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NSW Syllabuses

Learning across the curriculum

Learning across the curriculum content, including the cross-curriculum priorities and general capabilities, assists students to achieve the broad learning outcomes defined in the Board of Studies K–10 Curriculum Framework and Statement of Equity Principles, and in the Melbourne Declaration on Educational Goals for Young Australians (December 2008).

Cross-curriculum priorities enable students to develop understanding about and address the contemporary issues they face.

The cross-curriculum priorities are:

  • Aboriginal and Torres Strait Islander histories and cultures Aboriginal and Torres Strait Islander histories and cultures
  • Asia and Australia's engagement with Asia Asia and Australia's engagement with Asia
  • Sustainability Sustainability

General capabilities encompass the knowledge, skills, attitudes and behaviours to assist students to live and work successfully in the 21st century.

The general capabilities are:

  • Critical and creative thinking Critical and creative thinking
  • Ethical understanding Ethical understanding
  • Information and communication technology capability Information and communication technology capability
  • Intercultural understanding Intercultural understanding
  • Literacy Literacy
  • Numeracy Numeracy
  • Personal and social capability Personal and social capability

The Board's syllabuses include other areas identified as important learning for all students:

  • Civics and citizenship Civics and citizenship
  • Difference and diversity Difference and diversity
  • Work and enterprise Work and enterprise

Learning across the curriculum content is incorporated, and identified by icons, in the content of the Mathematics K–10 Syllabus in the following ways:

Aboriginal and Torres Strait Islander histories and cultures Aboriginal and Torres Strait Islander histories and cultures

Aboriginal and Torres Strait Islander peoples have a unique sense of identity, which can be demonstrated through the interconnected aspects of Country and Place, People, and Culture.

Mathematics is a representation of the world that has developed over thousands of years through many diverse cultural contexts. Aboriginal and Torres Strait Islander cultures have a rich understanding of mathematics that includes a broad range of applications of mathematical concepts.

The NSW K–10 Mathematics curriculum values Aboriginal and Torres Strait Islander perspectives of mathematics and provides opportunities for students to investigate various aspects of number, measurement and geometry, including time and location and relevant interrelationships, in Aboriginal and Torres Strait Islander contexts. Students can deepen and extend their understanding of the lives of Aboriginal and Torres Strait Islander peoples through the application and evaluation of statistical data.

Asia and Australia's engagement with Asia Asia and Australia's engagement with Asia

The Asia and Australia's engagement with Asia priority provides a regional context for learning in all areas of the curriculum. An understanding of Asia underpins the capacity of Australian students to be active and informed citizens working together to build harmonious local, regional and global communities, and build Australia's social, intellectual and creative capital. This priority is concerned with Asia literacy for all Australian students. Asia literacy develops knowledge, skills and understanding about the histories, geographies, cultures, arts, literatures and languages of the diverse countries of our region. It fosters social inclusion in the Australian community and enables students to communicate and engage with the peoples of Asia so that the students can live, work and learn effectively in the region.

In their study of the NSW K–10 Mathematics curriculum, students investigate the concept of chance using Asian games and can explore the way Asian societies apply other mathematical concepts, such as patterns and symmetry in art and architecture. Investigations involving data collection and representation can be used to examine issues pertinent to the Asia region.

Sustainability Sustainability

Sustainability is concerned with the ongoing capacity of Earth to maintain all life. Sustainable patterns of living meet the needs of the present without compromising the ability of future generations to meet their needs. Education for sustainability develops the knowledge, skills, understanding, values and attitudes necessary for people to act in ways that contribute to more sustainable patterns of living.

Mathematics provides a foundation for the exploration of issues of sustainability. It equips students with, for example, the skills to investigate data, to evaluate and communicate findings, and to make predictions based on those findings. They can measure and evaluate sustainability changes over time and develop a deeper appreciation of the world around them through such aspects of mathematics as patterning, three-dimensional space, symmetry and tessellations. Mathematical knowledge, skills and understanding are necessary to monitor and quantify both the impact of human activity on ecosystems and changes to conditions in the biosphere.

The NSW K–10 Mathematics curriculum provides students with knowledge, skills and understanding to observe, record, organise and analyse data, and to engage in investigations regarding sustainability. The curriculum supports students in early stages to build connections with the natural world and their local community. In later stages, students can use probability concepts, mathematical and computer modelling, chance and probability, multiple data sets and statistical analysis to understand more complex concepts relevant to sustainability.

Critical and creative thinking Critical and creative thinking

Critical and creative thinking are key to the development of mathematical understanding. Students use critical and creative thinking as they learn to generate and evaluate knowledge, ideas and possibilities, and when seeking new pathways or solutions. Mathematical reasoning and logical thought are fundamental elements of critical and creative thinking. They are integral to mathematical problem solving as students identify similarities and differences in mathematical situations and engage in reasoning and thinking about solutions to problems, and the strategies needed to find those solutions.

In their study of mathematics in K–10, students use critical and creative thinking in such activities as exploring properties of shapes, setting up statistical investigations, comparing actual to expected results, approximating and estimating, interpreting data displays, examining misleading data, and interpolating and extrapolating. Critical and creative thinking are also of fundamental importance in such aspects of the Mathematics curriculum as posing problems, modelling situations, justifying choices and strategies used, and giving reasons to explain mathematical ideas.

Ethical understanding Ethical understanding

Students develop ethical understanding as they learn about, and learn to act in accordance with, ethical principles, values, integrity and regard for others. There are various opportunities in the NSW K–10 Mathematics curriculum for students to develop and apply ethical understanding when, for example, collecting and displaying data, interpreting misleading graphs and displays, examining selective use of data by individuals and organisations, and detecting and eliminating bias in the reporting of information.

Information and communication technology capability Information and communication technology capability

Information and communication technology (ICT) includes digital technologies such as calculators, spreadsheets, dynamic geometry software, and computer algebra and graphing software. Students use ICT effectively and appropriately when investigating, creating and communicating ideas and information, including in representing mathematics in a variety of ways to aid understanding. ICT can be used by students to solve problems and to perform previously onerous tasks more readily.

In the Number and Algebra strand in the NSW K–10 Mathematics curriculum, students can use ICT in such topic areas as creating patterns, creating and interpreting graphs, investigating compound interest, and solving equations graphically. In the Measurement and Geometry strand of the curriculum, students can utilise ICT in such areas as exploring properties of angles and shapes, including symmetry; creating designs that involve shapes and transformations; representing, visualising and manipulating three-dimensional objects; investigating congruency and similarity; representing position and paths; making informal measures of length and area; and developing formulas for perimeter and area. In the Statistics and Probability strand, students can use ICT in such areas as recording and displaying data in various forms, comparing data sets, calculating measures of location and spread, modelling probability experiments, and using the internet to gather and analyse data presented by the media.

Intercultural understanding Intercultural understanding

Students develop intercultural understanding as they learn to understand themselves in relation to others. This involves students valuing their own cultures and beliefs and those of others, and engaging with people of diverse cultures in ways that recognise commonalities and differences, create connections, and cultivate respect.

Intercultural understanding can be enhanced if students are exposed to a range of cultural traditions in mathematics. It may be demonstrated, for example, through examining Aboriginal and Torres Strait Islander peoples' perceptions of time and weather patterns, and the networks embedded in family relationships, as well as in such activities as examining patterns in art and design, learning about culturally specific calendar days, comparing currencies, and showing awareness of cultural sensitivities when collecting data.

Literacy Literacy

Students become literate as they develop the skills to learn and communicate confidently. These skills include listening, reading and viewing, writing, speaking and creating print, visual and digital materials accurately and purposefully within and across all learning areas.

Literacy is an important aspect of mathematics. Students need to understand written problems and instructions, including the use of common words with a specific meaning in a mathematical context and metaphorical language used to express mathematics concepts and processes.

In their K–10 mathematics learning, students are provided with opportunities to learn mathematical vocabulary and the conventions for communicating mathematics in written form, including through its symbols and structures, as well as verbally through description and explanation. Mathematical literacy also extends to interpreting information from mathematical texts such as tables, graphs and other representations.

Numeracy Numeracy

Numeracy is embedded throughout the Mathematics K–10 Syllabus. It relates to a high proportion of the content across K–10. Consequently, this particular general capability is not tagged in the syllabus.

Numeracy involves drawing on knowledge of particular contexts and circumstances in deciding when to use mathematics, choosing the mathematics to use, and critically evaluating its use. To be numerate is to use mathematics effectively to meet the general demands of life at home, in work, and for participation in community and civic life. Students become numerate as they develop the capacity to recognise and understand the role of mathematics in the world around them and the confidence, willingness and ability to apply mathematics to their lives in constructive and meaningful ways. Highly numerate students interpret, apply and critically evaluate mathematical strategies, and communicate mathematical reasoning in a range of practical situations.

Numeracy is relevant and important across the range of learning areas in K–10, in further education, and in everyday life. Mathematics makes a special contribution to the development of numeracy in a manner that is more explicit and foregrounded than is the case in other learning areas. It is important that the Mathematics curriculum provides the opportunity to apply mathematical skills and understanding in context, both in other learning areas and in real-world contexts. The NSW K–10 Mathematics curriculum provides students with opportunities to use numerical, spatial, graphical, statistical and algebraic concepts and skills in a variety of contexts and involves the critical evaluation, interpretation, application and communication of mathematical information in a range of practical situations.

The key role that teachers of mathematics play in the development of numeracy includes teaching students specific skills and providing them with opportunities to select, use, evaluate and communicate mathematical ideas in a range of situations. Students' numeracy and underlying mathematical understanding will be enhanced through engagement with a variety of applications of mathematics to real-world situations and problems in other learning areas.

Personal and social capability Personal and social capability

Students develop personal and social competence as they learn to understand and manage themselves, their relationships and their lives more effectively. This includes establishing positive relationships, making responsible decisions, working effectively in teams, and handling challenging situations constructively.

The elements of personal and social competence relevant to mathematics include the application of mathematical skills for personal purposes, such as giving and following directions, visualisation and mapping skills, interpreting timetables and calendars, calculating with money and the Goods and Services Tax (GST), budgeting, using price comparison websites, evaluating discount offers, investigating payment on terms, and conducting statistical investigations in teams.

Work and enterprise Work and enterprise

Students develop work-related knowledge, skills and understanding through a variety of experiences. These experiences may include constructing budgets, calculating wage and salary earnings, investigating and determining leave loadings, using deductions and 'pay-as-you-go' (PAYG) instalments to calculate a tax liability or refund, and investigating tax rebates and levies. Students perform calculations involving discounts, and profit and loss, and use statistics to predict future earnings, monitor inventories, and analyse and interpret information gained from surveys.