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The New Zealand Curriculum��Mathematics and statistics Years 0 to 8

November 2024

Cami Sawyer & Kylie Begg

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Purpose Statement

Students learn about:

the power of symbolic representation, reasoning, and abstraction
investigating, interpreting, and explaining patterns and relationships in quantity, space, time, data, and uncertainty.

Every student in New Zealand can engage in mathematics and statistics and discover personal enjoyment and curiosity in their learning.
They learn that mathematics and statistics has an evolving history; many cultures have contributed to, and continue to contribute to, innovations that shape our current thinking.
Mathematics and statistics allow us to engage with important societal matters.
Learning how to use this knowledge purposefully and flexibly allows students to participate fully in an increasingly technology- and information-rich world of work.

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Understand-Know-Do Overview

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It is through the interweaving of Understand, Know, and Do that students develop their conceptual understandings and procedural fluency, supporting success and bringing richness and meaning to mathematics and statistics for them.

Conceptual understanding is the comprehension of mathematical concepts, operations, and relations. Teachers provide multiple opportunities and experiences for students to build understanding by connecting related ideas, representing concepts in different ways, identifying commonalities and differences between aspects of content, communicating their mathematical thinking and interpreting mathematical information.

Procedural fluency is providing opportunities and experiences for students to choose procedures appropriately and carry them out flexibly, accurately, and efficiently. It is not the same as memorisation of facts and steps; rather it is being able to activate what they know and when to use it.

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Mathematics and statistics learning area structure

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Phase Progress Outcome

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Year-by-year Teaching Sequence

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This change in focus is seen in how the Understand, Know, and Do progress outcomes are reflected in the year-by-year teaching sequences. The descriptors of what to teach each year have the stem ‘Informed by prior learning ...’ in order to reinforce that teachers will use their professional judgment about what content to teach and how to teach it. They will make these judgments in response to the prior knowledge, strengths, and experiences that students bring to their learning.

The year-by-year teaching sequences are organised in line with the strands from Know. They describe the incremental teaching required each year as students work towards the progress outcome.

The year-by-year content can be viewed both vertically and horizontally. The vertical view helps teachers know what to plan for the next year. The horizontal view allows teachers to follow the statements for one concept across several stages. This helps them understand the prior knowledge students may bring to their learning and helps them decide how to extend this learning.

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The language of mathematics and statistics

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Teaching Guidance

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Phase 1-5

A balance of all 4 of the following approaches:

Explicit teaching
Positive relationships with mathematics and statistics
Rich tasks
Communication in mathematics and statistics

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The teaching guidance for all phases of learning describes the elements of a comprehensive learning programme. It is important to consider each of these elements when planning, teaching and learning mathematics and statistics.

Developing positive relationships is an extremely important element of a mathematics and statistics programme. We know that students who feel connected, positive and supported are more likely to attend to the learning. Positive relationships support students to take risks, and view mistakes as part of the learning process. These behaviours can lead to successful experiences, which in turn, builds confidence.

Explicit teaching – there are a lot of research findings that support explicit teaching as an effective practice in mathematics and statistics. However, what we don’t mean is that this is the teacher standing up the front and lecturing. Explicit teaching is planned and purposeful. It involves demonstration and explanation of a concept, procedure or a process using clearly explained demonstrations – supported by carefully chosen representations inc materials, . Explicit teaching is interactive – there is a back and forward throughout as the teacher uses prompts questions, and students’ ideas and to support the explicit teaching and help students make connections.

Explicit teaching also includes opportunities for students to practice both in groups and independently in order to develop fluency, revisit and consolidate prior learning.

Investigation, exploring rich tasks, and problem solving are extremely important learning experiences in mathematics and statistics. Rich tasks are meaningful and motivational tasks that are sometimes described as having a ‘low floor and high ceiling’, with an entry point to include every student. Rich tasks can connect to the school community; to students’ experiences, cultures, and languages, as well as to interesting mathematical situations.

Rich tasks could be used as a motivational hook, or as an experience to encourage application and transfer of the concepts and procedures they have learned through explicit teaching. Teachers should plan to use rich tasks and explicit teaching in a dynamic way to deepen and extend learning.

Students and teachers communicate in mathematics and statistics both to learn new ideas, as well as to share, extend and clarify their thinking and reasoning. Planning opportunities for students to collaborate together, and with the teacher to explain, question, critique, and connect ideas is pivotal. Teachers encourage students to develop and use of mathematical and statistical language, vocabulary and notation to share their reasoning.

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Using the progress outcomes and teaching sequences to develop your teaching and learning plans

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Planning guidance

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Teaching the year level statements
Order to build on and extend
Connect and combine
Revisit / Consolidate
Inclusion

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From there, we can use the sequence to map out a coherent year programme – long term plan using the sequence statements for your year level. Over the course of the year teachers should plan to teach every sequence statement to every student for their year level. Units of work can be ordered to build on and extend prior learning.

It is not intended that teachers teach these statements one by one or consecutively (they are not prioritised). Instead, we can plan a unit that combines statements together in ways that connect and support (for example, you would teach the number structure statements together and you would most likely group operations with area or volume – mult/div at the same time as perimeter/area or angles and lines with 2D shapes. It is also important to plan to revisit and consolidate statements over the year.

Teachers use an inclusive approach to planning. This involves using formative assessment information to plan an entry point for each unit or new learning that all students can access using familiar contexts and numbers to prompt recall of previous learning and methods. For students who have not yet developed the prior learning for a statement or unit, teachers plan accelerative approaches such as targeted explicit teaching, verbal and visual prompts and materials, and fluency practice.

Further important points in this planning guidance is about flexible grouping based on the purpose of learning, and the use of technology/digital tool to enhance teaching and learning.

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Dedicated mathematics and statistics lessons

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Teaching Sequence – considerations

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You will also notice that we have included teaching considerations within the sequence. These consist of useful representations or approaches that can be used when teaching specific sequence statements.

We took feedback that teachers would like further examples of what the statements ‘look’ like and how they could be taught. We have used the DO mathematics and statistics processes to show how these can be used in the teaching and learning of specific statements. For example, connections with other concepts, useful representations to show underlying patterns and structures, possible investigations into the concepts, or important explanations or demonstrations.

These considerations are aimed to support planning of explicit teaching, rich tasks, communication and encourage positive relationships with mathematics and statistics.

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NZC - Mathematics and statistics (Years 0-8)

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