Format and presentation of this document

• Strands
• Achievement objectives by levels
• Suggested learning experiences
• Sample assessment activities
• Development band activities

There are six main achievement aims of the mathematics curriculum. Accordingly, the curriculum statement is presented in six "strands" each of which reflects a particular aim of the curriculum. The strands are headed:

Mathematical Processes
Number
Measurement
Geometry
Algebra
Statistics

This division is a convenient way of categorising the outcomes for mathematics education in schools. It emphasises that there are a number of aspects which are all equally important. The division does not mean that mathematics is expected to be learned in discrete "packages". On the contrary, the mathematical processes strand is deliberately intended to encourage teachers and students to make connections between the other strands wherever possible.

Each strand, other than "number", is divided into eight levels describing the development of the mathematics curriculum from junior primary school (Year 1) to seventh form (Year 13).

A number of achievement objectives are described in each strand, and at each level. The objectives define what students should be able to achieve after appropriate learning experiences in mathematics. They define the progression of learning outcomes which is the core of this curriculum statement in mathematics.

At each level the objectives are quite broad. It is expected that, in assessing students' progress, teachers will make judgments as to an individual's degree of achievement of particular objectives, and will include commentary on that degree of achievement when reporting to parents.

The number of levels has been chosen for consistency with the New Zealand Curriculum Framework. The division of the school mathematics curriculum into eight levels does not mean that there are eight well-identified stages, which learners pass through in the development of mathematical understanding. However, it is accepted that some concepts are better introduced to older students, and that the effective learning of some ideas depends on a prior understanding of other ideas. The judgment of experienced teachers as to what students can do at various ages has been combined with recent research into mathematical learning to place material into levels. The general relationship between the levels and years at school is described in the diagram below.

This scheme explicitly recognises that each learner is an individual whose learning development and rate of progress is different from others. different students will be ready for particular mathematical content and experiences at different times. It is not expected that all students of the same age will be achieving at the same level at the same time, nor that an individual student will necessarily be achieving at the same level in all strands of the mathematics curriculum.

The levels are not meant to be interpreted as the rungs of a ladder which is to be climbed as quickly as possible. Nor are they meant to be interpreted as hurdles over which each student must pass before moving to any new work. Rather, they are meant to focus the mathematics programmes of schools in a consistent way. They provide a basis for reporting students' achievements to parents in a way that is clear and demonstrates progression in learning.

The number strand is divided into six levels only. Most of the important achievement objectives for number are to be met in the early years of schooling. In later years, the classification of mathematics into strands is somewhat arbitrary. Some work, for example, numerical analysis, calculus, and complex numbers, which might have been classified under "number", has more usefully been placed in other strands, for example, algebra.

In each strand, and at each level, a range of suggested learning experiences is suggested. The activities and experiences which are included are drawn from the best of contemporary teaching practice, and are intended to help students meet the aims and achievement objectives of the mathematics curriculum.

There is not necessarily an exact match between the suggested learning experiences and the achievement objectives at each level. in some cases, this is because the learning experiences described contribute to concepts and skills which will take considerable time to develop, and appropriate achievement objectives are not described until later levels. At the same time, all of the suggested learning experiences contribute to the development of the broader aims of the curriculum and thus, for some, there may not be specifically associated achievement objectives.

The suggested learning experiences are, nevertheless, pointers only. It is not intended that the activities described in this document should limit the way teachers choose to teach mathematics. Indeed, teachers are encouraged to use their own judgment in designing courses to provide their students with mathematical experiences which will enable the students to achieve the broader aims and achievement objectives of the curriculum. Teachers in, for example, bilingual schools or Kura Kaupapa Māori may choose to offer mathematics in contexts which provide quite different activities and experiences.

The suggested learning experiences are carefully worded in active terms. This is to emphasise that mathematics is most effectively learned through students' active participation in mathematical situations, rather than through passive acceptance and repetition of knowledge.

Traditionally, assessment in mathematics has been focused on a quite narrow range of procedures. Procedures such as pencil and paper tests of algorithmic skills do not always reveal students' difficulties, nor do they allow assessment of the full range of students' achievements.

This curriculum statement provides, at each level in each strand, examples of activities in which teachers might engage students to assess their current level of achievement. An assessment programme modelled on these examples will help teachers to plan the next stages of learning for their students.

The models illustrate tasks that can be used to assess a full range of accomplishments, including, for example, the ability to collect and summarise data, the ability to communicate findings, the ability to present an argument, and the ability to exploit an intuitive approach to a problem. The suggestions include multiple assessment techniques including written, oral, and demonstration formats, which should be used in addition to more traditional tests and assignments. Suggestions for group and team assessments are included.

The activities illustrate assessment techniques which are not disruptive to normal classroom activities they could be carried out as an integral part of the teaching programme rather than at times specifically set aside for "tests". Assessment and evaluation strategies of this kind require teachers to make systematic observations of students at work, and to record their observations carefully.

As each achievement objective in this statement is capable of being achieved at a range of standards, teachers should choose assessment and reporting methods which reveal a student's degree of attainment of the objectives.

The few assessment activities suggested in the statement are exemplars which teachers could imitate in developing their own assessment programme. They provide for teachers a selection of activities which allow for observations of various manifestations of students' achievement. While it is expected that teachers will use the tasks described as models for developing their own assessment tasks and procedures, they are free to use different assessment methods if they wish, and are encouraged to do so. For example, teachers in bilingual schools or Kura Kaupapa Māori may decide to use alternative methods to assess students' progress towards the achievement objectives.

The examples do not cover all of the objectives of the curriculum. A comprehensive assessment programme remains the responsibility of the teacher.*

Some students develop faster in all aspects of mathematics than most of their peer group. Other students reach a particular achievement level in one strand or topic sooner or faster than most of their peer group without necessarily being equally competent in all other strands at the same level. A levels structure may be thought to imply that faster students should automatically be accelerated to the next level. This is not necessarily so, nor is it the aim of this curriculum. teachers should carefully appraise the experience and needs of students before deciding to move them to the next level.

It is very important, however, that students do not have their mathematical development inhibited by, for example, repeating work which they have clearly mastered.

The mathematics contained in the suggested learning experiences at any level is only a subset of the mathematics which students could possibly learn. Faster students can be extended in their mathematical experience without necessarily accelerating them to a higher level, which for many students may itself limit the extent of their learning.

The intention of the development band is to encourage teachers to offer broader, richer, and more challenging mathematical experiences to faster students. Work from the development band should allow better students to investigate whole new topics which would not otherwise be studied and to work at a higher conceptual level. Talented students should have their interest in mathematical ideas further stimulated and their understanding of the nature of mathematics deepened. Teaching approaches which may build on the interest of students include: allowing students themselves to select the topic or content they wish to pursue and to set their own goals; allowing the opportunity for individual and independent study, perhaps using a contract plan; and encouraging access to a broader range of higher level resources.

The development band must not be considered as an optional extra or simply a reward for good work. Students have a right to the opportunity to extend their mathematical knowledge and power. Accordingly, teachers have a responsibility to provide enrichment opportunities to students, and a responsibility to report to parents in a way that acknowledges the students' accomplishments.

This statement suggests some development band activities and students and teachers will identify many more fields worth pursuing. A valid development band activity is a significant new piece of work, not merely an extra "extension example" or set of examples. Teachers of senior secondary students will need to establish clear criteria for the evaluation of development band work and a system which allows some basis for comparability between the work of different students. Students might undertake "units" of development band work, for example.

Development band activities should include a measure of self-assessment. students should be encouraged to set their own goals in this work and to be self-critical. They should keep a portfolio of their development activities, including the goals they had set, their assessments, and their teachers' assessments, as a record of their extended progress. Possession of the portfolio should, among other things, ensure that students do not repeat development work in later years.