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- Title: ST Learning Matrix
- Description: Statistics Learning Matrix
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- Description: Statistics Learning Matrix
What is Statistics about?
Subject-specific terms can be found in the glossary.
People are at the heart of Statistics: the people who have collected information to study, the people who have gifted information about themselves or about places and objects important to them, and the people who use data to make decisions and communicate what they have found. Seeing Statistics as a whole, continuous process, starting from thinking about why data is being collected, through data gathering, to using the results, will help ākonga to think about how to uphold the mana of all of the people involved.
Statistics is the exploration and use of patterns and relationships in data. Mathematics and Statistics are two strong vines that weave together, sharing a secure foundation. Both equip ākonga with effective means for investigating, modelling, analysing, interpreting, and making sense of the world in which they live.
Statisticians use symbols, graphs, displays, and diagrams to help them find and communicate patterns and relationships in data. 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. The skills developed by evaluating information in this way strengthen career pathways into many sectors.
Subject-specific terms can be found in the glossary.
People are at the heart of Statistics: the people who have collected information to study, the people who have gifted information about themselves or about places and objects important to them, and the people who use data to make decisions and communicate what they have found. Seeing Statistics as a whole, continuous process, starting from thinking about why data is being collected, through data gathering, to using the results, will help ākonga to think about how to uphold the mana of all of the people involved.
Statistics is the exploration and use of patterns and relationships in data. Mathematics and Statistics are two strong vines that weave together, sharing a secure foundation. Both equip ākonga with effective means for investigating, modelling, analysing, interpreting, and making sense of the world in which they live.
Statisticians use symbols, graphs, displays, and diagrams to help them find and communicate patterns and relationships in data. 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. The skills developed by evaluating information in this way strengthen career pathways into many sectors.
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 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 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 7 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 7 and indicative learning for Level 8. 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 must relate to at least one Big Idea and may also link to other Big Ideas.
There are six Big Ideas in Statistics. The nature of this subject as a discipline means aspects of Significant Learning often cross over multiple Big Ideas, and vice versa. At all times at this level of study, learning needs to weave together relevant contextual information with the skills.
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 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 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 7 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 7 and indicative learning for Level 8. 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 must relate to at least one Big Idea and may also link to other Big Ideas.
There are six Big Ideas in Statistics. The nature of this subject as a discipline means aspects of Significant Learning often cross over multiple Big Ideas, and vice versa. At all times at this level of study, learning needs to weave together relevant contextual information with the skills.
Big Idea Body:
In statistics, observations are transformed into data, a set of variables which record characteristics of a person, object, or non-physical entity. Observations, whether from observational studies, experiments, or other less traditional sources of data, are located in a point in time, have a history, and carry mauri. Why and how data is collected is important. Thinking about ethics and the tikanga of data collection and use throughout the process of statistical enquiry will help students engage respectfully with data and with other participants in the investigative process.
Observations can be transformed into data which has whakapapa and is a taonga
In statistics, observations are transformed into data, a set of variables which record characteristics of a person, object, or non-physical entity. Observations, whether from observational studies, experiments, or other less traditional sources of data, are located in a point in time, have a history, and carry mauri. Why and how data is collected is important. Thinking about ethics and the tikanga of data collection and use throughout the process of statistical enquiry will help students engage respectfully with data and with other participants in the investigative process.
Big Idea Body:
Tāiringa kōrero is a thought put forward, on the basis of observations, which is yet to be proved. 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 statistical change unfolds. Ākonga can participate directly in these processes to enrich their comprehension.
Tāiringa kōrero allows for creativity and exploration, and the discovery of statistical concepts, theories, and models
Tāiringa kōrero is a thought put forward, on the basis of observations, which is yet to be proved. 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 statistical change unfolds. Ākonga can participate directly in these processes to enrich their comprehension.
Big Idea Body:
Ākonga can use statistical knowledge and techniques to create or use statistical models which generate data under certain assumptions and conditions. With statistical models, ākonga can investigate relationships between variables, make comparisons, simulate outcomes, and make inferences and predictions. When building a model, it is important to consider the history, quality, and source of the data that feeds into the model and think about the ownership of the data. This will allow ākonga to form models and respectfully communicate what they show.
Statistical models are used to explore situations and problems around us
Ākonga can use statistical knowledge and techniques to create or use statistical models which generate data under certain assumptions and conditions. With statistical models, ākonga can investigate relationships between variables, make comparisons, simulate outcomes, and make inferences and predictions. When building a model, it is important to consider the history, quality, and source of the data that feeds into the model and think about the ownership of the data. This will allow ākonga to form models and respectfully communicate what they show.
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 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 wānanga, which can be ways of making sense of observations and patterns.
Critical thinking 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 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 wānanga, which can be ways of making sense of observations and patterns.
Big Idea Body:
Through Statistics, ākonga will recognise the variation and uncertainty that is a part of their world. Statisticians need to balance controlling for variation by random sampling and the practicalities of data collection. Uncertainty is more than mathematical probability. We make decisions under uncertainty every day, and statistics helps us think about these decisions clearly and quantify the risks involved. Being able to honestly communicate uncertainty, and interpret information presented with uncertainty, will help ākonga to fully engage with society.
Statistical thinking acknowledges that variation and uncertainty is present and may be quantified and explained
Through Statistics, ākonga will recognise the variation and uncertainty that is a part of their world. Statisticians need to balance controlling for variation by random sampling and the practicalities of data collection. Uncertainty is more than mathematical probability. We make decisions under uncertainty every day, and statistics helps us think about these decisions clearly and quantify the risks involved. Being able to honestly communicate uncertainty, and interpret information presented with uncertainty, will help ākonga to fully engage with society.
Big Idea Body:
Wānanga is a process that values time and discourse as integral factors to support learning. In statistics, wānanga allows discussion, questions, answers, and critical thought to be transformed into knowledge and understanding. Statistics is not only a process or strategy for thinking. Through statistics, we can reach informed conclusions about the world, understand widely applicable concepts, and test claims against our understanding. As ākonga develop their own statistical knowledge, they will grow in their capacity to evaluate information, assess situations, respond to problems, and make evidence-based decisions.
In 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 statistics, wānanga allows discussion, questions, answers, and critical thought to be transformed into knowledge and understanding. Statistics is not only a process or strategy for thinking. Through statistics, we can reach informed conclusions about the world, understand widely applicable concepts, and test claims against our understanding. As ākonga develop their own statistical knowledge, they will grow in their capacity to evaluate information, assess situations, respond to problems, and make evidence-based decisions.
Key Competencies in Statistics
Developing Key Competencies through Statistics
Learning in 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 statistics, and develop their understanding of the role of mathematics and statistics in society. Wānanga and talanoa are useful tools that ākonga can use to engage with the Key Competencies.
Thinking
Students of Statistics will:
- develop statistical reasoning, critical-thinking skills, and the capability to work through problems systematically. Critical thinking includes Indigenous ways of acquiring knowledge, for example talanoa and collaboration
- develop statistical literacy for the purpose of interpreting and evaluating data
- use creative thinking and experimentation to further statistical comprehension
- understand how to apply statistical methods and concepts to material problems and contexts, within the world of work.
Using language, symbols, and texts
Students of Statistics will:
- develop their ability to make meaning of statistical symbols, equations, and expressions
- understand how to produce and interpret data visualisations and graphs
- explain working and reasoning when solving statistical problems
- interpret and communicate statistical ideas for varied purposes.
Relating to others
Students of Statistics will:
- understand how to express statistical information for different purposes and audiences
- collect and explore statistical data to enhance their understanding of situations which relate to life in Aotearoa New Zealand
- consider the interests and uphold the mana of everyone involved in a statistical process, including the providers of data, and anyone who data is collected about.
Managing self
Students of Statistics will:
- become capable learners as they develop confidence to apply statistical concepts to material problems and contexts, within the world of work
- make increasingly appropriate selection of statistical methods and processes in appropriate circumstances.
Participating and contributing
Students of Statistics will:
- be actively involved in communities through analysing local statistical information, and building upon their knowledge to participate in discussion and discourse
- apply 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 Statistics
Learning in 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 statistics, and develop their understanding of the role of mathematics and statistics in society. Wānanga and talanoa are useful tools that ākonga can use to engage with the Key Competencies.
Thinking
Students of Statistics will:
- develop statistical reasoning, critical-thinking skills, and the capability to work through problems systematically. Critical thinking includes Indigenous ways of acquiring knowledge, for example talanoa and collaboration
- develop statistical literacy for the purpose of interpreting and evaluating data
- use creative thinking and experimentation to further statistical comprehension
- understand how to apply statistical methods and concepts to material problems and contexts, within the world of work.
Using language, symbols, and texts
Students of Statistics will:
- develop their ability to make meaning of statistical symbols, equations, and expressions
- understand how to produce and interpret data visualisations and graphs
- explain working and reasoning when solving statistical problems
- interpret and communicate statistical ideas for varied purposes.
Relating to others
Students of Statistics will:
- understand how to express statistical information for different purposes and audiences
- collect and explore statistical data to enhance their understanding of situations which relate to life in Aotearoa New Zealand
- consider the interests and uphold the mana of everyone involved in a statistical process, including the providers of data, and anyone who data is collected about.
Managing self
Students of Statistics will:
- become capable learners as they develop confidence to apply statistical concepts to material problems and contexts, within the world of work
- make increasingly appropriate selection of statistical methods and processes in appropriate circumstances.
Participating and contributing
Students of Statistics will:
- be actively involved in communities through analysing local statistical information, and building upon their knowledge to participate in discussion and discourse
- apply 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
Statistics has connections with a large range of subjects throughout mathematics, sciences, social sciences, and technology. Statistics is most clearly connected to Mathematics, with some skills and knowledge being a core part of both subjects. Statistics also has a particular connection with Psychology, through a focus on experimental design and critical thinking about research. Other subjects such as Tourism, Agribusiness, and Pacific Studies will all provide opportunities to use the skills and capabilities developed in Statistics.
Statistics has connections with a large range of subjects throughout mathematics, sciences, social sciences, and technology. Statistics is most clearly connected to Mathematics, with some skills and knowledge being a core part of both subjects. Statistics also has a particular connection with Psychology, through a focus on experimental design and critical thinking about research. Other subjects such as Tourism, Agribusiness, and Pacific Studies will all provide opportunities to use the skills and capabilities developed in Statistics.
Learning Pathway
Statistics provides ākonga with skills and knowledge that is useful for a wide range of pathways. Some ākonga will pursue further study in statistics and look to careers as statisticians, biometricians, or data analysts. Statistics is also a valuable grounding for tertiary study in many subjects that involve analysis, such as sciences, psychology, or economics. Being able to understand and interpret data is a crucial skill for evidence-based decision-making in everyday life, as well as being valuable throughout the world of work in almost every field, from retail to primary production to the health and community sector.
Statistics provides ākonga with skills and knowledge that is useful for a wide range of pathways. Some ākonga will pursue further study in statistics and look to careers as statisticians, biometricians, or data analysts. Statistics is also a valuable grounding for tertiary study in many subjects that involve analysis, such as sciences, psychology, or economics. Being able to understand and interpret data is a crucial skill for evidence-based decision-making in everyday life, as well as being valuable throughout the world of work in almost every field, from retail to primary production to the health and community sector.
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- Title: ST Level 2 Course Outline 1
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Introduction to Sample Course Outlines
The Sample Course Outlines provide a clear overview of learning across one year and link to the Learning and Assessment Matrices. They are indicative only and do not mandate any particular context or approach. Course Outlines should be developed using the appropriate template.
The Sample Course Outlines provide a clear overview of learning across one year and link to the Learning and Assessment Matrices. They are indicative only and do not mandate any particular context or approach. Course Outlines should be developed using the appropriate template.
Assessment Matrix
Ākonga need to work independently on the data exploration.
Teachers must monitor students’ progress closely and familiarise themselves with students’ evolving work.
Students cannot receive any scaffolding, instruction, teaching, or other form of guidance during the assessment event.
Teachers must 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 presentation and evidence produced outside of class time or teacher supervision.
Data can be primary (collected) or secondary (existing). The planning, collecting, sourcing, and creating of datasets can be done in groups, with or without teacher support, as it does not form part of the assessment.
Kaiako will provide guidance to ākonga on the selection of datasets, or provide datasets themselves, as this is not part of the assessment. Datasets should be appropriate to ākonga and their environment.
Ākonga will need access to appropriate technology and resources.
Ensuring Authenticity of Evidence
Teachers must be familiar with additional generic guidance on assessment practice in schools or learning centres. The authenticity of students’ work must be ensured according to NZQA’s Assessment (including Examination) Rules for Schools with Consent to Assess 2021. This guidance must be read in conjunction with these Conditions of Assessment.
Evidence for applicable parts of this assessment can be in te reo Māori, English, or New Zealand Sign Language.
This section provides guidelines for assessment against internally assessed Standards. Guidance is provided on:
- appropriate ways of, and conditions for, gathering evidence
- ensuring that evidence is authentic
- any other relevant advice specific to an Achievement Standard.
NB: Information on additional generic guidance on assessment practice in schools is published on the NZQA website. It would be useful to read in conjunction with these Conditions of Assessment.
The school's Assessment Policy and Conditions of Assessment must be consistent with the Assessment Rules for Schools With Consent to Assess. These rules will be updated during the NCEA review. The above link includes guidance for managing internal moderation and the collection of 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.
It is also recommended that the collection of evidence for internally assessed Standards should not use the same method that is used for any external Standards in a programme/course, particularly if that method is using a time bound written examination. This could unfairly disadvantage students who do not perform well under these conditions.
A separate assessment event is not needed for each Standard. Often assessment can be integrated into one activity that collects evidence towards two or three different Standards from a programme of learning. Evidence can also be collected over time from a range of linked activities (for example, in a portfolio).
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.
Authenticity of student evidence needs to be assured regardless of the method of collecting evidence. This needs to be in line with school policy. For example, an investigation carried out over several sessions could include teacher observations or the use of milestones such as a meeting with the student, a journal, or photographic entries recording progress etc.
Ākonga need to work independently on this task but the task may be open book.
Ākonga will either be given a dataset to explore, or summarised data, or may collect their own data.
Ākonga will have access to appropriate technology and resources, including assistive technology.
Ākonga will have access to all of the relevant formulae.
Ensuring Authenticity of Evidence
Teachers must be familiar with additional generic guidance on assessment practice in schools or learning centres. The authenticity of students’ work must be ensured according to NZQA’s Assessment (including Examination) Rules for Schools with Consent to Assess 2021. This guidance must be read in conjunction with these Conditions of Assessment.
Evidence for applicable parts of this assessment can be in te reo Māori, English, or New Zealand Sign Language.
This section provides guidelines for assessment against internally assessed Standards. Guidance is provided on:
- appropriate ways of, and conditions for, gathering evidence
- ensuring that evidence is authentic
- any other relevant advice specific to an Achievement Standard.
NB: Information on additional generic guidance on assessment practice in schools is published on the NZQA website. It would be useful to read in conjunction with these Conditions of Assessment.
The school's Assessment Policy and Conditions of Assessment must be consistent with the Assessment Rules for Schools With Consent to Assess. These rules will be updated during the NCEA review. The above link includes guidance for managing internal moderation and the collection of 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.
It is also recommended that the collection of evidence for internally assessed Standards should not use the same method that is used for any external Standards in a programme/course, particularly if that method is using a time bound written examination. This could unfairly disadvantage students who do not perform well under these conditions.
A separate assessment event is not needed for each Standard. Often assessment can be integrated into one activity that collects evidence towards two or three different Standards from a programme of learning. Evidence can also be collected over time from a range of linked activities (for example, in a portfolio).
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.
Authenticity of student evidence needs to be assured regardless of the method of collecting evidence. This needs to be in line with school policy. For example, an investigation carried out over several sessions could include teacher observations or the use of milestones such as a meeting with the student, a journal, or photographic entries recording progress etc.