understand and are able to use numbers with greater ease.

Ø The increased understanding of numbers leads to improved understanding of the other strands in the Mathematics Curriculum.