Mathematics proficiencies | The Australian Curriculum (Version 8.4)

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<div class="container"> <div class="container"> <br/> <section> <ul class="breadcrumbs"> <li> <a href="/">Home</a> </li> <li> <a href="/resources/">Resources</a> </li> <li class="active">Mathematics proficiencies</li> </ul> </section> </div> <section> <div class=""> <h3>Introduction</h3> <div class="anno-letterbox"><iframe src="https://www.youtube.com/embed/bkDqWrf_WVY?rel=0" frameborder="0" allowfullscreen="allowfullscreen" style="height: 100%; width: 100%;" webkitallowfullscreen="webkitallowfullscreen" oallowfullscreen="oallowfullscreen" msallowfullscreen="msallowfullscreen" mozallowfullscreen="mozallowfullscreen"></iframe></div> </div> </section><section> <div class=""> <p>The Australian Curriculum: Mathematics aims to be relevant and applicable to the 21st century. The inclusion of the proficiencies of understanding, fluency, problem-solving and reasoning in the curriculum is to ensure that student learning and student independence are at the centre of the curriculum. The curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, reasoning, and problem-solving skills. These proficiencies enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.</p> <p>The proficiency strands describe the actions in which students can engage when learning and using the content of the Australian Curriculum: Mathematics.</p> </div> </section><section> <div class=""> <div class="accordion"> <div class="accordion-head"> <a id='accordion-2e5c113f-9660-4c2d-9601-d717a6ebacc0' data-dropdown-target='#accordion-2e5c113f-9660-4c2d-9601-d717a6ebacc0-content-pane' href="#"> <h3>Understanding</h3> </a> </div> <div class="accordion-body collapse" id='accordion-2e5c113f-9660-4c2d-9601-d717a6ebacc0-content-pane'> <p><span>Students build a robust knowledge of adaptable and transferable mathematical concepts. They make connections between related concepts and progressively apply the familiar to develop new ideas. They develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics. Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and when they interpret mathematical information</span></p> </div> </div> </div> </section><section> <div class=""> <div class="accordion"> <div class="accordion-head"> <a id='accordion-aa8f9478-37ef-4474-81fa-c037ab0bba66' data-dropdown-target='#accordion-aa8f9478-37ef-4474-81fa-c037ab0bba66-content-pane' href="#"> <h3>Fluency</h3> </a> </div> <div class="accordion-body collapse" id='accordion-aa8f9478-37ef-4474-81fa-c037ab0bba66-content-pane'> <p><span>Students develop skills in choosing appropriate procedures; carrying out procedures flexibly, accurately, efficiently and appropriately; and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions.</span></p> </div> </div> </div> </section><section> <div class=""> <div class="accordion"> <div class="accordion-head"> <a id='accordion-54c274ef-0281-4f02-a909-e40e28619008' data-dropdown-target='#accordion-54c274ef-0281-4f02-a909-e40e28619008-content-pane' href="#"> <h3>Problem-Solving</h3> </a> </div> <div class="accordion-body collapse" id='accordion-54c274ef-0281-4f02-a909-e40e28619008-content-pane'> <p><span>Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.</span></p> </div> </div> </div> </section><section> <div class=""> <div class="accordion"> <div class="accordion-head"> <a id='accordion-eb008665-1ae8-4d3e-8549-f13ccd9cddc7' data-dropdown-target='#accordion-eb008665-1ae8-4d3e-8549-f13ccd9cddc7-content-pane' href="#"> <h3>Reasoning</h3> </a> </div> <div class="accordion-body collapse" id='accordion-eb008665-1ae8-4d3e-8549-f13ccd9cddc7-content-pane'> <p><span>Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and when they compare and contrast related ideas and explain their choices.</span></p> </div> </div> </div> </section><section> <div class=""> <div class="accordion"> <div class="accordion-head"> <a id='accordion-9ac1ea9c-dc15-4f71-8b23-d5b958e09957' data-dropdown-target='#accordion-9ac1ea9c-dc15-4f71-8b23-d5b958e09957-content-pane' href="#"> <h3>Useful Links</h3> </a> </div> <div class="accordion-body collapse" id='accordion-9ac1ea9c-dc15-4f71-8b23-d5b958e09957-content-pane'> <ul class="home-box-links"> <li><a rel="noopener" href="http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1" target="_blank" class="home-box-link">Australian Curriculum: Mathematics F–10</a></li> <li><a rel="noopener" href="http://subs.emis.de/journals/ZDM/zdm026r1.pdf" target="_blank" class="home-box-link">Review by Kaye Stacey of 'Adding it up: helping children learn mathematics' report</a></li> <li><a rel="noopener" href="/media/6611/peter-sullivan-presentation-designing-learning-experiences-that-exemplify-the-proficiencies.pptx" target="_blank" title="Peter Sullivan Presentation Designing Learning Experiences That Exemplify The Proficiencies" class="home-box-link" data-udi="umb://media/c04940a105c2423d8c8921f7223f9e57">Peter Sullivan presentation: Designing learning experiences to exemplify the proficiencies</a></li> <li><a rel="noopener" href="/media/6612/peter-sullivan-presentation-create-your-own-lessons.pptx" target="_blank" title="Peter Sullivan Presentation Create Your Own Lessons" class="home-box-link" data-udi="umb://media/14083f8938394c39a3bbb026d8f8abf0">Peter Sullivan presentation: Create your own lessons</a></li> <li><a rel="noopener" href="/media/6610/using-the-proficiencies-to-enrich-mathematics-teaching-and-assessment.pdf" target="_blank" title="Using The Proficiencies To Enrich Mathematics Teaching And Assessment" class="home-box-link" data-udi="umb://media/83672d8fe5c74f2e9d3dbacba60d54e2">Peter Sullivan paper: Using the proficiencies to enrich mathematics teaching and assessment</a></li> </ul> </div> </div> </div> </section> <div class="accordion-group lpwul"> </div> <h3> Explore Mathematics proficiencies portfolios and illustrations </h3> <div class="row no-gutter margin-top-20"> <div class="col-s-3"> <div class="margin-bottom-30 text-align-center" > <a class="card " href="/resources/mathematics-proficiencies/portfolios/understanding/" target="_self"> <div class="card-image"> <img class="card-image-img" src="/media/3317/curriculum-icons_mathematics-proficiencies_understanding.png?width=500" alt="Understanding" style="height: 100%; max-width: 100%; "> </div> <h3> Understanding </h3> </a> </div> </div> <div class="col-s-3"> <div class="margin-bottom-30 text-align-center" > <a class="card " href="/resources/mathematics-proficiencies/portfolios/fluency/" target="_self"> <div class="card-image"> <img class="card-image-img" src="/media/3314/curriculum-icons_mathematics-proficiencies_fluency.png?width=500" alt="Fluency" style="height: 100%; max-width: 100%; "> </div> <h3> Fluency </h3> </a> </div> </div> <div class="col-s-3"> <div class="margin-bottom-30 text-align-center" > <a class="card " href="/resources/mathematics-proficiencies/portfolios/problem-solving/" target="_self"> <div class="card-image"> <img class="card-image-img" src="/media/3315/curriculum-icons_mathematics-proficiencies_problem-solving.png?width=500" alt="Problem-Solving" style="height: 100%; max-width: 100%; "> </div> <h3> Problem-Solving </h3> </a> </div> </div> <div class="col-s-3"> <div class="margin-bottom-30 text-align-center" > <a class="card " href="/resources/mathematics-proficiencies/portfolios/reasoning/" target="_self"> <div class="card-image"> <img class="card-image-img" src="/media/3316/curriculum-icons_mathematics-proficiencies_reasoning.png?width=500" alt="Reasoning" style="height: 100%; max-width: 100%; "> </div> <h3> Reasoning </h3> </a> </div> </div> <div class="col-s-3"> <div class="margin-bottom-30 text-align-center" > <a class="card " href="/resources/mathematics-proficiencies/illustrations-of-practice/" target="_self"> <div class="card-image"> <img class="card-image-img" src="/media/5061/iops_version_2-002.png?width=500" alt="" style="height: 100%; max-width: 100%; "> </div> </a> </div> </div> </div> </div> </main> <div class="social-bar "> <div class="container"> <span>Follow ACARA:</span> <a rel="external noopener noreferrer" target="_blank" href="https://www.facebook.com/acara.edu.au"> <svg class="svg-facebook-dims facebook-fill"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#facebook" /> </svg> </a> <a rel="external noopener noreferrer" target="_blank" href="https://twitter.com/ACARAeduau"> <svg class="svg-twitter-dims twitter-fill"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#twitter" /> </svg> </a> <a rel="external noopener noreferrer" target="_blank" href="http://www.linkedin.com/company/668120?trk=tyah&trkInfo=tas%3AACARA%2Cidx%3A1-2-2"> <svg class="svg-linkedin-dims linkedin-fill"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#linkedin" /> </svg> </a> <a rel="external noopener noreferrer" target="_blank" href="https://www.youtube.com/channel/UCXN7Dkh7vEKbcmpIXjUiebw"> <svg class="svg-youtube-dims youtube-fill"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#youtube" /> </svg> </a> </div> </div> <footer role="contentinfo" class=""> <div class="container"> <div class="row"> <div class="col-m-4"> <h3>Contact details</h3> <p> Australian Curriculum, Assessment and Reporting Authority (ACARA) </p> <address> Level 13, Tower B, Centennial Plaza,<br /> 280 Elizabeth Street, Sydney, NSW 2000 </address> </div> <div class="col-m-4"> <h3>Other links</h3> <ul> <li><a href="/about-the-australian-curriculum/">About the Australian Curriculum</a></li> <li><a href="/sitemap/">Sitemap</a></li> <li><a href="/copyright-and-terms-of-use/">Copyright and terms of use</a></li> <li><a href="/accessibility/">Accessibility</a></li> <li><a href="https://www.acara.edu.au/contact-us/privacy">Privacy policy</a></li> <li><a href="http://rdf.australiancurriculum.edu.au">Machine readable Australian Curriculum (MRAC)</a></li> </ul> </div> <div class="col-m-4"> <h3>Feedback / Enquiries</h3> <label for="feedback">We welcome your feedback and queries.</label> <label for="feedback">Please <a href="/ContactUs"><u>click here</u></a> to contact us.</label> </div> </div> <div class="row footer-logos"> <div class="col-s-4"> <a rel="external noopener noreferrer" target="_blank" href="http://www.acara.edu.au/"> <svg class="footer-logo"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#acara2" /> </svg> </a> </div> <div class="col-s-4"> <a rel="external noopener noreferrer" target="_blank" href="https://www.nap.edu.au/"> <svg class="footer-logo"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#nap" /> </svg> </a> </div> <div class="col-s-4"> <a rel="external noopener noreferrer" target="_blank" href="https://www.myschool.edu.au/"> <svg class="footer-logo"> <use xlink:href="/css/src/site/img/icons/sprite/sprite.svg#my-school" /> </svg> </a> </div> </div> </div> </footer> <div> <div class="footer-copyright"> © Australian Curriculum, Assessment and Reporting Authority </div> </div> <script type="text/javascript" src="/scripts/main.min.js"></script> <script type="text/javascript" src="/scripts/site.es5.min.js"></script> <script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-MML-AM_CHTML"> </script>  <script> $('.media-placeholder').bind('click', function (event) { $("iframe").each(function () { $(this)[0].contentWindow.postMessage('{"event":"command","func":"' + 'pauseVideo' + '","args":""}', '*'); 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Mathematics proficiencies | The Australian Curriculum (Version 8.4)