What is mathematics and statistics 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?
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.
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.
Assessment to Support Teaching and Learning of Mathematics
The primary purpose of assessment is to improve students’ learning and teachers’ teaching as students and teacher respond to the information it provides.
This section is designed to help teachers understand the available assessment tools to meet their assessment needs. If you are viewing this document in digital version then the blue writing is a hyperlink to that tool on the nzmaths website.
National Standards Illustrations
A collection of Illustrations of the National Standards for Mathematics are being developed. Each task includes a page describing the task that was used to generate the work samples and a collection of two or more work samples, each illustrating work at a particular standard. The work samples are annotated to indicate features that are representative of that standard.
JAM (Junior Assessment of Mathematics)
The JAM assesses the achievement of a student in relation to levels one and two of The New Zealand Curriculum (NZC) and the mathematics standards for years 1–3. The assessment consists of 9 modules. Each module can be used as a separate assessment, or the modules can be combined to provide a broader assessment. The JAM is available on the nzmaths website.
NumPA (Diagnostic Interview)
This diagnostic interview is administered in an individual interview. It is used to fully assess a student’s knowledge in all five of the knowledge domains and strategy in all three of the strategy domains. However, as this method of assessment is time-consuming, it is not intended that it be used with every member of a class on a regular basis. More information about NumPA is available from the nzmaths online PD. The Diagnostic Interview is Book 2 of the Numeracy Development Projects Books.
The GloSS assessment enables you to identify the strategy stage students are operating at across all three strategy domains, known as the global strategy stage. It consists of a series of strategy questions which can be administered to individual students in a few minutes. Multiple forms of the interview are available so that students do not become too familiar with the questions. More information is available from the nzmaths online PD. The GloSS assessments are available on the nzmaths website.
The IKAN assessment identifies the knowledge stages students are operating at across all five knowledge domains, known as the global knowledge stage. The IKAN interview is for students at the counting stages of the number framework. It can be carried out formally in a one-on-one situation or in a small group setting. The IKAN written test is for students at the part-whole stages of the number framework. Whilst IKAN informs what we know about a student's number knowledge, this assessment on its own is insufficient to give a full picture of a student's achievement in number. More information is available from the nzmaths online PD. The IKAN assessments are available on the nzmaths website.
PAT:Mathematics is a series of 9 multiple choice tests designed for students in years 3 to 10. Each test can be used at multiple year levels. Achievement on each test can be reported on a common measurement scale. The scale allows formative and summative reporting. A marking and analysis service is available. More information about PAT assessments is available from the NZCER website.
The Assessment Resource Banks (ARBs) include a collection of mathematics assessment resources for levels two to five. They are intended for assessment within New Zealand classrooms and include tasks for students and a teacher information page. Many of the resources include formative assessment support for teachers and students. Tasks can be selected for a specific learning objective. More information about the ARBs is available from the NZCER website.
asTTle provides teachers, students, and parents with information about students’ achievement, relative to the curriculum achievement levels for levels 2 to 6 including and national norms of performance for students in years 4 to 12. More information about asTTle is available from the TKI website.