## What is Mathematics and Statistics about?

##
[ Video Resource ]

- Title: Mathematics and Statistics
- Description: Mathematics and Statistics Subject Expert Group members discuss their experiences in the Review of Achievement Standards
- Video Duration: 5 minutes
- Video URL: https://player.vimeo.com/video/571920130
- Transcript: In conversation with Jim Davis Liz Sneddon Katalina Ma Transcript below: I reckon the biggest change you'll notice is

In conversation with

Jim Davis

Liz Sneddon

Katalina Ma

#### Transcript below:

I reckon the biggest change you'll notice is, that the whole subject has been unpacked. It's not siloed anymore. So they actually have that chance to teach across the curriculum in one go, and assess from across the curriculum.

Knowledge of Mathematics and Statistics isn't compartmentalised anymore. I think it's a good thing, because we tend to just focus on one area. Then, when we want students to be able to go back to that area of learning, they thought it was just for the beginning of the year. So yeah, real exciting stuff.

For ākonga, they'll develop their maths more holistically, and realise that it is all connected. But not only that, with only four standards, they are... Their workload is going to go down significantly. So pretty much each term they might have only one assessment. So more time on the teaching and learning, less time on the assessment.

We're still assessing, still learning the same stuff, but the balance has changed. I think there's the opportunity to assist in a different way for our students. Not all our students like the sort of sit-down traditional kind of testing. Sort of being able to look at a possible project way of learning and way of assessing, as well as opportunities to do integrated units, cross-curricular with other subjects.

The idea that people who, or any student, that picks up any of these assessments, will be able to see themselves in it. Therefore will be able to bring their own mātauranga into what they're doing. Into their learning and their products, that they're making. I think that's what we'll see.

I know for me personally, I've got a better understanding than I had. I've still got a long way to go on my journey. But I've got a much better understanding than I had of what it means to be completely inclusive.

Yeah, I think it's really important, that we reiterate the fact, that the Learning Matrix we've put together has nothing new in it. It has nothing omitted from it. It is what was always there for curriculum level six. All we are asking our teachers to do now is maybe approach that differently, and have a different understanding of how they link together. You want students to take these skill sets and be able to build their communities with it, build themselves as individuals, use it later on in life.

That it's a... If we're wanting to produce these lifelong learners, that it's evident in what we're delivering in terms of our curriculum. We've had so many varied experiences from a range of different schools. From a range of different types of students, from all of that kind of stuff. It means that each of us are coming in with our own ideas, and putting it together to make something that is bigger than any one of us by ourselves.

We're able to form something cohesive that takes elements off everyone, and everyone has contributed to in amazing ways. It's not to say it's been a smooth sailing, there's definitely been difficult conversations. But as a teacher and as a person, I know I've grown.

Some of the research readings that we've had, oh my gosh, it has blown my mind. Because it's made me grow, and think, and reflect in ways that I hadn't before. That has been so powerful for me. To have that opportunity has been phenomenal.

I think for me, the biggest takeaway I've had from being in the group is the confidence to enact change. As a head of a faculty, at a fairly large one, with some teachers have been there a while, it's not always easy to make change. But I think for them to see me involved in this, and me to bring the expertise of the group back to our faculty, and help us develop and grow as a team, that's been for me the biggest personal growth. And you're right, there was some sort of uncomfortable, sort of conversations and stuff but conversations that needed to happen.

The biggest piece of advice I'll give is be open-minded. We haven't redesigned maths. We've just redesigned the approach to maths. For the absolute purist out there, nothing's gone, nothing's been removed, nothing's been dumbed down. It's just how we approach it. We want them to be inclusive, we want them to explore, and be free to teach in the way that we love teaching.

Find those problems that we want to tackle, that we enjoy. Pull out from the kids that love of Maths and that love of Stats that we have. We want to be able to get out of them. And that's the real value, let's get back into some of that really amazing, connected stuff. Build those relationships with your students, get to know who they are. Then figure out what Maths might work for them, and let's see how far we can take this.

*Subject-specific terms can be found in the glossary.*

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 involve different ways of thinking and solving problems. Both equip ākonga with effective means for modelling, analysing, and interpreting the world in which they live.

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

*Subject-specific terms can be found in the glossary.*

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 involve different ways of thinking and solving problems. Both equip ākonga with effective means for modelling, analysing, and interpreting the world in which they live.

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

## Big Ideas and Significant Learning

This section outlines the meaning of, and connection between, the Big Ideas and Significant Learning, which together form the Learning Matrix. It then explains each Mathematics and Statistics Big Idea.

The Mathematics and Statistics Learning Area, including its whakataukī, inform this subject's Significant Learning – learning that is critical for students to know, understand, and do in relation to a subject by the end of each Curriculum Level. This covers knowledge, skills, competencies, and attitudes. It also includes level-appropriate contexts students should encounter in their Level 6 learning. The Learning Area's whakataukī is:

Kei hopu tōu ringa ki te aka tāepa, engari kia mau ki te aka matua.

Cling to the main vine, not the loose one.

This whakataukī comes from the pūrākau of Tāne's ascent to the heavens to collect te kete ngā mātauranga, or the baskets of knowledge. The main vine is strong and has secure foundations, whereas the loose vine can be buffeted by the wind, so anyone climbing it will not reach the top. The pūrākau helps to illustrate that knowledge, as in te kete ngā mātauranga, is a taonga, and to show the need for hard work and problem-solving to gain solid knowledge.

The subject's Big Ideas and Significant Learning are collated into a Learning Matrix for Curriculum Level 6. Teachers can use the Learning Matrix as a tool to construct learning programmes that cover all the not-to-be-missed learning in a subject. There is no prescribed order to the Learning Matrix within each level. A programme of learning might begin with a context that is relevant to the local area of the school or an idea that students are particularly interested in. This context or topic must relate to at least one Big Idea and may also link to other Big Ideas.

There are five Big Ideas in Mathematics and Statistics. The nature of this subject as a discipline means aspects of Significant Learning often cross over multiple Big Ideas, and vice versa.

Unpacking the Learning Matrix

The Mathematics and Statistics Big Ideas are ideas about how to work with, and understand, mathematics and statistics. Within the Learning Matrix, the Significant Learning sit under the five Big Ideas. Each piece of Significant Learning might relate to any, or all, of the five Big Ideas. This highlights the relevance of the Big Ideas to all learning.

The Learning Matrix is framed in this way to show that most learning in Mathematics and Statistics is cross-topic. Topics can be taught together, and not unnecessarily compartmentalised. The Learning Matrix provides a starting point for kaiako to weave the topics together - kaiako will have their own ideas about how to do this weaving. This interwoven approach forms a solid base at Curriculum Level 6, which gives school leavers a workable mathematical toolbox and enables further specialisation at Curriculum Levels 7 and 8.

The Big Ideas of wānanga, hononga, and tāiringa kōrero highlight the importance of Aotearoa New Zealand’s identity in how ākonga conceptualise the world and solve problems. Mātauranga Māori recognises the importance of socio-cultural context when learning and applying mathematical and statistical skills. The content of mathematics is universal, but it will be accessed, and engaged with, by different cultures in distinct ways.

The Significant Learning comprises all the skills that ākonga are entitled to leave Curriculum Level 6 with. The Learning Matrix structure reflects that although Mathematics and Statistics involves a broad range of skills, the Big Ideas are the common underlying processes and knowledge that pull these skills together. It is important that learning is firmly embedded in a context which resonates with ākonga and that recognises their cultures. Kaiako are encouraged to match Significant Learning to the interests and needs of ākonga. Course Outlines and Assessment Activities will provide guidance on how teaching can be linked to the particular contexts and future pathways of ākonga.

What is new?

The pieces of Significant Learning are not materially different to what has previously been taught in Mathematics and Statistics. This collection of mathematical learning remains an excellent collection of capabilities for ākonga.

The real change is focused on how the Significant Learning is taught and assessed. Firstly, teaching across topics allows learners to engage with all sides of a problem. Exploring how different mathematical and statistical principles apply to anything and everything can empower ākonga to actively use mathematics in all contexts. Secondly, the four new Achievement Standards are designed for flexibility. The Standards are wide enough that kaiako will be able to design Assessment Activities that ākonga can see themselves in, and which prepare them for the diverse pathways they follow after school.

This section outlines the meaning of, and connection between, the Big Ideas and Significant Learning, which together form the Learning Matrix. It then explains each Mathematics and Statistics Big Idea.

The Mathematics and Statistics Learning Area, including its whakataukī, inform this subject's Significant Learning – learning that is critical for students to know, understand, and do in relation to a subject by the end of each Curriculum Level. This covers knowledge, skills, competencies, and attitudes. It also includes level-appropriate contexts students should encounter in their Level 6 learning. The Learning Area's whakataukī is:

Kei hopu tōu ringa ki te aka tāepa, engari kia mau ki te aka matua.

Cling to the main vine, not the loose one.

This whakataukī comes from the pūrākau of Tāne's ascent to the heavens to collect te kete ngā mātauranga, or the baskets of knowledge. The main vine is strong and has secure foundations, whereas the loose vine can be buffeted by the wind, so anyone climbing it will not reach the top. The pūrākau helps to illustrate that knowledge, as in te kete ngā mātauranga, is a taonga, and to show the need for hard work and problem-solving to gain solid knowledge.

The subject's Big Ideas and Significant Learning are collated into a Learning Matrix for Curriculum Level 6. Teachers can use the Learning Matrix as a tool to construct learning programmes that cover all the not-to-be-missed learning in a subject. There is no prescribed order to the Learning Matrix within each level. A programme of learning might begin with a context that is relevant to the local area of the school or an idea that students are particularly interested in. This context or topic must relate to at least one Big Idea and may also link to other Big Ideas.

There are five Big Ideas in Mathematics and Statistics. The nature of this subject as a discipline means aspects of Significant Learning often cross over multiple Big Ideas, and vice versa.

Unpacking the Learning Matrix

The Mathematics and Statistics Big Ideas are ideas about how to work with, and understand, mathematics and statistics. Within the Learning Matrix, the Significant Learning sit under the five Big Ideas. Each piece of Significant Learning might relate to any, or all, of the five Big Ideas. This highlights the relevance of the Big Ideas to all learning.

The Learning Matrix is framed in this way to show that most learning in Mathematics and Statistics is cross-topic. Topics can be taught together, and not unnecessarily compartmentalised. The Learning Matrix provides a starting point for kaiako to weave the topics together - kaiako will have their own ideas about how to do this weaving. This interwoven approach forms a solid base at Curriculum Level 6, which gives school leavers a workable mathematical toolbox and enables further specialisation at Curriculum Levels 7 and 8.

The Big Ideas of wānanga, hononga, and tāiringa kōrero highlight the importance of Aotearoa New Zealand’s identity in how ākonga conceptualise the world and solve problems. Mātauranga Māori recognises the importance of socio-cultural context when learning and applying mathematical and statistical skills. The content of mathematics is universal, but it will be accessed, and engaged with, by different cultures in distinct ways.

The Significant Learning comprises all the skills that ākonga are entitled to leave Curriculum Level 6 with. The Learning Matrix structure reflects that although Mathematics and Statistics involves a broad range of skills, the Big Ideas are the common underlying processes and knowledge that pull these skills together. It is important that learning is firmly embedded in a context which resonates with ākonga and that recognises their cultures. Kaiako are encouraged to match Significant Learning to the interests and needs of ākonga. Course Outlines and Assessment Activities will provide guidance on how teaching can be linked to the particular contexts and future pathways of ākonga.

What is new?

The pieces of Significant Learning are not materially different to what has previously been taught in Mathematics and Statistics. This collection of mathematical learning remains an excellent collection of capabilities for ākonga.

The real change is focused on how the Significant Learning is taught and assessed. Firstly, teaching across topics allows learners to engage with all sides of a problem. Exploring how different mathematical and statistical principles apply to anything and everything can empower ākonga to actively use mathematics in all contexts. Secondly, the four new Achievement Standards are designed for flexibility. The Standards are wide enough that kaiako will be able to design Assessment Activities that ākonga can see themselves in, and which prepare them for the diverse pathways they follow after school.

**Critical thinking, and mathematical and statistical generalisations emerge from te hononga of different observations, knowledges, and processes**

Big Idea Body:

As ākonga build critical thinking skills, they move from relying on their intuition, or instincts, to working systematically to solve problems, form generalisations, and reach conclusions. Critical thinking skills can be developed through engagement with information from varying sources. As ākonga grow to recognise the connections between different observations, knowledges, and processes, their capabilities in making mathematical and statistical generalisations will improve. Hononga is the concept of identifying these connections and links to reach conclusions. Te hononga can be built through talanoa and wanānga, which can be ways of making sense of observations and patterns.

### Critical thinking, and mathematical and statistical generalisations emerge from te hononga of different observations, knowledges, and processes

As ākonga build critical thinking skills, they move from relying on their intuition, or instincts, to working systematically to solve problems, form generalisations, and reach conclusions. Critical thinking skills can be developed through engagement with information from varying sources. As ākonga grow to recognise the connections between different observations, knowledges, and processes, their capabilities in making mathematical and statistical generalisations will improve. Hononga is the concept of identifying these connections and links to reach conclusions. Te hononga can be built through talanoa and wanānga, which can be ways of making sense of observations and patterns.

**Tāiringa kōrero allows for elegance, creativity, and exploration of mathematical and statistical ideas**

Big Idea Body:

Tāiringa kōrero is a thought put forward, on the basis of observations, which is yet to be proved. Mathematical and statistical discovery can begin with these observations. Tāiringa kōrero is marked by exploration, creativity, discovery, and conjecture. Experimentation and exploration are the mechanisms through which mathematical and statistical change unfolds. Ākonga can participate directly in these processes to enrich their comprehension.

### Tāiringa kōrero allows for elegance, creativity, and exploration of mathematical and statistical ideas

Tāiringa kōrero is a thought put forward, on the basis of observations, which is yet to be proved. Mathematical and statistical discovery can begin with these observations. Tāiringa kōrero is marked by exploration, creativity, discovery, and conjecture. Experimentation and exploration are the mechanisms through which mathematical and statistical change unfolds. Ākonga can participate directly in these processes to enrich their comprehension.

**In Mathematics and Statistics, wānanga stimulates logical argument, investigation, analysis, and justification, supporting critical evaluation and reasoned conclusions**

Big Idea Body:

Wānanga is a process that values time and discourse as integral factors to support learning. In mathematics and statistics, wānanga allows discussion, questions, answers, and critical thought to be transformed into knowledge and understanding. Mathematics and statistics are not only processes or strategies for thinking. Through mathematics and statistics, we can reach informed conclusions about the world, understand widely applicable concepts, and test claims against our understanding. As ākonga develop their own mathematical and statistical knowledge, they will grow in their capacity to evaluate information, assess situations, respond to problems, and make evidence-based decisions.

### In Mathematics and Statistics, wānanga stimulates logical argument, investigation, analysis, and justification, supporting critical evaluation and reasoned conclusions

Wānanga is a process that values time and discourse as integral factors to support learning. In mathematics and statistics, wānanga allows discussion, questions, answers, and critical thought to be transformed into knowledge and understanding. Mathematics and statistics are not only processes or strategies for thinking. Through mathematics and statistics, we can reach informed conclusions about the world, understand widely applicable concepts, and test claims against our understanding. As ākonga develop their own mathematical and statistical knowledge, they will grow in their capacity to evaluate information, assess situations, respond to problems, and make evidence-based decisions.

**Mathematical and statistical concepts, patterns, and relationships can be represented in multiple ways**

Big Idea Body:

The focus of this Big Idea is equivalency. Understanding the various ways in which a mathematical and statistical concept can be represented is an essential foundation for problem solving and manipulation. Accessing a mathematical or statistical concept through different strands of learning encourages open-minded thinking. This allows ākonga to look at problems from new perspectives and angles and engage fluently with the wider implications of their work. When ākonga move beyond a compartmentalised understanding, they can see more ways into problems, and more fully understand the fluid nature of mathematics and statistics.

### Mathematical and statistical concepts, patterns, and relationships can be represented in multiple ways

The focus of this Big Idea is equivalency. Understanding the various ways in which a mathematical and statistical concept can be represented is an essential foundation for problem solving and manipulation. Accessing a mathematical or statistical concept through different strands of learning encourages open-minded thinking. This allows ākonga to look at problems from new perspectives and angles and engage fluently with the wider implications of their work. When ākonga move beyond a compartmentalised understanding, they can see more ways into problems, and more fully understand the fluid nature of mathematics and statistics.

**Mathematical and statistical methods can be used to explore, solve, or model problems while recognising variation, certainty, and uncertainty**

Big Idea Body:

Ākonga should understand how their mathematical and statistical literacy can apply to tangible problems outside the classroom. This involves correctly identifying when to explore (considering variation and uncertainty), solve with certainty, or create and use a mathematical or statistical model.

### Mathematical and statistical methods can be used to explore, solve, or model problems while recognising variation, certainty, and uncertainty

Ākonga should understand how their mathematical and statistical literacy can apply to tangible problems outside the classroom. This involves correctly identifying when to explore (considering variation and uncertainty), solve with certainty, or create and use a mathematical or statistical model.

## Key Competencies in Mathematics and Statistics

### Developing Key Competencies through Mathematics and Statistics

Learning in Mathematics and Statistics provides meaningful contexts for developing Key Competencies from *The New Zealand Curriculum*. These Key Competencies are woven through, and embedded in, the Big Ideas and Significant Learning. Students will engage with critical thinking and analysis, explore different perspectives through mathematics and statistics and develop their understanding of the role of mathematics and statistics in society.

### Thinking

Students in Mathematics and Statistics will:

- develop mathematical and statistical reasoning, critical-thinking skills, and the capability to work through problems systematically (critical thinking includes indigenous ways of acquiring knowledge eg
*talanoa*and collaboration) - develop mathematical and statistical literacy for the purpose of interpreting and evaluating mathematical and statistical data
- use creative thinking and experimentation to further mathematical and statistical comprehension
- understand how to apply mathematical methods and concepts to material problems and contexts within the world of work.

### Using language, symbols, and texts

Students in Mathematics and Statistics will:

- develop their ability to make meaning of mathematical and statistical symbols, equations, expressions, and graphs
- explain working and reasoning when solving mathematical or statistical problems
- interpret and communicate mathematical and statistical ideas to for varied purposes including solving problems.

### Relating to others

Students in Mathematics and Statistics will:

- understand how to express mathematical and statistical information for different purposes and audiences
- collect and explore mathematical and statistical data to enhance their understanding of problems and situations which relate to life in Aotearoa New Zealand.

### Managing self

Students in Mathematics and Statistics will:

- become capable learners as they develop confidence to apply mathematical concepts to material problems and contexts, within the world of work
- make increasingly appropriate selection of mathematical and statistical methods and processes in appropriate circumstances.

### Participating and contributing

Students in Mathematics and Statistics will:

- be actively involved in communities through analysing local mathematics and statistics information, and building upon their knowledge to participate in discussion and discourse
- apply mathematical and statistical skills to problems outside of the classroom.

### Key Competencies

This section of *The New Zealand Curriculum Online* offers specific guidance to school leaders and teachers on integrating the Key Competencies into the daily activities of the school and its Teaching and Learning Programmes.

### Developing Key Competencies through Mathematics and Statistics

Learning in Mathematics and Statistics provides meaningful contexts for developing Key Competencies from *The New Zealand Curriculum*. These Key Competencies are woven through, and embedded in, the Big Ideas and Significant Learning. Students will engage with critical thinking and analysis, explore different perspectives through mathematics and statistics and develop their understanding of the role of mathematics and statistics in society.

### Thinking

Students in Mathematics and Statistics will:

- develop mathematical and statistical reasoning, critical-thinking skills, and the capability to work through problems systematically (critical thinking includes indigenous ways of acquiring knowledge eg
*talanoa*and collaboration) - develop mathematical and statistical literacy for the purpose of interpreting and evaluating mathematical and statistical data
- use creative thinking and experimentation to further mathematical and statistical comprehension
- understand how to apply mathematical methods and concepts to material problems and contexts within the world of work.

### Using language, symbols, and texts

Students in Mathematics and Statistics will:

- develop their ability to make meaning of mathematical and statistical symbols, equations, expressions, and graphs
- explain working and reasoning when solving mathematical or statistical problems
- interpret and communicate mathematical and statistical ideas to for varied purposes including solving problems.

### Relating to others

Students in Mathematics and Statistics will:

- understand how to express mathematical and statistical information for different purposes and audiences
- collect and explore mathematical and statistical data to enhance their understanding of problems and situations which relate to life in Aotearoa New Zealand.

### Managing self

Students in Mathematics and Statistics will:

- become capable learners as they develop confidence to apply mathematical concepts to material problems and contexts, within the world of work
- make increasingly appropriate selection of mathematical and statistical methods and processes in appropriate circumstances.

### Participating and contributing

Students in Mathematics and Statistics will:

- be actively involved in communities through analysing local mathematics and statistics information, and building upon their knowledge to participate in discussion and discourse
- apply mathematical and statistical skills to problems outside of the classroom.

### Key Competencies

This section of *The New Zealand Curriculum Online* offers specific guidance to school leaders and teachers on integrating the Key Competencies into the daily activities of the school and its Teaching and Learning Programmes.

## Connections

Mathematics and Statistics is a rich area of study with kuleana to many others. It opens up new languages and new ways of thinking, which can be utilised by ākonga across all Learning Areas. In turn, ākonga enrich their study of Mathematics and Statistics by exploring processes and knowledges in a broad range of contexts.

In the Learning Areas of Learning Languages, English, and Te Reo Māori, Mathematics and Statistics allows ākonga the opportunity to apply their knowledge in a wide range of cultures.

Mathematics and Statistics has wide applications in the Social Sciences. Reading and interpreting graphs, maps, and timelines accurately allows ākonga to examine and justify claims.

Science and Technology uses Mathematics and Statistics as a tool in representing visual and physical relationships. Mathematical language and reasoning are used to support scientific studies and ideas.

Patterns and structures applying concepts of Mathematics and Statistics are used in The Arts to add order, elegance, and precision.

Health and Physical Education use Mathematics and Statistics to measure, record, analyse, and describe action. Observations and analysis of health and movement are used to improve wellbeing.

Mathematics and Statistics is a rich area of study with kuleana to many others. It opens up new languages and new ways of thinking, which can be utilised by ākonga across all Learning Areas. In turn, ākonga enrich their study of Mathematics and Statistics by exploring processes and knowledges in a broad range of contexts.

In the Learning Areas of Learning Languages, English, and Te Reo Māori, Mathematics and Statistics allows ākonga the opportunity to apply their knowledge in a wide range of cultures.

Mathematics and Statistics has wide applications in the Social Sciences. Reading and interpreting graphs, maps, and timelines accurately allows ākonga to examine and justify claims.

Science and Technology uses Mathematics and Statistics as a tool in representing visual and physical relationships. Mathematical language and reasoning are used to support scientific studies and ideas.

Patterns and structures applying concepts of Mathematics and Statistics are used in The Arts to add order, elegance, and precision.

Health and Physical Education use Mathematics and Statistics to measure, record, analyse, and describe action. Observations and analysis of health and movement are used to improve wellbeing.

## Learning Pathway

Mathematics and Statistics equips ākonga with skills that will be put to use in all potential pathways following secondary school. Numerical literacy will enable measurement and calculation of quantity, time, and space, as well as the foundations of financial literacy. These skills underpin many scenarios beyond the classroom. Ākonga enhancing their mathematical and statistical capabilities will empower not only themselves, but also their whānau and wider communities.

For students moving into employment, pathways include:

- business and retail
- health and community care
- agriculture and horticulture
- defence force
- marketing and social media
- trades
- hospitality.

Students who complete Level 1 Mathematics and Statistics could choose to specialise in either or both disciplines at Level 2.

For students moving into further studies, Mathematics and Statistics provide foundation for:

- Data Science and Modelling
- Computer Science, Design and Programming
- Engineering
- Environmental and Earth Studies
- Finance and Social Sciences
- Science and Technology
- Education.

Mathematics and Statistics equips ākonga with skills that will be put to use in all potential pathways following secondary school. Numerical literacy will enable measurement and calculation of quantity, time, and space, as well as the foundations of financial literacy. These skills underpin many scenarios beyond the classroom. Ākonga enhancing their mathematical and statistical capabilities will empower not only themselves, but also their whānau and wider communities.

For students moving into employment, pathways include:

- business and retail
- health and community care
- agriculture and horticulture
- defence force
- marketing and social media
- trades
- hospitality.

Students who complete Level 1 Mathematics and Statistics could choose to specialise in either or both disciplines at Level 2.

For students moving into further studies, Mathematics and Statistics provide foundation for:

- Data Science and Modelling
- Computer Science, Design and Programming
- Engineering
- Environmental and Earth Studies
- Finance and Social Sciences
- Science and Technology
- Education.

## Introduction to Sample Course Outlines

Sample Course Outlines are intended to help teachers and schools understand the new NCEA Learning Matrix and Achievement Standards. Examples of how a year-long Mathematics and Statistics course could be constructed using the new Learning Matrix and Achievement Standards are provided here. They are indicative only and do not mandate any particular context or approach.

Sample Course Outlines are intended to help teachers and schools understand the new NCEA Learning Matrix and Achievement Standards. Examples of how a year-long Mathematics and Statistics course could be constructed using the new Learning Matrix and Achievement Standards are provided here. They are indicative only and do not mandate any particular context or approach.

## Assessment Matrix

## Conditions of Assessment for internally assessed standards

These Conditions provide guidelines for assessment against internally assessed Achievement Standards. Guidance is provided on:

- specific requirements for all assessments against this Standard
- appropriate ways of, and conditions for, gathering evidence
- ensuring that evidence is authentic.

Assessors must be familiar with guidance on assessment practice in learning centres, including enforcing timeframes and deadlines. The NZQA website offers resources that would be useful to read in conjunction with these Conditions of Assessment.

The learning centre’s Assessment Policy and Conditions of Assessment must be consistent with NZQA’s Assessment Rules for Schools with Consent to Assess. This link includes guidance for managing internal moderation and the collection of evidence.

**Gathering Evidence**

Internal assessment provides considerable flexibility in the collection of evidence. Evidence can be collected in different ways to suit a range of teaching and learning styles, and a range of contexts of teaching and learning. Care needs to be taken to allow students opportunities to present their best evidence against the Standard(s) that are free from unnecessary constraints.

It is recommended that the design of assessment reflects and reinforces the ways students have been learning. Collection of evidence for the internally assessed Standards could include, but is not restricted to, an extended task, an investigation, digital evidence (such as recorded interviews, blogs, photographs, or film), or a portfolio of evidence.

Effective assessment should suit the nature of the learning being assessed, provide opportunities to meet the diverse needs of all students, and be valid and fair.

**Ensuring Authenticity of Evidence**

Authenticity of student evidence needs to be assured regardless of the method of collecting evidence. This must be in line with the learning centre’s policy and NZQA’s Assessment Rules for Schools with Consent to Assess.

Ensure that the student’s evidence is individually identifiable and represents the student’s own work. This includes evidence submitted as part of a group assessment and evidence produced outside of class time or assessor supervision. For example, an investigation carried out over several sessions could include assessor observations, meeting with the student at a set milestone, or student’s use of a journal or photographic entries to record progress.

These Conditions provide guidelines for assessment against internally assessed Achievement Standards. Guidance is provided on:

- specific requirements for all assessments against this Standard
- appropriate ways of, and conditions for, gathering evidence
- ensuring that evidence is authentic.

Assessors must be familiar with guidance on assessment practice in learning centres, including enforcing timeframes and deadlines. The NZQA website offers resources that would be useful to read in conjunction with these Conditions of Assessment.

The learning centre’s Assessment Policy and Conditions of Assessment must be consistent with NZQA’s Assessment Rules for Schools with Consent to Assess. This link includes guidance for managing internal moderation and the collection of evidence.

**Gathering Evidence**

Internal assessment provides considerable flexibility in the collection of evidence. Evidence can be collected in different ways to suit a range of teaching and learning styles, and a range of contexts of teaching and learning. Care needs to be taken to allow students opportunities to present their best evidence against the Standard(s) that are free from unnecessary constraints.

It is recommended that the design of assessment reflects and reinforces the ways students have been learning. Collection of evidence for the internally assessed Standards could include, but is not restricted to, an extended task, an investigation, digital evidence (such as recorded interviews, blogs, photographs, or film), or a portfolio of evidence.

Effective assessment should suit the nature of the learning being assessed, provide opportunities to meet the diverse needs of all students, and be valid and fair.

**Ensuring Authenticity of Evidence**

Authenticity of student evidence needs to be assured regardless of the method of collecting evidence. This must be in line with the learning centre’s policy and NZQA’s Assessment Rules for Schools with Consent to Assess.

Ensure that the student’s evidence is individually identifiable and represents the student’s own work. This includes evidence submitted as part of a group assessment and evidence produced outside of class time or assessor supervision. For example, an investigation carried out over several sessions could include assessor observations, meeting with the student at a set milestone, or student’s use of a journal or photographic entries to record progress.

Assessor involvement during the assessment event is limited to providing guidance on a student's plan for their investigation, ensuring that any collected or sourced data allows students to explain different sources of variation. Assessors will provide guidance to students on the selection of appropriate data sets, including the sample size. Assessors can provide a milestone check which offers enough guidance to keep a student on track but should not compromise the authenticity of student work. Guidance or feedback should avoid correction of specific detail.

At the start of the assessment event, students are able to choose the direction of their own investigation, including investigative question or statement, with assessor approval. Assessors must ensure an appropriately worded investigative question or statement is used. Assessors may correct the wording, or provide an appropriately worded investigative question or statement. Assessors will identify the population for any collected or sourced data.

Students may use appropriate technology and resources.

Students may work in groups to plan and source data but must work individually on all other stages of this Standard.

Evidence for all parts of this assessment can be in te reo Māori, English, or New Zealand Sign Language.

Assessor involvement during the assessment event is limited to identifying the broad areas of mathematics required to complete the activity, for example, Pythagoras' theorem, volume, and graphs, and providing feedback on a student's plan for their exploration. The identification of the broad areas of mathematics could be provided verbally or as a written statement in the Assessment Activity. Assessors should ensure that the mathematical methods identified by the student in their plan reflect the level of mathematics found in the Learning Matrix for Mathematics and Statistics. Assessors cannot give direct instructions on what to do. For example, assessors cannot indicate to a student that they should use Pythagoras' theorem to find a specific length within an identified problem. Guidance or feedback should avoid correction of specific detail.

Each process, chosen and applied correctly, needs to come from within a different line in the following list. Refer to the companion pages of the Learning Matrix for specifics.

- Number:
- Reasoning with linear proportion, including inverse percentage change or more complex rates and ratios
- Integer exponents or scientific form.

- Algebra:
- Manipulating and using formulae, including rearranging for a purpose
- Manipulating and simplifying expressions, including expanding or factorising
- Linear inequalities
- Linear tables, equations, graphs, or patterns
- Quadratic tables, equations, graphs, or patterns
- Exponential tables, graphs, or patterns
- Simultaneous linear equations with two unknowns
- Optimising solutions.

- Measurement:
- Surface area of prisms, pyramids, cones, or spheres
- Volume of pyramids, cones, spheres, or composite shapes including prisms
- Converting between more complex metric units.

- Geometry and Space:
- Properties of similar shapes
- Pythagoras’ theorem in two or three dimensions
- Trigonometric ratios in right-angled triangles.

Selection of evidence for submission is to be carried out by the student.

Students will submit their plan for feedback. After receiving feedback, students will work independently to complete the activity.

Students may use appropriate technology and resources.

Evidence for all parts of this assessment can be in te reo Māori, English, or New Zealand Sign Language.