cambridge curr

8/6/2019 Cambridge Curr

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Introduction

Curriculum is at the heart of education.

The Curriculum Framework for Kindergarten to Year 12 Education in Western Australia aims toimprove the learning outcomes of all students and to enable schools to develop learning and teachingprograms which meet the needs of their students and which respond to changes in society.

The great majority of students will spend fourteen years of their lives in schooling. It is important thatduring this time they develop the tools to deal effectively with the opportunities and challenges whichthey encounter, both now, as young people, and in the future, as adults. Our society is characterised byrapid technological development, increasing cultural diversity and changing family and institutionalstructures. Changes in the nature of work, the growing interdependence of world communities, globalenvironmental issues and social, political and economic conditions will continue to pose challenges andoffer opportunities throughout the twenty-first century.

The Curriculum Framework reflects contemporary thinking about what students need to learn in orderto lead successful and rewarding lives in the twenty-first century and how schools and teachers can besthelp them to learn. It provides teachers, parents, employers, those responsible for post-schooleducation and the community with a clear statement of what students are expected to achieve as aresult of their kindergarten to year 12 education.

The Framework helps teachers to develop specific programs and judge the effectiveness of theirteaching by the outcomes students achieve. It provides a basis for schools to review their performanceand plan for improvement. It is used by those responsible for the education of mature-aged studentsreturning to education or students not in formal school situations. It forms the basis of supportdocuments and resources and of professional development for teachers.

Key f ea tur es of th e Curriculum Fr am ew ork

The Curriculum Framework has two key features which make it different from previous syllabusdocuments: its focus on outcomes and its Kindergarten to year 12 approach.

Th e focus on outcomesAn outcomes approach means identifying what students should achieve and focusing on ensuring thatthey do achieve. It means shifting away from an emphasis on what is to be taught and how and when, toan emphasis on what is actually learnt by each student.

Some schools in Western Australia have been moving towards an outcomes approach for some time.The implementation of the Curriculum Framework will advance the process for all schools.

The Framework sets out a series of outcomes agreed to be essential for all students to achieve. Theseoutcomes describe what students should know, understand, value and be able to do as a result of theircurriculum experiences. Students achieve the outcomes at increasing levels of complexity as theyprogress through their schooling.


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The agreed outcomes form a common core of achievement. The outcomes-focused approach willprovide schools with more flexibility to enable teachers to develop different learning and teachingprograms to help their particular students achieve the outcomes. Schools will respond to their ownethos or that of their system, the needs of their community and the situations of their students bypursuing the common outcomes and by developing additional outcomes that match the specific needsof the students.

The outcomes provide clarity of focus for students, parents, teachers and the general community andare an effective basis for monitoring and reporting to parents and others.

Th e K-12 approac h

Another important feature of the Framework is its kindergarten to year 12 approach. While particularstages of schooling make unique contributions and may require different approaches, the K-12 approachadopted by the Framework provides a picture of the total span of students schooling. It encourages adevelopmental and integrated approach to curriculum planning, teaching and learning. It enablesstudents to progress smoothly through their education and avoids the major disjunctions betweenstages of schooling evident in some previous approaches to curriculum. It provides the basis forcontinuity and consistency in students education.

T he structur e of th e Curriculum Fr a m ew ork

The Curriculum Framework consists of this Overarching Statement and eight LearningArea Statements.

Th e Overarc h ing Statement This Overarching Statement outlines seven key principles which underpin the Curriculum Frameworkand describes the Overarching learning outcomes to which all learning areas contribute. It describes

learning and assessment strategies that are consistent with the Curriculum Framework and whichpromote achievement of the outcomes.

Particular attention is given to the importance of maintaining a holistic view of curriculum, theresponsibility of curriculum as a whole for such vital skills as literacy, numeracy and social cooperation,and the need to integrate knowledge, skills and values across all learning areas. The fundamental role of curriculum in the promotion of students enjoyment of learning andexcellence in learning is alsoemphasised. This statement provides a guide for whole-school planning and review.

Th e Learning Area Statements

Learning areas individually and collectively contribute to the achievement of the Overarching learningoutcomes. Learning Area Statements are provided for The Arts; English; Health and Physical Education;Languages Other Than English; Mathematics; Science; Society and Environment; and Technology andEnterprise. These areas are a useful way of categorising the knowledge, skills and values essential for theeducation of students in Western Australia. They provide a structure for defining learning outcomes, forproviding breadth and balance in students education and for ensuring attention is given to specificdisciplines.


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The learning areas are consistent with those endorsed by the Australian Education Council as the basisfor curriculum development in Australian schools and which almost allAustralian States and Territoriesuse. Adoption of these eight learning areas for the Curriculum Framework is in the interests of studentswho move between jurisdictions and reflects a spirit of cooperation among educators from all AustralianStates and Territories.

P rincipl es of th e Curriculum Fr a m ew ork

The Curriculum Framework for WesternAustralian schools is underpinned by seven key principles.These principles guide schools in whole-school planning and curriculum development.

1. An encompassing view of curriculum

Curriculum is much more than a syllabus.A syllabus normally outlines the content to be taught.Curriculum on the other hand is dynamic and includes all the learning experiences provided forthe student. It encompasses the learning environment, teaching methods, the resourcesprovided for learning, the systems of assessment, the school ethos and the ways in whichstudents and staff behave towards one another. All of these provide experiences from whichstudents learn. Together, they add meaning, purpose and enjoyment to students lives.Particular attention is required to ensure that there is congruence between the variousdimensions of curriculum.

2. An explicit acknowledgment of core values

P e opl e s va lues influ enc e th e ir b e ha viour a nd giv e m ea ning and purpo se to th e ir liv es. Whil e th e re is a ra ng e of v a lue po sition s in our plur a listic soci e t y, th e re is a lso a cor e of sha re dva lues. The Curriculum Fr a m ew ork i s und e rpinn ed b y th ese sha red v a lues, which c an b e

summ a rise d as follo ws:

o a commitm e nt to th e pur suit of kno wledg e and a chie ve m e nt of pot e nti a l, res ulting ina di spo sition to wa rd s striving to und e rst and th e world and ho w b es t on e ca n m ake a contribution to it , a nd th e pur suit of ex ce llenc e in a ll fie ld s of ex p e rie nc e a ndend ea vour;

o se lf a cce pt anc e a nd r es pe ct of se lf , res ulting in attitud es and action s which d eve lopea ch p e rson suniqu e pot e nti a l - ph ysica l, e motion a l, aes th e tic , spiritu a l, int e llectu a l, mor a l a nd soci a l;

o res p ect a nd conc e rn for oth e rs a nd th e ir right s, res ulting in se nsitivit y to and conc e rnfor th e we ll-b e ing of oth e rs, res p ect for oth e rs a nd a sea rch for con structiv e ways of

m a na ging conflict;o soci a l and civic r es pon sibilit y, res ulting in a commitm ent to ex ploring a nd promoting

th e common good; m ee ting individu a l n ee d s in ways which do not infring e th e right s of oth e rs; p a rticip a ting in d e mocr a tic proc esses ; soci a l ju stic e a nd cultur a l div e rsity;and

o environm e nt a l res pon sibilit y, res ulting in a res pe ct a nd conc e rn for th e na tur a l andcultur a l environm e nt s a nd a commitm e nt to r ege ne ra tiv e a nd su st a inabl e res ourc e


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Ove ra rching L ea rning Outcom es

The development of knowledge, skills and values is a lifelong process, and occurs in many places besidesschool. This section of the Overarching Statement describes the outcomes which all students need toattain in order to become lifelong learners, achieve their potential in their personal and working livesand play an active part in civicand economic life. These outcomes apply across all learning areas and arethe responsibility of all teachers. The outcomes for each learning area contribute to the achievement of the Overarching learning outcomes, and each learning area statement includes a description of the linksbetween the learning area outcomes and the overarching learning outcomes. The statement of eachoutcome is accompanied by a more detailed description of that outcome. Each description includes anumber of examples of the ways in which students might demonstrate progress towards the outcome atdifferent stages in their schooling from kindergarten to year 12.

1. Students use language to understand, develop and communicate ideas and information andinteract with others.

Students read, view, listen, speak and write with an awareness of and responsiveness todifferent cultural conventions and interpretations. They understand the ways in which languageis structured and use language effectively to deal with everyday situations. Their command of language includes an ability to use StandardAustralian English appropriately. This ability is builtupon and in addition to their home languages and dialects. They use language as a means of learning across the curriculum and are aware of the special ways language is used in each of thelearning areas. Students know the specialist vocabulary for particular disciplines, the typical texttypes used in a subject area and the conventions of these text types. They understand and usevisual images and symbolic forms, such as numbers, musical notation, diagrams, graphs andtabular information: for example, students may ask directions from someone; contributeappropriately to a discussion; describe an experience using Auslan (sign language); explain a

mathematics operation to another student; prepare a chart which explains a scientificphenomenon; write a set of directions for using a machine; write a letter requesting informationfrom an organisation; explain why people vary their language in different social situations;critically analysethe language in a newspaper article; or present the findings of a project on theInternet and call for comment.

2. Students select, integrate and apply numerical and spatial concepts and techniques.

Students deal easily with everyday situations which require the use of quantitative and spatialconcepts and skills. These may involve such tasks as mentally calculating the discount for a saleitem, reading an article on best buys for computers, adjusting and measuring the ingredients fora recipe, making and laying out a shirt pattern, interpreting a scale drawing or weather map, orcalculating the likelihood of success in a game. In doing so, they ask and answer questions aboutsuch things as the cheapest, best, biggest, quickest or most likely. Students also draw on theirquantitative and spatial knowledge to understand new information and situations, solveproblems not previously encountered, and judge the reasonableness of particular uses of mathematics: for example, they may use their knowledge to assist them to plan a new gardenbed; choreograph a dance; calculate the travelling time to a destination; understand a neweconomics concept; design an unusual cupboard; work out how to calculate monetary exchange


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rates for the first time; or question a claim in the media about the costs and benefits of highereducation.

3. Students recognise when and what information is needed, locate and obtain it from a range of sources and evaluate, use and share it with others.

Students frame and clarify questions, collect information, organise it and represent it in wayssuited both to the type of information and to their purposes. They analyse and interpretinformation, judge its quality and decide what conclusions or inferences might reasonably bedrawn, taking into account the element of chance involved in its collection: for example,students may find out a fact about an animal; search the Internet for information on the effectof a recent volcanic eruption on weather patterns; integrate information from several brochuresto plan a trip; reorganise data about favourite foods to answer new questions; investigateimmunisation practices in Australia and prepare a poster to communicate conclusions to peers;produce statistics and graphs to compare responses of students and parents to a survey on theage of transition to secondary school; review the evidence in a foreign newspaper article on theimpact of industry on the environment; or use the Internet to work with and share informationwith students in other schools.

4. Students select, use and adapt technologies.

Students have the motivation and confidence to develop and use technological solutions tomeet needs. They apply or operate a specific technology and choose between or integratevarious technologies for a purpose. They adapt familiar or existing technologies to meet thedemands of new tasks or situations. As confident and capable users of a wide range of technological applications and processes, they critically appreciate the consequences of

technological innovation. They have the skills to acquire and evaluate information in order totake ethical advantage of technological change: for example, students may use a conceptcomputer keyboard; word-process a document; design and make a stage lighting system; makean ethical judgement about the school s choice of using scheme or bore water; use a computerpackage to understand a science idea; make a skateboard ramp; produce a multimediapresentation; or use a range of communication technologies to establish relationships withothers outside the school.

5. Students describe and reason about patterns, structures and relationships in order tounderstand, interpret, justify and make predictions.

One of the main ways in which wemake sense of the world is by observing similarities andconnections between objects and events and making generalisations about them. xStudentsrecognise, describe, explain and project patterns in a wide range of phenomena. They alsoclassify things, recognising, developing and using structures and forms. They reason logicallyabout these regularities, making predictions and drawing conclusions: for example, the patternsand structures they explain and use may include spelling rules and their exceptions; therelationship between seasonal vegetation and survival in the outback; classifications of foodtypes; metrical form in poetry and rhythms in music; a network representing kinship; the effect


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of doubling linear dimensions on the surface area and volume of things; the relationshipbetween exercise, diet and health; or the relationship between molecular structure and theproperties of substances.

6. Students visualise consequences, think laterally, recognise opportunity and potential and areprepared to test options.

In approaching issues and problems, students think laterally, offer possibilities, explore andevaluate new ideas, and generate a range of positions and solutions. They are often stimulatedby curiosity and see opportunity and potential in developing and extending ideas, includingthose based on intuition, insight or speculation. They investigate alternatives, visualiseconsequences and implications and are willing tochange direction when necessary: for example,students may apply their language knowledge in unfamiliar contexts; collaborate to solve amathematical problem in an unorthodox way; identify alternative solutions to a localenvironmental problem; visualise their future beyond school and explore work opportunities;experiment with the ingredients in a recipe; or develop and market their own products, such asnovelties for festivals or celebrations.

7. Students understand and appreciate the physical, biological and technological world and havethe knowledge, skills and values to make decisions in relation to it.

Students have the confidence, knowledge and skills to satisfy questions about the workings of the physical, biological and technological world and recognise thatcultural preconceptionsinfluence their understanding. They are able and willing toparticipate in community debate anddecision making and can make informed decisions about sustainable development and itsimpact on people and the environment. They show concern for the environment , understandthe consequences of choices in using natural resources and the environment, and have theknowledge and skills to look after both. Students understand that the connection of Aboriginal

people to the environment is profoundly significant to their identity and well-being. They devisesolutions to problems arising from their own needs and have methods for testing the validity of their observations and assumptions in relation to the natural and built worlds: for example,students may pose questions about the habitat of an animal; experiment with mixing colours tofind out what happens with various combinations; investigate the causes of water salinity;recognise the consequence of reducing wetlands in the urban environment; investigate housingdesigns which minimise energy use; or use landscapes for inspiration in the arts.

8. Students understand their cultural, geographic and historical contexts and have the knowledge,skills and values necessary for active participation in life inAustralia.

Students use historical, geographical, political, sociological and economic knowledge to analyseand understand local, national and international events. They participate actively andresponsibly in democratic processes within the school and wider community. They understandand value the cultural experiences and contributions of Aboriginal people. They understand andvalue differing world views and perspectives and the contributions that various cultural andreligious groups make to life inAustralia: for example, students may explore the diverse culturalbackgrounds of fellow students; recognise that the land has different meanings and uses fordifferent groups; explain the different roles of State and Federal governments; recognise theimpact of a technology on social relationships; research the historical experiences of Aboriginal


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activity, social activity and study; play a team sport with skill and confidence; discuss theinfluence of the media on health decisions; work to improve communication in a relationship; orexplore issues of personal meaning.

12. Students are self-motivated and confident in their approach to learning and are able to workindividually and collaboratively.

Students plan, reflect on and direct their own learning. When needed, they seek help fromadults, peers, print resources and technology. They have available a range of strategies to helpthem get started, work through, persist with and learn from problems independently. They alsorecognise when collaboration will enhance their work. They work well with others andcontribute in various ways, sometimes leading and sometimes following, accepting, sharing,integrating or adapting ideas from others and building on various positions flexibly andresponsively: for example, students may prepare their own work plan for completing a project;cooperate in small groups to make a construction from blocks; conduct a class meeting; play in ateam; undertake cycles of problem posing, conjecture and justification to investigate amathematical situation; help produce a newsletter or play; negotiate with potential clientsregarding a design; work with community members on a local issue; or use the Internet to workcollaboratively on a project with students in another school

13. Student recognise that everyone has the right to feel valued and be safe, and, in this regard,understand their rights and obligations and behave responsibly.

Students respect the rights of others to equal access to resources and to a work and leisureenvironment which is non-threatening and free from harassment such as teasing, sarcasm orremarks that stereotype or denigrate others or their efforts. They understand the rights and

responsibilities associated with living in a democratic society. Theycooperate with their peersand try to understand those whose backgrounds, experiences or values differ from their own.They show by their actions that they recognise and appreciate differences between people.They are aware of the impact of their behaviour on others, take responsibility for their ownactions, and reflect on the effects of their actions in order to learn from their experiences. Theyrecognise a collective obligation to assist others to be respected and safe and accept that theymust take some personal responsibility for their own emotional and physical safety. Studentsare aware of and understand the need for policies and laws which provide redress for, andsanctions against, certain forms of unacceptable behaviour: for example, students may showconcern for the welfare of other students; explain the reasons for a classroom rule; sharelimited resources; welcome new students to the school; work cooperatively with a wide range of other students; or show respect for the feelings of others.

T he S cop e of th e Curriculum

TH E LEARN I NG AREAS

In The Arts students develop creative skills, critical appreciation and knowledge of artistic techniquesand technologies in dance, drama, media, music, visual arts and combinations of arts forms. TheArts


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develop students sense of personal and cultural identity and equips them for lifelong involvement inthe appreciation of the arts.

In English, students learn about the English language and how to use it effectively. The study of Englishplays a vital role in the development of literacy, enhances students learning in all areas of thecurriculum and provides them with the communication skills and critical understanding of languagenecessary for active participation in society.

Health and Physical Educationdevelops an understanding of health issues and the skills needed forconfident participation in sport and recreational activities. It enables students to make responsibledecisionsabout health and physical activity and to promote their own and others health and well-being.

In Languages Other Than English, students communicate effectively in languages other than English andfurther develop their skills and understandings in English. They gain an understanding of other societies,the ability to interact with people and cultures other than their own , and practical skills which they canuse in future social, cultural and vocational areas.

In Mathematics, students use ideas about number, space and chance, and mathematical ways of representing patterns and relationships, to describe, interpret and reason about their social and physicalworld. Mathematics plays a key role in the development of students numeracy and assists learningacross the curriculum.

In Science, students investigate, understand and describe the physical, biological and technologicalworld and value the systems and processes that support life on our planet. Science helps students tobecome critical thinkers who use evidence to construct conclusions.

Society and Environment, develops students understanding of how individuals and groups live togetherand interact with their environment. Students develop a respect for cultural heritage and a commitment

to social justice, democratic processand ecological sustainability.

In Technology and Enterprise, students apply knowledge, skills and resourcesin the development of practical solutions to problems. Through this process they learn to be innovative, adaptable andreflective as they select and use appropriate materials, information and systems to achieve worthwhileresults.

T he lea rning a reas and th e ov e ra rching l ea rning outcom es

All of the overarching learning outcomes are seen as the province of all learning areas: for example,while the Technology and Enterprise learning area could be considered to contribute in a major way to

the outcome Students select, use and adapt technologies , all learning areas in some way contributetowards the achievement of this outcome.

Different learning areas contribute to the overarching learning outcomes in different ways. Eachestablishes outcomes specific to that area and shows how these link to the overarching learningoutcomes. Schools will use the Learning Area Statements as guides to the construction of acomprehensive, broad and balanced curriculum, rather than using them to divide up the curriculum,create artificial boundaries or fragment the curriculum.


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Children achieve the outcomes when their learning experiences enable them, through play andexperimentation, to observe, manipulate and explore objects, materials, technologies, physicalmovement and other phenomena. They need frequent opportunities to make, build, design and drawfor both utilitarian and creative purposes in both indoor and outdoor settings.

Children s exploration of their world includesreflection on behaviours, values, language and socialpractices as well as physical phenomena. They are encouraged to pose personally-meaningfulquestionsand to seek ways of answering such questions.

Young children need to discuss, describe, label, classify, communicate and represent their observationsand experiences in ways which are meaningful to them. They should have appropriate opportunities todevelop their control and understanding of the symbolic representations associated with writtenlanguage and mathematics. These skills help children to understand their world and to achievecompetence and personal satisfaction.

Experiences will typically integrate knowledge, understandings, skills, and values and attitudes acrosslearning areas.

As the child moves through this phase of development, the teacher continues to rely on closeobservation and responds to the child s emerging intellectual and social understandings.

MIDDLE CHILDHOOD(typically years 3 to 7)

As children grow, their sense of themselves and their world expands. They begin to see themselves asmembers of larger communities. They are interested in and like to speculate on other times, places and

societies. They begin to understand and appreciate different points of view, develop the ability to thinkin more abstract terms and undertake sustained activities for longer periods.

Students abilities towork collaboratively and to develop their social skills should be fostered byactivities which require group planning and decision making, and interaction with people inside andoutside their classroom. They should be given increased responsibility for managing and organisingactivities, individually and in groups of varying sizes.

As in the early years, activities will typically be integrated across learning areas.An investigation into theecosystem of a local park or bushland, for example, could provide an opportunity to achieve outcomesfrom a variety of learning areas.

In exploring their physical, social, cultural and technological world, students should be encouraged topose more focused questions and to carry out investigations in which they form predictions, hypothesesor conjectures, test them and reflect on their findings. The investigation of categories and patterns intheir world should become more refined and include relationships, structures, systems and processes.As in the early years, this will include exploration of behaviours, values, language and social practices aswell as physical phenomena.


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Increasingly students will be learning to draw on a wider range of sources of information in answeringquestions and consider phenomena more widely. This ability will be enhanced by introducing them toexperiences beyond their immediate environment including those of people from other times, placesand cultures, both directly and vicariously. These learning experiences should emphasise and lead to anappreciation of both the commonality and diversityof human experience and concerns.

Students explore a wider range of technologies and forms of communication and representation, andexperiment with them to investigate the advantages of different representational forms andtechnologies for different materials, purposes and situations. They develop a sound grasp of writtenlanguage and numeric conventions and use these in a range of different learning situations in purposefulways to achieve outcomes across all learning areas.

Students reflect on their learning and work practices and consider ways in which these might beimproved, modified or adapted for different situations. p

EARLYADOLESCENCE(typically years 7 to 10)

In early adolescence, students often align strongly with their peer groups and may begin to questionestablished conventions, practices and values. Their interests extend well beyond their owncommunities and they begin to develop concerns about wider issues. Students interest in the natural,social and technological world is often related to the impact on them personally and can help them intheir current and future lives. They also begin to develop an interest in particular fields of knowledge orendeavour for their own sake or for the personal satisfaction they provide.

Students growing independence and peer-group orientation is built upon by providing opportunities forthem to participate in important forms of decision making within the classroom and school and towork

with others. Through such experiences students assume increased responsibilities, develop decisionmaking skills, explore values and further refine their social and collaborative work skills.

Students continue their exploration of the physical, social and technological world and gain familiarityand confidence with the methods, conceptual frameworks and languages of particular disciplines. Theyshould begin to see these as ways of understanding the world and operating in it, by participating inreal-life applications.

Their induction to specific areas of learning builds on their earlier work in investigating patterns,processes and phenomena, and exploring forms of representation and technology. They understandthat particular ways of working and thinking have developed over time for particular reasons but may

still besubject to debate, revision and change.Students are encouraged to see the links between areas of learning and the interconnectedness of various fields of human endeavour. Activities or programs of study that allow them to achieve outcomesin a number of learning areas at the same time should continue to be provided. These can make asignificant contribution to learning and progress towards desired outcomes.


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Learning and teaching programs should assist students to develop a broader and more comprehensiveunderstanding of the contexts of their lives and the world in which they live. They should, for example,lead to an increased understanding of the complexity of the natural environment, society andtechnology; an awareness of the potential and problems of increased knowledge and technology; andan understanding of the relationship between knowledge, technology and values.

While enabling students to see themselves as the recipients of particular social, intellectual, linguistic,artistic and technological heritages, teaching and learning programs should encourage an open andquestioning view of them with students exploring other ways of thinking and world views and seeingthemselves as active participants in their own continuing development of and that of their society andthe world.

Learning experiences enable students to draw on increasingly diverse and complex sources of information that facilitate comparison, contrast, synthesis, questioning and critiquing of information.

LATEADOLESCENCE/EARLYADULTHOOD(typically years 10 to 12)

In this phase, students have a stronger sense of their own strengths, interests and goals. They play amajor role in determining the decisions that affect their lives and in shaping their learning experiences.They have a developing sense of themselves as active players who have some responsibility for thedirection of community life,and are often concerned about major social and environmental issues andthe ethical implications of human activity and knowledge.

Curricula and courses of study are influenced by the use of more formal assessment such as externalexaminations, the need for accreditation and certification, and the post-school aspirations of students.Increasingly students may achieve some of the desired learning outcomes in school, vocationaleducation and training or in the workplace.

Many students study particular fields in greater depth than others. As well as extending studentsknowledge and skills in their chosen areas in ways that meet their personal aspirations, learningprograms should emphasise the ways in which different forms of knowledge, endeavour andrepresentation are based on particular assumptions, values and world views, the nature of which isconditional, tentative or partial. Students investigate the implications for, and the applications of,knowledge and skills, focusing onethical issues and on how changing values and social mores can affecttheir learning.

Learning and teaching programs provide opportunity for students to demonstrate a high level of responsibility in the management of a wide range of tasks and in the management of their own learning.Learning experiences should enable students to plan and manage complex tasks, both individually and

collaboratively. Students should have the opportunity to show initiative, creativity and problem-solvingskills. This will be achieved by experiences that require them to consider, test and evaluate variousapproaches to achieving goals or solving problems.

Experiences should be provided which continue to develop high levels of language competence,including competence within the specialised language demands of particular fields of endeavour.Students should also have experience in using language in ways that enhance their abilities to interactsuccessfully with others in a wide range of situations, both formal and informal. Language is used for


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practical and aesthetic purposes and as a means of learning. Learning experiences should enablestudents to attain a high level of competence and confidence in the use of language for a range of complex and relatively sophisticated purposes.

Students should also have experiences which continue to develop their ability to seek, use and evaluateinformation for a range of complex purposes. They should be involved in tasks which require them toclarify goals and approaches in relation to the information they need, show initiative and perseverancein accessing appropriate information, compare and evaluate information and ideas from differentsources, and critically select and synthesise information in ways relevant to different purposes.

In all areas emphasis is placed on understanding conceptual frameworks and methods rather thanacquiring knowledge in isolation, as a means of developing transferable skills.

Lea rning , T ea ching & A ssess m e nt

This section describes the principles which should guide learning, teaching and assessment for studentsto achieve the outcomes in the Framework. The focus is on the provision of a school and classroomenvironment which is intellectually, socially and physically supportive of learning. These principles assistwhole-school planning and individual classroom practice. It will be essential, therefore, to ensure thatthere is a shared understanding of them within particular school communities and a collaborative effortto implement these principles in ways appropriate to individual schools.

LEARN I NG AND T EAC H I NG

The following principles about learning and teaching are based on what we value and our beliefs aboutthe learning environment schools should provide and contemporary research and professionalknowledge about how learning can be supported. As such, they should lead to school and classroompractices which are effective in helping students to achieve the outcomes in this Curriculum Framework.

y Opportunity to learn y Connection and challengey Action and reflection y Motivation and purpose y Inclusivity and difference y Independence and collaboration y Supportive environment

ASSESSM EN T

A primary purpose of assessment is to enhance learning. Another purpose is to enable the reporting of students achievement. Assessment practices have a powerful impact on learning and teaching. Issuessuch as what evidence to collect, how to collect it and how to interpret it need to be addressed anddebated widely within the school community. Developing a shared understanding of the outcomesenhances the validity and consistency of judgements about students learning. In turn, this improveslearning and teaching by improving the quality of information upon which teachers and students act.


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Teachers are also then able to report more credibly to other teachers, parents and the widercommunity.

Whether at the level of the classroom, school or system, assessment information should enable judgements to be made about students progress towards the desired outcomes in a way that is fair andcontributes to continued learning. Thus, assessment information should enable teachers and students toknow what students can do assisted and what they can do unassisted and what they can do whenworking in groups and when working alone. It should enable them to distinguish between work that isoriginal and non-routine and work that is reproductive or memorised. Fair assessment is based oncriteria which are valid and transparent and applied with consistency and without discrimination. Thesein turn require an assessment regime based upon multiple kinds and sources of evidence. Assessment islikely to enhance learning when the criteria are valid and explicit and when the assessment activities arethemselves educative.

y Valid y Educative y Explicity Fair y Comprehensive

curriculum fr a m ew ork - ov e ra rching st a t em entlink s acro ss th e curriculum

Links between the Overarching Statement learning outcomes and the learning outcomes in each of theLearning Area StatementsAll of the links identified in this table will be useful for teachers to consider in planning holistic learningand teaching and experiences.

OverarchingStatementLearning Outcomes

The Arts EnglishHealth &PhysicalEducation

LOTE Mathematics Science Society &EnvironmentTechnology& Enterprise

1.

Students use language tounderstand,develop andcommunicateideas andinformation andto interact withothers.

Dire ct 1, 3 Indir e ct 2, 4 The use of artslanguage iscentral tothe processof developing,

respondingto andcriticallyevaluatingarts works.

Dire ct 1 to 9 The use of languageunderpinsthedevelopment of theconventionsof Standard

AustralianEnglish,understanding of context andtheapplicationof languagemodes.

Dire ct 1, 2, 5 Indir e ct 3 Communicatingknowledgeandunderstanding of health

and physicalactivityconceptsand justifyinghealthdecisionsinvolve theuse of language.

Dire ct 4, 5 Indir e ct 1, 2, 3 Indevelopinganunderstanding of thesystem of

the targetlanguage,studentsfurtherdevelop anunderstanding of thestructure of StandardAustralianEnglish.

Dire ct 3, 4, 5 Using thelanguage of mathematicsinvolvesreading,writing,listening andtalking while

developing anunderstanding of mathematicalsymbols andvocabulary.

Dire ct 1, 2 Indir e ct 3 to 9 Communicating scientificallyinvolvescommunicating scientificunderstandingusing

technicallanguage.

Dire ct 1, 4 Indir e ct 2, 3, 5, 6, 7 The processesof investigationcommunication andparticipation

use anddevelop arange of communication methods.

Dire ct 1 Indir e ct 2-7 The use of language tocommunicate andnegotiateabout ideasand

solutions isan integralpart of thetechnologyprocess.


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2. Students select,integrate andapply numericaland spatialconcepts andtechniques.

Dire ct 2 Numberand spaceare used inarts skillsandprocessessuch aschoreographing,planningandbuildingsets,countingbeats andpreparingglazes ordyes.

Indir e ct 4, 7, 8, 9 Thecollection,comprehension andpresentation of informationor ideasincludesnumerical,graphic andvisual forms.

Dire ct 1, 3 Indir e ct 4 Numericaland spatialconceptsandtechniquesare appliedto health-relatedmonitoringandstatisticsand ingames,physicalactivity andmovementskills.

Indir e ct 1, 4, 5 Numericaland spatialconceptscan beinterpretedand appliedthrough thesystem of the targetlanguage.

Dire ct 1 , 4, 6 to 11 , 15 , 16 , 18 , 19 Indir e ct 2, 3, 5 Workingmathematically, number,measurement, chance anddata, space,and algebraoutcomesenablestudents toselect,integrate andapplynumerical andspatialconcepts andtechniques.

Dire ct 1, 2, 3, 6 to 9 Indir e ct 4, 5 Workingscientificallyinvolvesprocessessuch asmeasurement,modelling andquantification,and thedevelopmentof scienceconceptsrequires theapplication of numerical andspatialconcepts.

Dire ct 1 Indir e ct 2 to 7 Numericaland spatialconcepts areapplied inexplainingsocial andenvironmental phenomena.Statisticaldata, graphingand mappingtechniquesare selectedand used torepresent,analyse andevaluateinformation.

Dire ct 1 to 6 Thetechnologyprocessrequires theselectionandapplicationof conceptsandtechniquessuch asmeasuring,calculatingandestimating.




3. Studentsrecognise whenand whatinformation isneeded, locateand obtain it froma range of sourcesand evaluate, useand share it withothers.

Indir e ct 1to 4 Use of informationis integralto theformulationof artsideas, thedevelopment of skillsandprocesses,responsesandunderstanding of therole of thearts insociety.

Dire ct 4 Indir e ct 5 to9 Theprocessesandstrategiesdevelopedencompasstheclarificationof informationneeds andthe location,criticalevaluation,synthesisingandcommunication of information.

Indir e ct 1, 2, 4 Thecollectionand use of informationis central tothedevelopment of knowledge,understandings,attitudesand valuesandunderpinsstudentsself-management skills.

Indir e ct 1, 2, 4 Use of informationis integral toaccessing arange of sources,understanding theculture andrespondingin the targetlanguage

Dire ct 4, 5, 13 , 14 Throughworkingmathematically and chanceand data, theskills andprocesses aredeveloped toframequestions;gatheranalyse andinterpret dataand representthem.

Dire ct 1 to 3 , 5 Indir e ct 4, 6to 9 Generation,use andcommunication of information isintegral to theprocess of workingscientificallyand underpinsall conceptualunderstandings in thelearning area.

Dire ct 1 Indir e ct 2 - 7 The inquiryapproachcentral toinvestigation,communication &participationinvolvescreatingpropositions,collectingrelevant andreliableinformation,communicating and using itfor decisionmaking.

Dire ct 1, 3 Indir e ct 2, 4, 5 , 7 The skills of investigation andevaluationaredevelopedthrough thetechnologyprocess.Informationhandling iscentral totheselection,organisationandtransmission of information.



LOTE Mathematics Science Society &

Environment

Technology

& Enterprise

4. Students select,use and adapttechnologies.

Dire ct 2 Indir e ct 1, 4 Througharts skillsandprocesses,traditionalandemerging

Dire ct 4 , 7 Indir e ct 5, 6, 8, 9 A range of technologies is selectedand used toaccess andproduce a

Dire ct 3 Informationabouthealth andphysicalactivities isselectedusing arange of

Indir e ct 1 , 2, 3, 6 Technologyis selectedand used tolisten to,read, viewand write inthe target

Dire ct 4, 8, 9, 10 , 13 , 14 Indir e ct 17 , 18, 19 The selectionand use of arange of technologiesis integral to

Dire ct 1, 2 Indir e ct 6, 7, 8, 9 When workingscientifically,technologiesare used andadapted togather

Dire ct 1, 4 Indir e ct 2, 3, 5, 6 The selection,use andadaptation of a range of technologiesis central to

Dire ct 1 to 7 Thetechnologyprocessfocuses ontheselection,use,developmen


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technologies are usedandadapted tocreate,interpret,explore,develop,generateandcommunicate the arts.

variety of texts.

technologies.Specialisedequipmentis also used;for example,to producenutritiousmeals and inleisure andrecreationalpursuits.

language. workingmathematically, number,measurement, change &data &algebra.Outcome 13also developsethicalunderstandings of theimpact of technologiesused in datacollection.

information,conductactivities andcommunicateresults.

collectingdata andcommunicating findings andtheconsequencesof ethicalimplicationsof innovationsis understood.

t andadaptationof a range of technologies to meetneeds andrealiseopportunities.




5. Students describeand reason aboutpatterns,structures andrelationships inorder tounderstand,interpret, justifyand makepatterns.

Dire ct 2, 3 Indir e ct 1, 4 Criticalprocessesare used toanalysesimilaritiesanddifferences,makepatternsand drawconclusionsthusrespondingto patterns,structuresandrelationships.

Indir e ct 1 to9 Patterns,structuresandlanguageconventionsarerecognised,appreciatedand usedwithunderstanding andcriticalawareness.

Indir e ct 1 to5 Patternsandconnectionsbetweenknowledgeandunderstandings,attitudesand values,and skillsaredevelopedto enablestudents toleadhealthy,activelifestyles.

Dire ct 4, 5 Indir e ct 1, 2, 3, 6 Understanding of thesystem of the targetlanguageenables therecognitionof patternsand rules of languageuse and theapplicationof thisknowledgeto createspoken,written andvisual texts.

Dire ct 1 to 19 Throughworkingmathematically and usingspace,number,algebra andchance anddataunderstandings,generalisations, predictions,transformations,interpretations andidentificationsof mathematicalpatterns aredeveloped.

Dire ct 1, 3 to9 Indir e ct 2 Throughworkingscientifically,patterns,structures andrelationshipsareinvestigated,identified anddescribed intheformulation of theories anddevelopmentof concepts.

Dire ct 1, 2, 3, 6, 7 Indir e ct 4, 5 Social andenvironmental contexts areused toreason abouttherelationshipsbetweenstructures,processes andsystems andhow thesemay changeover time.

Dire ct 1 to 6 Indir e ct 7 Identification andinvestigation of patterns,structuresandrelationships arefundamental toimplementation of thetechnologyprocess andthe use,modificationanddevelopment of systems.




6. Students visualiseconsequences,think laterally,recogniseopportunity andpotential and areprepared to testoptions.

Dire ct 1, 2, 3 Explorationanddevelopment of artsideas usemanydifferentstartingpoints.Ideas arevisualisedandinterpretedthrough anactiveprocess of

Dire ct 4 to 9 Indir e ct 2 Through arange of processesandstrategies,studentsdevelop theability to bereflectiveandexperimental in theiruse of language.

Dire ct 2, 3, 4 Indir e ct 1 V isualisationandpredictionsabout futurehealth leadto theselection of courses of action,which aretested andmodified asrequired.

Indir e ct 3, 4, 5, 6 Contextualclues areused topredictmeaning.Individualsthoughtsand ideasareexpressed ina contextthatsupportscriticalthinking,problem

Dire ct 1, 3, 4, 5, 15 Throughappreciatingmathematicsand workingmathematically theattitudes,appreciationsand workhabitsdevelopedsupportcritical andcreativethinking.Different

Dire ct 1 , 2, 3 Indir e ct 5 to 9 Throughworkingscientifically,ideas areexplored andlateralthinking isapplied aspredictionsare made andfurtherinvestigationsand actionsare proposed.

Dire ct 1, 2, 3, 7 Throughinvestigation,communication,participationand activecitizenship,abilities toreflect onexperiences,criticallyanalyse,predictanswers anddevelopstrategies are

Dire ct 1, 4, 5 Indir e ct 2, 3, 7 Through thetechnologyprocess,problemsareidentifiedand ideasand designsare createdandinitiated.Models orprototypesare made,


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lateralthinking.

solving anddecisionmaking .

conjecturesareinvestigatedandalternativesare tested.

developed. evaluatedandchanged.



LOTE Mathematics Science Society &Environment Technology& Enterprise

7. Studentsunderstand andappreciate thephysical,biological andtechnologicalworld and havethe knowledgeand skills andvalues to makedecisions inrelation to it.

Indir e ct 1, 2, 3 Understanding of aspects of thephysical,biologicalandtechnological world isenhancedthrougharts skillsandprocesses.

Indir e ct 2 to9 Anunderstanding of languageand theability touse iteffectivelyempowerstudents tounderstandtheir worldand makedecisions inrelation toit.

Dire ct 1 Indir e ct 2 Decisionsabout ahealthy,activelifestyle areinformed byknowledge,understandings,attitudesand valuesrelated tothe physicalandbiologicalworld.

Indir e ct 4 Understandings of thephysical,biologicalandtechnologicalcircumstances of targetlanguagecommunities areenhancedby learningin targetlanguages.

Indir e ct 3, 4, 5 Bycontributingto studentsnumeracy,mathematicsprovidesimportanttools for thedevelopmentof understandings of thephysical,biological andtechnologicalworld.

Dire ct 1 to 9 Understanding andappreciationof the earthand beyond,energy andchange, lifeand living andnatural andprocessedmaterials areenhancedthroughworkingscientifically.

Dire ct 1 to 4 , 6, 7 Indir e ct 5 Decisions aremade as aresult of understandings developedthroughinquiry intothe elementsof andinterplaybetweentime, place,space,resources andnaturalsystems.

Dire ct 1, 2, 4 Indir e ct 5, 7 Understanding andappreciatingthetechnological world andemployingskills andunderstandings to makedecisionsabout thedevelopment and use of technologies isfundamental to thetechnologyprocess.




8. Students

understand theircultural,geographic andhistorical contextsand have theknowledge, skillsand valuesnecessary foractiveparticipation inlife inAustralia.

Dire ct 4

Indir e ct 3 Recognitionandunderstanding of thediversity of cultures,particularlywithinAustralianart, isdevelopedthrougharts,responsesandexamination of therole of artsin society.

Dire ct 1, 2,

3 Indir e ct 4 to9 Anunderstanding thatlanguage isinfluencedby bothsituationandsociocultural contextsassistsstudents todevelop andcommunicate values andto theparticipatein debateand decisionmaking.

Indir e ct 1,

2, 3 Understanding of thevarioussocial,cultural,environmental andpoliticalcontextsprovidesperspectivesthatcontributeto healthy,activeparticipation in life inAustralia.

Dire ct 4

Indir e ct 5 Understandings of andabilities tointeractwithmembers of targetlanguagecommunities areenhancedthroughlearningabout thecultural,geographicandhistoricalcontexts of peopleusing targetlanguages.

Dire ct 1, 2

Throughvaluing andapplyingmathematics,studentsunderstandtheir cultural,geographicand historicalcontexts andhave theknowledge,skills andvaluesnecessary intheir society.

Dire ct 5, 6

Indir e ct 1, 2, 3, 7, 8, 9 Understandings about thephysicalstructures of the earth andknowledgeand valuesdevelopedthroughinvestigationof science insocietyenhance thecapacity toparticipate inlife inAustralia.

Dire ct 1 to 7

Understandings needed foractiveparticipationare enhancedbyinvestigationof allelements of the Australiansociety andenvironmentand how theyhave changedanddevelopedover time.

Indir e ct 1 to

7 Understandings of cultural,geographical andhistoricalcontexts areappliedwhen usingthetechnologyprocess todevelopsolutions.





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9. Students interactwith people andcultures otherthan their ownand are equippedto contribute tothe global

community.

Indir e ct 2, 3, 4 Artsresponsesand anunderstanding of arts insocietyenhancetherecognitionand valuingof thediversity of culturesand thecontribution of the artsto theworld.

Dire ct 1 , 2 Indir e ct 3 to9 Theapplicationof communication skillsandunderstanding of languageand how itworksenhancesstudentsability tocommunicate effectivelywith peopleand culturesother thantheir own.

Indir e ct : 1, 2, 5 Through anappreciationof thesportingachievements of othercountriesand thecontributionothercultureshave madeto dietaryhabits,studentsdevelop abroaderworld view.

Dire ct 1 to 6 By learningin targetlanguages,relatedculturalunderstandings aredevelopedthat enablestudents tointeractwith peopleand culturesother thantheir own.

Indir e ct 2 Mathematicshas its originsin manycultures andcan enhanceunderstanding of the worldandparticipationin the globalcommunity.

Indir e ct 1, 2, 5, 6, 9 An awarenessthat science isa collectiveglobalendeavourcan lead togreaterappreciationof culturaldiversity andan enhancedcapacity tocontribute tothe globalcommunity.

Dire ct 4, 7 Indir e ct 1, 5 An awarenessof the socialand culturalperspectivesof others aredevelopedthroughinvestigation,communication andparticipation,culture andactivecitizenship.

Indir e ct 1, 3, 7 Throughexaminationof the roleof technologyin societyandapplicationof technologyprocessesstudentscancontributeto the globalcommunitythrough thedevelopment of solutions.




10. Studentsparticipate increative activityof their own andunderstand andengage with theartistic, culturaland intellectualwork of others.

Dire ct 1 to4 Throughparticipation in thedevelopment of artsideas,studentsdevelopskills andprocessesand usetheirunderstanding of thearts insociety tocreate,respond toand reflecton theirown artsworks andthat of others.

Dire ct 5 to 9 Throughexperiencing andstudying awide rangeof texts,studentsappreciatethe culturalandintellectualwork of others andengage intheir owncreativeuses of language.

Indir e ct 1, 3, 4, 5 Throughparticipation in physicalactivity,students areable toengage withthe artisticand culturalworks of others.

Indir e ct 2, 3, 4 Learning intargetlanguagesbetterequipsstudents toappreciatethe creativeand artisticexpressionsof targetlanguagecultures.

Indir e ct 2, 5 There is anappreciationthatmathematicsis developedby people of all culturesand a respectfor its originsin humanintuition,creativity andreason.Creativeengagementcan occurthrough allaspects of mathematics.

Dire ct 1, 5 Indir e ct 2, 3, 4, 6 to 9 Anappreciationof the work of important andinfluentialscientists isdeveloped asstudents workscientifically,building onthe creativeintellectualwork of othersto enhancetheirexplanations.

Dire ct 1 Indir e ct 2 - 7 Throughinvestigation,communication andparticipationoriginal andwell-craftedexplanationsandargumentscan bedevelopedthat show anappreciationof theintellectualand culturalachievementsof others.

Dire ct 1, 5 Indir e ct 2, 3, 4, 7 Development of solutionsrequirescreativityandengagementwith theintellectualwork of others.




11. Students valueand implementpractices thatpromotepersonal growthand well being.

Dire ct 3 Indir e ct 1, 2, 3 Creativeexpressionenablesstudents tounderstand

Indir e ct 2, 5to 9 Anunderstanding of languageand theability to

Dire ct 1 to 5 Throughacquisitionof knowledge,understandings, physicalactivity, self-

Indir e ct 4 Development of knowledgeof targetlanguagecommunities provides

Indir e ct 1 to19 Theapplication of mathematicalskills andunderstandings contributes

Dire ct 8 Indir e ct 3, 4 Throughworkingscientifically,studentsdevelopunderstanding

Dire ct 7 Indir e ct 1 Personalgrowth isenhanced byknowledge,values andskills

Dire ct 7 Indir e ct 6 Thedevelopment of enterpriseand anunderstandi


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theirdevelopment andchanges intheir livesand tosafelyexploreideas thatmay befrighteningordamagingthrough thesymbolicrepresentation of experience.

use iteffectivelyenablestudents tocriticallyanalysemessagesrelated toidealisedimages of self.

management andinterpersonal skills,studentsvalue andimplementpracticesthat reflectpersonalgrowth andwell-being.

opportunities to extendunderstandings of thedifferentdimensionsof personalgrowth andwell-beingin a moreglobalsense.

to anunderstanding of and anability toimplementpractices thatpromotegrowth andwell-being.

s of their ownbiology thatcontribute totheir personalgrowth andwell-being.

developedthroughparticipationin democraticprocesses andactivecitizenship.

ng of therole of technologyin societycontributeto a sense of well-being.

12. Students areself-motivatedand confident intheir approach

to learning andare able to workindividually andcollaboratively.

Policies and initiatives at the school level based on principles of learning and teaching described in the OverarchingStatement and each Learning Area Statement will allow students to develop the appropriate knowledge, skills,attitudes and values that will assist them to be self-motivated and confident learners who are able to work and learnindividually and collaboratively. Key aspects of such development are: self-discipline, goal setting, an ability to set andmeet deadlines, decision making, cooperation, self-respect, respect for others, willingness to accept responsibility forlearning, interpersonal skills, effective communication, problem solving, critical thinking.

13. Studentsrecognise thateveryone hasthe right to feelvalued and besafe, and, in thisregard,understand theirrights andobligations andbehaveresponsibly.

Policies and initiatives at the school level should support and reflect the democratic aims of schooling inAustraliansociety. Students should be provided with opportunities to examine and act on their rights and obligations whereverand whenever relevant to their learning and should be allowed to participate in their learning community without fearof prejudice. The principles of learning. teaching and assessment promote the provision of a safe and supportivelearning environment.

TOPl NEXT

M a th e m a tic s

In mathematics,students learn to use idesa about number, space, measurement and chance, and mathematical ways of representing patterns and relationships, to describe, interpret and reason about their social and physical world. Mathematics plays a key role in the development of students' numeracy and assists learning across the curriculum.

Definition a nd R a tion a le

De finition and R a tion a le


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In the Mathematics learning area, students learn about mathematics, what it is and how it is used inmaking decisions and solving problems. Mathematics involves observing, representing and investigating

patterns and relationships in social and physical phenomena and between mathematical objectsthemselves: Mathematics is often defined as the science of space and number [but] a more apt definition [is that] mathematics is the science of patterns. The mathematician seeks patterns in number,in space, in science, in computers, and in imagination. Mathematical theories explain the relationsamong patterns Applications of mathematics use these patterns to explain and predict natural

phenomena (Steen, L.A. (1988), The science of patterns , Science, 240, 29, 616.)

Mathematics can enhance our understanding of the world and the quality of our participation in society.Since it is valuable to us individually and collectively, it should be an integral part of the generaleducation of every young person.

This statement is based on three premises:

y All students are capable of learning the mathematical ideas and skills that underpin a wide rangeof everyday uses and can benefit from doing so.

y All students have a right to learn mathematics in a way that enables them to see thatmathematics itself makes sense, that they can make sense of mathematics, and that workingmathematically can help them make sense of their world.

y For students to become confident and capable users and learners of mathematics we will needcommon high standards and flexible curriculawhich respond to students non-standard learningneeds.

Students future personal and occupational needs will vary, as will the demands of the times. Studentsshould, however, learn to deal readily and efficiently with commonly occurring situations that canbenefit from the use of mathematics: for example, everyday decision making often involves askingquestions about the cheapest , best , biggest , furthest along , quickest , most reliable or most

likely , and answering such questions requires facility with number, measurement and chance. Planning,planting and maintaining a garden, making garden furniture, and sewing covers for chairs all makeconsiderable demands of spatial and measurement skills.

Students also need to be able to use their mathematics in tackling new or unfamiliar tasks. A studentnurse trying to understand how the amount of medication in the bloodstream is related to the timesince administration began may need to find a previously unseen formula, read symbolic expressions,ensure that the measurements to be used are in the right units, and rearrange the computation neededto enter it efficiently into a calculator. Activities such as making sense of a magazine article that uses theterms fertility and mortality to describe birth and death rates, rather than states, also call formathematical thinking, albeit less obviously so.

Being numerate is about having the disposition and competence to use mathematics to solve practicalproblems outside mathematics and as a tool for learning beyond the mathematics classroom. TheMathematics Learning Area takes a major, although not sole, responsibility for the development of students numeracy. Students should learn to read, write and speak mathematics in a variety of contextsand forms so that they can interpret and convey mathematical ideas, interpret prose containingmathematical forms, and continue to use and learn mathematics autonomously. Whether dealing withfamiliar or unfamiliar tasks, they need to:


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y recognise when mathematics might help;y choose appropriate mathematics;y decide on levels of precision and accuracy;y do the mathematics;y interpret the results; andy judge the reasonableness of results and appropriateness of the methods used.

Informed numeracy involves knowing what mathematics is and isn t, and what it can and cannot do, inorder to judge and question the appropriateness of its use in particular situations. Students need tolearn to ask about and question the assumptions underpinning particular uses of mathematics: forexample, upon reading an advertisement that claims a bank had 10 million happy customers in theprevious three months, the critical reader would say: That figure doesn t make sense. It s half thepeople in Australia. Upon what assumptions were the numbers based? Importantly, students shouldalso learn that mathematics cannot determine what we should or should not do in any particularcircumstance. Thus, it may assist us to predict the effect on groups of individuals of introducing a newtax, but not whether we should introduce the tax the latter is a matter for ethical and otherconsiderations.

Many students develop strong views about mathematics during their schooling: what it is about,who it is for, and what kind of people need it and are good at it. Some are effectively excludedfrom some of life s opportunities because they, and others, assume that they cannot do it . Forthis reason, it is essential that school mathematics be as rewarding as we can make it, that allstudents feel, and be, able to learn mathematics , and that students develop a positive attitudeto their own continued use of it. Every student needs to develop an awareness of the nature of mathematics, how it is created, used and communicated, for what purposes, and how it bothinfluences and is influenced by the things we believe and the values we hold.M a th e m a tic s Lea rning Outcom es

Introduction

The expected outcomes in this section provide a framework for curriculum in mathematics. Theseoutcomes are common and comprehensive in that all students should have access to learning programswhich addresses the complete set of outcomes and, in general, will be expected to achieve in relation toall of them. The outcomes are not all encompassing, however, since they will not address all of theneeds of every student. There will be other outcomes which some students will be expected to achieveduring their school education: for example, students undertaking specialist studies in the post-compulsory years or education support students developing independent living skills.

The outcomes are organised into seven clusters: Appreciating Mathematics, Working Mathematically,Number, Measurement, Chance and Data, Space, and Algebra. Judgements can be made about thesuccess of students learning in each of these clusters but, in the case of the first of theAppreciatingMathematics outcomes, the focus of judgements may be groups of students rather than individuals. Theparagraphs accompanying each outcome provide elaboration and clarification of the meaning of theoutcome, drawing on examples from across the years of schooling.

M a th e m atic s Lea rning Outcom es


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APP RECIATING M ATH EM ATICS Students appreciate the role mathematics has had, and continues to have, in their own and othercommunities. In particular, they:

1. Show a disposition to use mathematics to assist with understanding new situations, solving problemsand making decisions, showing initiative, flexibility and persistence when working mathematically and apositive attitude to their own continued involvement in learning and doing mathematics.

Students respond positively to their own use of mathematics and are inclined to ask, Will mathematicshelp here? , even in situations where it is not specifically required of them. For example, unpromptedthey count to decide whether they have enough straws for their classmates, use ideas about symmetrywhen classifying plants, work out their chances of winning a game with different strategies, and sketch agraph to help understand a paragraph in a textbook which describes a relationship betweenunemployment and immigration.

Students understand that they will continue to learn and use mathematics for all of their lives, and have confidence in their capacityto do so. They are willing to learn from others by listening to, and observing,the mathematical activity of peers, teachers and families. They appreciate, however, that workingmathematically also, and often, involves finding out for themselves. They persist with mathematicaltasks, pose mathematical questions, make conjectures, try alternatives and pursue different ideas. They

also read mathematics to explore mathematical ideas which they have not explicitly been taught and tounderstand material containing mathematical ideas. Confronted with a situation in which mathematicsthey have not yet learned might help, they do not retreat but rather are inclined to believe that they canlearn what they need or want to kno


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2. Appreciate that mathematics has its origins in many cultures, and its forms reflect specific social andhistorical contexts, and understand its significance in explaining and influencing aspects of our lives.

Students appreciate that mathematics is developed by people of all cultures in response to practical,aesthetic and spiritual needs, and that it is influenced by, and influences, our world views.They explain,for example, how they and others use mathematics in regulating their lives: at school we eat when theclock says 12 o clock; in netball we have to stay within the semicircle when shooting a goal; and we areadmitted to higher education if our score exceeds a certain number. They also comment on how suchuses of mathematics both reflect and influence the way we live and the things we value. Students mightdescribe how the need for a form of social organisation adapted to local conditions led to Aboriginalkinship systemsthat can be seen as mathematical in nature. They might also describe the impact of thecollection of public statistics on the daily lives and thinking of allAustralians, consider how they may beused to legitimise authority structures, and analyse the ethical implications of such uses in respect of human rights and social justice.

Students understand something of the nature, power and scope of mathematical activity and respect itsorigins in human intuition, creativity and reason. They appreciate the intellectual leap people needed tomake to invent zero, understand why people gain pleasure from number and spatial patterns, andrecognise the special nature of mathematical argument. Students take a constructively criticalview of the uses of mathematics, identifying situations where mathematics can enhance their own and otherslives, but also where it is misused or used to mislead or intimidate

WOR KING M ATH EM AT ICALLY Students use mathematical thinking processes and skills in interpreting and dealing with mathematicaland non-mathematical situations. In particular, they:

3. Call on a repertoire of general problem solving techniques, appropriate technology and personal andcollaborative management strategies when working mathematically.

Students draw on a range of general strategies when dealing with mathematical problems to which theyhave no readily available method of solution. These include such things as: act it out; guess, check andimprove; look for patterns; draw a picture or make a model; solve a simpler version of the problem first;identify and attempt sub-tasks; generate and systematically list possibilities; and eliminate possibilities.They make thoughtful use of technology to enhance their mathematical work and have a range of management strategies to help them get started and keep going in individual and collaborative problemsolving. They know that working independently on a problem can enable them to get a firm grasp of itsfeatures and bring their own unique perspective to its solution. But they also recognise the value of

working with others, cooperating to pool ideas and welcoming, and dealing constructively with,conflicting perspectives and views.

4. Choose mathematical ideas and tools to fit the constraints in a practical situation, interpret and makesense of the results within the context and evaluate the appropriateness of the methods used.

Students recognise when mathematics may assist in dealing with a practical problem. They choosemathematical ideas, procedures and technology which suit the physical, social orethical constraints in a


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situation, considering the assumptions they need to make in order to use the mathematics involved.Thus, they know that for most people multiplying the distance they can run in a minute by 60 won t givea good estimate of how far they can run in an hour, but multiplying the water lost from a dripping tap ina minute by 60 will give a good estimate of the water lost in an hour.

They consider the levels of precision and accuracy needed, make appropriate use of the results of usingtechnology and express results in ways suited to the context, perhaps by rounding to a sensible number:for example, asked how many buses are needed to transport 397 students if each bus can hold 54, theysay 8 rather than the 7.3518518 which appears on their calculator or the 7 to which the calculatoranswer rounds. They also judge the appropriateness of the methods used. Thus, given a problem of sixhungry children and only three apples, they respond to a suggestion that the children draw lots for theapples by querying whether having an equal chance of getting an apple makes this a fair or goodsolution and ask, Is there a better way?

5. Investigate, generalise and reason about patterns in number, space and data, explaining and justifyingconclusions reached.

Students observe regularities and differences and describe them mathematically. By identifyingcommon features in mathematical situations, they make generalisations about numbers, space anddata. Thus, they may observe that every time they combine 3 things with 9 things, they get 12 thingsand make the generalisation that 3 add 9 is always 12. They know that many patterns may be observedin the one situation, and generate and investigate a number of different conjectures about it. Studentsunderstand that a mathematical generalisation must be true always rather than mostly and that oneexception invalidates it. They attempt to confirm or refute their own and others generalisations andprepare arguments to convince themselves and others that a generalisation must hold in every case andnot only for all the cases tried. Thus, in investigating quadrilaterals they may note that every four-sided

figure which they try tessellates. This leads them to conjecture that all quadrilaterals tessellate and tosearch for a general argument which will convince both themselves and their peers of this. They write(and speak) mathematics clearly and precisely, expressing and explaining their generalisations verballyand with standard algebraic conventions.

NUMB ER Students use numbers and operations and the relationships between them efficiently and flexibly. Inparticular, they:

6.R

ead, write and understand the meaning, order and relative magnitudes of numbers, moving flexiblybetween equivalent forms.

Students read, write, say, interpret and use numbers in common use, including whole numbers,fractions, decimals, percentages and negative numbers. They can order numbers and understand therelevance of the order: for example, they know that if they have 9 shells and 7 honky nuts, they do nothave to line up the items to say whether they have more shells or nuts. They also know that cordialwhich is one quarter concentrate will be stronger than cordial which is one-fifth concentrate: that a


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library book with call number 7.52 is located after one with call number 7.513; and that a temperatureof -16C is colder than -3C. They understand the relative magnitudes of numbers: for example, 9 isalways 2 more than 7, 30% off is not quite as good as one third off and one million is a thousandtimes as big as a thousand. They choose forms of numbers helpful in particular contexts and recognisecommon equivalences, such as that one-fifth is the same as 1/5, two-tenths, 0.2 and 20%. They interpretlarge and small numbers for which few visual or concrete referents are available and represent them,including using scientific notation. Their number repertoire includes irrational numbers such as p and 2 which arise in practical contexts.

7. Understand the meaning, use and connections between addition, multiplication, subtraction anddivision.

Students understand the meaning of addition, subtraction, multiplication and division as distinct fromhow to carry out the calculations associated with them. They decide which operation is needed, evenwhen no obvious verbal cues indicate which operation is expected: for example, they understand thatthey can solve take away and comparison situations by subtracting, and write the appropriatesubtraction. They recognise the need to multiply and divide in situations involving repeated addition,arrays, rates and conversions, areas, and enlargements and reductions. They know that multiplicationdoes not always make bigger or division smaller and can say under what circumstances each doesand does not. They also recognise and can deal with familiar and unfamiliar situations involving ratioand proportion. They understand key relationships within and between the four basic operations anduse these to construct equivalent expressions, find unknown quantities and assist computation: forexample, they can think of 9 as composed of 4 and 5, so that 9 = 4 + 5, but also 9 4 = 5 and 9 5 = 4,and understanding such relationships enables them readily to solve problems such as [ ] 7 = 11, oreven [ ] 348 = 434.

8. Choose and use a repertoire of mental, paper and calculator computational strategies for eachoperation, meeting needed degrees of accuracy and judging the reasonableness of results.

Students are justifiably confident of their capacity to deal, correctly and efficiently, with everydaycounting and computational situations. They can count a collection one-to-one, recognise skip countingin twos or threes as a more efficient way of getting the same result, and combine collections usingstrategies such as counting on. They know the addition facts to 10 + 10 and multiplication facts to10 10, and extend these with a flexible repertoire of mental strategies for each of the four operationson whole numbers, money and simple fractions. They use written approaches as a back-up for

calculations they cannot store completely in the head . These may include diagrams, jottings, standardroutines, and supporting technology for students with disabilities. They understand that calculators orcomputers are the sensible choice for repetitive, complex or lengthy calculations and use themefficiently, correctly interpreting calculator displays. Students judge the appropriate level of accuracy,are accurate when necessary, and otherwise estimate and approximate. Unprompted, they check thatthe results of their computations make sense, both in terms of the numbers and operations involvedand the context in which the calculation arose.


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M EAS UREM ENT Students use direct and indirect measurement and estimation skills to describe, compare, evaluate, planand construct. In particular, they:

9. Decide what needs to be measured and carry out measurements of length, capacity/volume, mass,area, time and angle to needed levels of accuracy.

Students know that the same things can be compared and ordered by different attributes such aslength, capacity or mass, depending upon the purpose of the measurement. They also realise that theattribute chosen will make a difference to the order. They describe their comparisons appropriately: forexample, using taller-shorter , wider-narrower . They understand that we use a unit when we want toquantify how big or how much bigger and that generally measurements are only as accurate as theunit chosen. When choosing a unit (that is, deciding what attribute to measure and how accurate theyneed to be), students think about the purpose of the measurement and the closeness of thecomparisons to be made. Thus, to check whether a large box will fit through a door, they recognisehandspans as probably good enough units but, if it looks like being a tight squeeze, will find a smallerunit.

They know that standard units are not more accurate than non-standard units but they do help withrecord keeping and communication and are usually needed when using formulae. Students use commonmeasuring equipment and graduated scales, such as rulers, clocks and shop and kitchen scales, choosingequipment or techniques to suit the situation. They express measurements in suitable units and usetheir understanding of the common metric prefixes to move flexibly between units and to judge size.

10. Select, interpret and combine measurements, measurement relationships and formulae todetermine other measures indirectly.

Indirect measurement is used when direct comparison or measurement of quantities is impossible,impractical or simply tedious. Students choose and use a range of methods of indirect measurement.They may weigh a few pieces of fruit at a time and add the weights because their scales won taccommodate more than 500 g. They predict when a video will finish by taking the time now and addingon the length of the film. They may also use division or averaging to find measurements moreaccurate than their equipment allows: for example, measuring the thickness of a ream of paper in orderto calculate the thickness of one sheet. They also use formulae for finding lengths, areas and volumes;scale and similarity; Pythagoras theorem and trigonometric ratios for finding lengths and distances inthree dimensional contexts; and rates and derived measures, such as speed and density, for calculatingquantities.

11. Make sensible direct and indirect estimates of quantities and are alert to the reasonableness of measurements and results.

Students have a good idea of the size of common standard units, make sensible estimates with them,and have the disposition and skills to judge the reasonableness of estimates and measurements. Theyknow that to estimate which of two rocks has the bigger volume, looking may be sufficient, but tocompare their masses, hefting will probably be needed. They have a range of benchmarks which they


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use in estimation: for example, they may know which of their fingers is about a centimetre wide, what alitre container of ice-cream looks like, and how heavy a kilogram of rice feels. They use thesebenchmarks to judge reasonableness, saying, for example, that the average height of children in theirclass simply cannot be 2.3 metres they must have made a mistake. Students also reason from knownand collected quantities to estimate quantities which cannot be found directly or conveniently: forexample, to estimate how much food is put in the school s bins each week or how many cats there are inWestern Australia.

CH ANCE AND DAT A Students use their knowledge of chance and data handling processes in dealing with data and withsituations in which uncertainty is involved. In particular, they:

12. Understand and use the everyday language of chance and make statements about how likely it isthat an event will occur based on experience, experiments and analysis.

Students recognise that many situations are somewhat unpredictable: for example, winning the netball,whether it will rain on the way home from school or getting a good hand in a game of cards. They makeappropriate use of the everyday language of chance such as might , could , likely and unlikely ,

certain and uncertain , possible and impossible , probably , odds , fifty-fifty . They realise thasituations with uncertain individual outcomes may show long-term patterns in their behaviour and thatwe use this to help interpret data and make predictions in order to address questions such as: Howmany mice will we have by next month? What will the weather be like for our celebration in July?

How long will the battery last? Students compare events, using numerical and other information toorder them from those least to those most likely to happen. They know that probability is the way wequantify how likely it is that something will happen and they can interpret the probability scale from 0 to1. They estimate probabilities from experiments and simulations, using the long-run relative frequency.

They also use systematic lists, tables and tree diagrams to assist them to analyse and explain possibleoutcomes of simple experiments, and to calculate probabilities by analysis of equally likely events.

13. Plan and undertake data collection and organise, summarise and represent data for effective andvalid interpretation and communication.

Students systematically collect, organise and record data to answer their own questions and those of others: for example, Which school lunch is liked best? Which animal is most scary? What shapesand proportions do people like best? How does absenteeism from school relate to the time of year?

How much water is used in the school each year and for what? Does having a part-time job impact onschool results? . They clarify and refine questions and plan surveys, experiments and simulations to help

answer them in unbiased ways, considering both the data collection instruments and the size and natureof samples.

Students understand that (1), classification underlies the organisation of data; (2), how we classifydepends upon the questions we want to answer; (3), the way the data are organised can illuminate ormask certain of their features; and (4), this influences how the data are interpreted and used: forexample, one classification of sports preferences might suggest that students prefer ball games; anothermight suggest that balls as such are not relevant, rather that students prefer team to individual sports.


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They, therefore, realise that data can be distorted accidentally or deliberately to reach inappropriateconclusions.

Students describe patterns in data and make concise but meaningful summaries using statistics todescribe proportions, averages and variability. They choose and use diagrams, tables, plots and graphswhich are suited to the kind of data and the purpose of the display. They co

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