The following resources have been developed to support teachers to implement the F–10 Mathematics curriculum.
This resource will help teachers and schools identify strong links between Mathematics and the capabilities. It will also help teachers design learning activities.
The resource assumes familiarity with the Mathematics curriculum. It links aspects of this curriculum with Ethical Capability, Critical and Creative Thinking, Intercultural Capability and Personal and Social Capability.
Note: It is a school decision as to which capabilities are linked to which learning area(s). To help support these decisions, this resource provides general advice on teaching and assessment, as well as specific illustrative advice related to Mathematics.
Why link learning in Mathematics to a capability?
The knowledge and skills learnt through the capabilities are highly transferable across learning areas and are applicable throughout schooling and in later life.
The capabilities support Mathematics in empowering individuals to become active and critical citizens and to make informed decisions and solve problems efficiently in a range of contexts.
Identifying a strong link between a capability and Mathematics supports learning in both curriculum areas. There is strong justification to link a learning area and a capability in instances where:
- knowledge and skills taught in a capability would deepen students’ understanding of particular knowledge and skills in the learning area
- the learning area would provide context, background knowledge and other skills for the development of the capability.
How do we find strong links between Mathematics and the capabilities?
Looking over each capabilities curriculum, we begin to see broad links between the strands in different capabilities and in aspects of various strands and sub-strands of the Mathematics curriculum.
Linking the Critical and Creative Thinking strands to Mathematics
Critical and Creative Thinking consists of three interrelated strands. The table below provides an overview of each strand and how it links to Mathematics.
Questions and Possibilities
Explore the nature of questioning and a range of processes and techniques to develop ideas
Mathematics and Critical and Creative Thinking mutually support students to …
develop their curiosity and pose effective questions as part of designing investigations
Reasoning
Explore how to compose, analyse and evaluate arguments and reasoning
Mathematics and Critical and Creative Thinking mutually support students to …
reason mathematically and understand underlying concepts such as deduction and inference
Meta-Cognition
Explore the use of strategies to understand, manage and reflect on thinking, problem-solving and learning processes
Mathematics and Critical and Creative Thinking mutually support students to …
manage their learning, thinking and problem-solving to design investigations and plan their approaches; select and apply strategies to seek solutions; and discuss their thinking
Linking the Ethical Capability strands to Mathematics
Ethical Capability consists of two interrelated strands. The table below provides an overview of each strand and how it links to Mathematics.
Understanding Concepts
Understanding and applying key concepts and ideas concerned with ethical issues, outcomes, principles and values
Mathematics and Ethical Capability mutually support students to …
identify, analyse and evaluate the application of mathematics to our lives
Decision Making and Actions
Understanding ways to respond to ethical problems and factors and challenges that influence ethical decision-making and action, and applying this understanding to different contexts
Mathematics and Ethical Capability mutually support students to …
respond to ethical issues, identifying, analysing and evaluating the role of and application of mathematics and ethical concepts to fair, informed and accurate discourse
Linking the Intercultural Capability strands to Mathematics
Intercultural Capability consists of two interrelated strands. The table below provides an overview of each strand and its broad links to Mathematics.
Cultural Practices
Describing, observing and analysing characteristics of their own cultural identities and those of others; and using critical reflection to better understand the perspectives and actions of individuals and groups in specific situations and how these can be shaped by culture
Mathematics and Intercultural Capability mutually support students to …
identify and understand the links between mathematics and some aspects of cultural expression; and deepen their understanding of how intercultural experiences contribute to the development of mathematics as a discipline
Cultural Diversity
Understanding the nature of cultural diversity and critically examining the concept of respect, challenges and opportunities created by cultural diversity and the way in which cultural diversity shapes and contributes to social cohesion
Mathematics and Intercultural Capability mutually support students to …
understand how mathematics contributes to the representation of cultural diversity and social cohesion; and to identify, analyse and evaluate the strengths and limitations of collecting and interpreting data related to cultural diversity and social cohesion
Linking the Personal and Social Capability strands to Mathematics
Personal and Social Capability consists of two interrelated strands. The table below provides an overview of each strand and its broad links to Mathematics.
Self-Awareness and Management
Develop the knowledge and skills to regulate, manage and monitor their emotions and interpret and assess their personal characteristics in the context of development of resilience
Mathematics and Personal and Social Capability mutually support students to …
develop knowledge and skills to work independently and show initiative
Social Awareness and Management
Learn to participate in positive, safe and respectful relationships; critique societal constructs and discrimination; and negotiate with others and work collaboratively
Mathematics and Personal and Social Capability mutually support students to …
develop skills for collaborative problem-solving and investigating
Asking the following questions can be a first step in identifying strong links:
- Which of the learning area content descriptions reflect concepts or other knowledge and skills in a capability?
- Would explicit teaching and learning related to the identified link support progress towards the achievement standards for the learning area and/or capability?
The example below identifies a link between two content descriptions in the Level 7 Mathematics sub-strand Statistics and Probability and a Levels 7 and 8 Ethical Capability content description. The identified link is between the choice of data, its currency, its integrity and the way it is displayed (Mathematics) and the role of context and experience in ethical decision-making and actions (Ethical Capability).
Once a strong link is identified, a learning activity can be designed that enables progression towards the appropriate Mathematics achievement standard as well as the appropriate capability achievement standard (again, see the example below). This may involve incorporation of other relevant content descriptions to create a sequence of learning.
Example: Linking two Level 7 Mathematics content descriptions and a Levels 7 and 8 Ethical Capability content description
This table includes selected content descriptions and an achievement standard extract for both Mathematics Level 7 and Ethical Capability Levels 7 and 8, plus linking notes and an activity idea.
| | Mathematics, Level 7 | Linking notes and activity idea | Ethical Capability, Levels 7 and 8 |
|---|
Content descriptions | Identify and investigate issues involving numerical data collected from primary and secondary sources
(VCMSP268) Construct and compare a range of data displays including stem-and-leaf plots and dot plots
(VCMSP269) | Can both Ethical Capability and Mathematics help us to understand the link between data and statistics and fair, informed and accurate discourse on ethical issues? Yes. Ethical Capability can help us understand how context influences identification and responses to ethical issues and Mathematics can help us understand how representation and interpretation of data and statistics can influence claims about context. Students use Mathematics and Ethical Capability to explore an ethical issue such as the uneven distribution of income and how interpretation of its context influences responses to the issue. They compare data displays in the media and other online sources with government-issued source documents and discuss how choice of data display influences thinking about context and the implications this might have for debates and decision-making and action. | Discuss the role of context and experience in ethical decision-making and actions
(VCECD018) |
Achievement
standard extract | Students identify issues involving the collection of discrete and continuous data from primary and secondary sources. | By the end of Level 8, students … analyse the role of context and experience in ethical decision-making and action. |
How do we assess the capabilities?
Student understanding of a capability’s knowledge and skills is assessed against the achievement standards of the capability. The key to formative and summative assessment is explicit teaching of the discrete knowledge and skills underpinning the capability’s content descriptions in such a way that students are supported to progress towards the targeted achievement standard. Explicit teaching builds shared understanding of concepts, which provides a foundation for setting transparent expectations of what should be shown in student work and for feedback.
For general advice on teaching and assessment and transfer of learning, see
General resources for the capabilities.
Examples of learning activities that link Mathematics and the capabilities
All examples are illustrative only and assume familiarity with the Mathematics curriculum.
Learning activity idea: Students undertake an investigation to compare masses of objects using balance scales. As part of their investigation, they develop a range of questions to guide the kind of objects that are selected and how they are compared.
This activity would strengthen learning in both Mathematics and Critical and Creative Thinking through increasing the range of questions posed by introducing different kinds of question stems and providing an opportunity to apply these to gather information (see Critical and Creative Thinking content description
VCCCTQ001).
Learning activity idea: Students use and develop efficient mental and written strategies to solve a range of problems. They compare strategies, such as commutativity, and doubling and halving for multiplication, and reflect on their choice of strategy and its effectiveness, including how strategies can be selected and applied when engaging with a challenging problem.
This activity would strengthen learning in Mathematics, Personal and Social Capability and Critical and Creative Thinking through deepening students’ understanding of how knowledge and application of strategies can support management of a mathematical challenge, including how to be persistent (see Personal and Social Capability content description
VCPSCSE018 and Critical and Creative Thinking content description
VCCCTM020)
Learning activity idea: As part of an investigation into transformation on simple and composite shapes, students research historical and current examples of different kinds of tessellations, including examples from different cultures. They reflect on why tessellations are a design feature on cultural objects across many cultures, including how all tessellations conform to a common set of mathematical rules, and they create tessellations with simple composite shapes.
This activity would strengthen learning in both Mathematics and Intercultural Capability through examining how aspects of our lives can be culturally influenced, how some aspects of mathematics are common across cultures, and how what we have in common can assist in reaching understanding between culturally diverse groups (see Intercultural Capability content description
VCICCD011).
Learning activity idea: As part of a sequence of lessons on extending and applying the laws and properties of arithmetic to algebraic terms and expressions, students are given examples of problems with solutions that have the right answer but contain errors in method. They are guided to recognise that this is common for mathematicians of all abilities when faced with challenging problems and to understand why it is important to have correct method. They identify the reasoning errors in a range of examples and are guided to reflect on how this can be positively transferred to their own learning.
This activity would strengthen learning in Mathematics, Personal and Social Capability and Critical and Creative Thinking through fostering a positive attitude to mathematical challenges, identifying and developing this as a personal strength; introducing common reasoning errors in mathematics and strategies to identify and resolve them; and building understanding of why coherent reasoning is important (see Personal and Social Capability content descriptions
VCPSCSE035 and
VCPSCSE037 and Critical and Creative Thinking content descriptions
VCCCTR035 and
VCCCTM041).
Learning activity idea: Students investigate how the identification of issues and questions for statistical investigation relate to the integrity of the work. They use case studies, such as the ‘Closing the Gap’ policy, which aims to improve the life outcomes of Aboriginal and Torres Strait Islander people, to examine why selection of targets is important and in particular how selection of targets has implications for associated measures and data. Students reflect on how considering associated measures and data, and what they may or may not indicate, when selecting targets can play a role in decision-making about an ethical issue.
This activity would strengthen learning in both Mathematics and Ethical Capability through introducing reasons why considering issues related to statistical targets and associated measures and data is a factor to be managed when responding to an ethical issue, and strategies for how it can be managed (see Ethical Capability content description
VCECD023).
For more resources to support the teaching of all four capabilities, see the individual capability resources webpages and
General resources for the capabilities
The following external links are for teacher reference purposes. They do not constitute VCAA endorsement of the views or materials contained on these sites.
Aligned Australian Curriculum Resources (Mathematics)
Australian Bureau of Statistics (ABS)
The ABS provides useful data sets for statistical investigations as well as pedagogical resources.
The
Australian Mathematics Trust (AMT) is a not-for-profit organisation which provides a range of competitions, teaching resources and professional learning opportunities in mathematics, computational thinking and algorithmics.
The Discovery series of problems is a free teacher resource for teachers covering themed problem sets for Year 3 – 10, with hints, solutions and videos of mathematicians and other presenters working through sample solutions.
The
Computational and Algorithmic Thinking (CAT) competition provides an introduction to algorithms without the need to understand programming, and the online version of this competition is currently free to schools.
Australian Taxation Office (ATO)
The Australian Taxation Office’s
Education Zone provides a range of resources aligned to the 7 - 10 mathematics curriculum that supports the implementation of content related to financial mathematics.
Tax Super and You is a free on-line teaching and learning resource of several modules with interactive elements that provide real-world mathematical contexts for the teaching and learning of financial literacy.
Code
A non-profit US organisation that provides a range of learning resources and free educational materials related to coding. These link to US Common Core Mathematics, which is similar to the Victorian Curriculum F–10 Mathematics.
Computer Science Unplugged (CS Unplugged)
A project of the Computer Science Education Research Group at the University of Canterbury, New Zealand. The project has developed a range of
free resources and activities
(note: large pdf download) that cover concepts, skills and processes involving computational thinking and algorithms independently of implementation by particular digital technology or programming language. Many of the examples, problems and activities used are mathematical in nature and relate closely to the Victorian Curriculum Mathematics, in particular, the primary years.
FUSE is a Department of Education and Training (DET) website which provides access to digital resources that support the implementation of the Victorian Curriculum F – 10. This includes an extensive range of activities and other resources for
primary mathematics and
secondary mathematics.
International Mathematical Modelling Challenge (IMMC)
A free team-based competition developed to support the real-world application of learning, build proficiency, encourage collaboration, and challenge students. It provides a range of teaching and learning resources and professional learning in mathematical modelling, including the
Teacher and student guide to mathematical modelling.
MathWorld
A free on-line digital mathematics encyclopaedia resource by Wolfram Research and is linked to the free on-line computational engine
WolframAlpha. Together these provide teachers and students with access to mathematical knowledge and examples through online queries in natural language, and also a means of carrying out related numerical, graphical, statistical and symbolic computations.
MoneySmart Teaching resource
F–10 teachers are encouraged to access MoneySmart Teaching, an initiative funded by the Australian Securities and Investment Commission (ASIC). MoneySmart Teaching has developed a range of teaching resources designed to help children and young people improve their levels of consumer and financial literacy.
National Library of Virtual Manipulatives (NLVM)
The University of Utah’s NLVM collection of digital resources provides learning activities corresponding to a broad range of mathematical topics.
NRICH enriching mathematics
This University of Cambridge project provides a range of teacher and students resources.
reSolve: Mathematics by Inquiry
Is the flagship mathematics education program from the Australian Academy of Science. reSolve provides teachers with free access to a suite of high-quality teaching and learning resources
The program has developed a set of free F–10
resources for Australian schools, teachers and students that are designed to support mathematics learning in engaging and innovative ways.
The Australian Mathematical Sciences Institute (AMSI)
A collaborative non-profit organisation representing mathematical interests in Australia. It supports mathematics educators and teachers through various activities and includes
a collection of online modules designed to support teachers further develop their mathematical background in selected topics.
One of its resources is
Mathematics of Planet Earth, a source of classroom materials that use mathematics and statistics to understand the challenges facing the world in fun and accessible ways, whilst providing teachers with related support materials, links and contacts.
Wolfram Demonstrations Project and
Computational Thinking Initiative
Wolfram Demonstrations Project provides a range of free interactive demonstrations of various topics across the school mathematics curriculum.
The Computational Thinking Initiative includes a range of cloud-based sample activity lesson plans.
Wolfram
A resource provided by the Victorian Department of Education to support the implementation of STEM in the curriculum.
It includes discussion forums for the STEM areas, including mathematics, and resources for the use of Mathematica, Wolfram Alpha and System Modeller as tools to support teaching and learning in and across these areas of the curriculum.
Mathematics teaching and learning references
The following references provide overviews of student mathematical development and related aspects of curriculum, pedagogy and assessment for the primary and/or secondary years.
Booker G, Bond D, Sparrow L, and Swan P (2010).
Teaching Primary Mathematics
4th edition. Sydney: Pearson.
Goos M, Stillman G and Vale C (2008).
Teaching Secondary School Mathematics – Research and practice for the 21st century. Sydney: Allen & Unwin.
Hattie J, Fisher B, Frey N, Gojak L, Delano Moore S and Mellman W. (2016).
Visible Learning for Mathematics: Grades K-12: What Works Best to Optimize Student Learning. London: Corwin.
Hine G, Reaburn R, Anderson J, Galligan L, Carmichael C, Cavanagh M, Ngu B and White B. (2016).Teaching Secondary Mathematics. Melbourne: Cambridge.
Hunting R, Mousley, J and Perry, B. (2012).Young Children Learning Mathematics. Melbourne: ACER Press.
Johnston T. (2016).
Becoming the Math Teacher You Wish You'd Had: Ideas and Strategies from Vibrant Classrooms. York: Stenhouse.
MCEETYA (2006).
Statements of Learning for Mathematics. Carlton: Curriculum Corporation.
Prochazka, H. (2014).
The Mathematics Book … anyone can do it!. Trevallyn: Zenolith
Serow P, Callingham R and Muir T. (2016).Primary Mathematics : Capitalising on ICT for today and tomorrow. Melbourne: Cambridge.
Siemon D, Beswick K, Brady K, Clark J, Faragher R and Warren, E. (2015).
Teaching Mathematics: Foundation to Middle Years 2nd edition. South Melbourne: Oxford University Press.
Skemp R. (1989).
Structured Activities for Primary 1 and 2. London: Routledge.
Van De Walle J A, Karp K S and Bay Williams, J M. (2010).
Elementary & Middle School Mathematics - Teaching Developmentally 7th edition. Boston: Pearson.
Third party (commercial) digital resources
There are a range of third-party (commercial) digital resources that schools may choose to use as part of their suite of teaching and learning materials. Schools and teachers will need to develop and apply their own criteria and processes for trialling and evaluating the suitability of such resources for their contexts.
To assist schools and teachers, the VCAA has reviewed several resources with respect to the following broad criteria:
- the resource covers four or more consecutive years of learning
- the resource maps to the Victorian Curriculum: Mathematics and cover all three mathematics strands
- the resource supports teachers to identify additional learning needs and appropriate intervention/s after a teaching and learning sequence has taken place and diagnostic data obtained
- the resource provides digital (and possibly other) materials to support targeted teaching/learning for individuals, small groups and larger groups of students
- the resource provides diagnostic tools and/or analytics to help monitor and evaluate student progress and achievement.
See
information about third party resources which meet the above criteria.