Making the Case for Computer-Based Maths Education

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href="/the-maths-fix/" title="The Math(s) Fix">The Math(s) Fix</a></li> <li class="hide show__600"><a href="/pisa/" title="PISA 2025">PISA 2025</a></li> <li><a href="/case-for-computer-based-math-education.php" title="The Change" id="making-the-case">The Change</a></li> <li id="resources-menu"><a href="#" title="Try Now" id="resources">Try Now</a><button class="resources-button"></button> <ul class="resources dropdown"> <li><a href="/self-study-resources/" title="Self study">Self-Study</a></li> <li><a href="/inside-module/" title="Teaching Platform">Teaching Platform</a></li> <li><a href="/project-repository/" title="Project Repository">Project Repository</a></li> </ul> </li> <li><a href="/take-action/ " title="Campaign" id="take-action">Campaign</a></li> <li><a href="//www.conradwolfram.com/media" title="News and Views" id="news" target="_blank">News</a></li> <li id="about-menu"><a href="/about/" title="About Us" id="what-is-cbm">About</a><button class="about-button"></button> <ul class="about dropdown"> <li><a href="/community/" title="Join Community" id="community">Community</a></li> <li><a href="/materials/" title="Materials">Materials</a></li> </ul> </li> </ul> </div> <div id="sub-nav"> <div class="nav-inner"> <div class="sub-nav"> <span class="sub-nav-link"> <a href="/the-maths-fix/" title="The Math(s) Fix"><i>The Math(s) Fix</i><span class="hide__600"> book by Conrad Wolfram</span></a> </span> <span class="divider"></span> <span class="sub-nav-link"> <a href="//www.conradwolfram.com/writings/chatgpt-in-education" title="Latest: Answers for the ChatGPT era">Latest: Answers for the ChatGPT era<span class="hide__600"></span></a> </span> </div> </div> </div> </nav>  <main id="main"> <section id="intro"> <div class="inner"> <img src="/img/case-infinity-header.png" alt=""> <h2>Computer-Based Maths:</h2> <h1>The Change</h1> <p>CBM is a new subject that starts from maths in the real world and works back to redefine the educational subject to match. A crucial change is to have computer-based (rather than human-powered) computation at its heart—redefining maths as the anchor subject for computational thinking across all subjects, centred on real-life problem solving, not historical hand-calculating techniques.</p> <hr> </div> <div id="quote"> <blockquote>Computers liberated real-world maths from hand-calculating to go far further and faster than anyone could have imagined. Now it's vital that educational maths stands on this automation too.</blockquote> <div class="speaker"> <a href="/the-maths-fix" class="flex"> <img src="img/book-icon.png" alt="The Math(s) Fix book" width="57" height="79" class="margin-l-"> <p><em>Conrad Wolfram</em> | Founder, author of <em>The Math(s) Fix</em></p> </a> </div> </div> </section> <section id="the-header" class="the-header"> <div class="inner"> <div class="nav-group"> <a href="#the-problem" id="the-problem-nav" class="nav-item">The Problem</a> <a href="#the-fix" id="the-fix-nav" class="nav-item">The Fix</a> <a href="#the-summary" id="the-summary-nav" class="nav-item">The Summary</a> <a href="#the-change" id="the-change-nav" class="nav-item">The Change</a> </div> </div> </section> <section id="the-problem"> <div class="inner"> <h1>The Problem</h1> <h2>What's wrong with today's maths?</h2> <p>It's 80% a different subject from what is required in the real world. Computers have mechanised computation beyond previous imagination, yet today's maths education spends 80% of the curriculum time gaining expertise in hand–calculation methods rather than using a computer to do the calculating. The curriculum is ordered by the difficulty of the skills necessary to complete the calculation, rather than the difficulty of understanding the complexity of the topic. <em>Computational</em> difficulty rather than <em>conceptual</em> difficulty.</p> <p>The very reason mathematics is seen as so important in education today is because mathematical or computational thinking skills appear so widespread and deeply embedded in all walks of life. But this is a relatively new phenomenon. Before mechanised computing, the use of mathematics above very basic arithmetic was much narrower and only applicable to fields such as some areas of physics and accountancy. It did not work well on anything requiring larger amounts of data, or messier or less immediately quantitative problems. Computers have made this fundamental change and without them many other current and rapidly emerging fields would not exist.</p> <h3>Traditional Method</h3> <img src="/img/case-traditional-path.png" alt=""> <h3>CBM</h3> <img src="/img/case-cbm-path.png" alt=""> </div> </section> <section id="the-fix"> <div class="inner"> <h1>The Fix</h1> <h2>How will CBM fix the problem?</h2> <div> <h3 class="fix-header"><span>Fix 1</span><span>The Right Basics</span></h3> <div class="fix"> <p>Students solve problems using the Computational Thinking Process (CTP). This is a process in which one creatively applies a four-step problem-solving cycle to real-world problems in order to develop and test solutions. The emphasis is learning how to take real-life situations and abstract them to a computational setting—often code—so that a computer can calculate the answer.</p> <p>Some problems may require going through the cycle multiple times. It is helpful to represent this iteration as ascending a helix made up of a roadway of the four steps, repeating in sequence until “success” is declared.</p> <div class="grid cols-1 heirs-width-full heirs-padding-b-2 show__900"> <div class="grid width-full"> <img src="/img/case-helix.png" alt="" class="right-overlap"> <div> <ul id="rocket-vertical" class="tiles grid heirs-width-full heirs-padding-b-0"> <li> <div class="yellow-box description"> <div class="bar-title-wrapper padding-bt-0"> <div class="bar-title"> <div class="title-content display-ib"> <span class="title margin-r-1-2">1 | Define <span class="sub-title">Questions</span></span> </div> </div> </div> <p>Think through the scope and details of the problem, defining manageable questions to tackle. Identify the information you have or will need to obtain in order to solve the problem.</p> </div> <div class="yellow-down-arrow"></div> </li> <li> <div class="red-up-arrow"></div> <div class="red-box description"> <div class="grid cols-3"> <div class="bar-title-wrapper padding-bt-0"> <div class="bar-title"> <span class="title margin-r-1-2">2 | Abstract <span class="sub-title">To Computable Form</span></span> </div> </div> </div> <p>Transform the question into an abstract precise form, such as code, diagrams or algorithms ready for computation. Choose the concepts and tools to use to derive a solution.</p> </div> <div class="red-down-arrow"></div> </li> <li> <div class="purple-up-arrow"></div> <div class="purple-box description"> <div class="grid cols-3"> <div class="bar-title-wrapper padding-bt-0"> <div class="bar-title"> <span class="title margin-r-1-2">3 | Compute <span class="sub-title">Answers</span></span> </div> </div> </div> <p>Turn the abstract question into an abstract answer using the power of computation, usually with computers. Identify and resolve operational issues during the computation.</p> </div> <div class="purple-down-arrow"></div> </li> <li> <div class="lime-up-arrow"></div> <div class="lime-box description"> <div class="grid cols-3"> <div class="bar-title-wrapper padding-bt-0"> <div class="bar-title"> <div class="title-content display-ib"> <span class="title margin-r-1-2">4 | Interpret <span class="sub-title">Results</span></span> </div> </div> </div> </div> <p>Take the abstract answer and interpret the results, recontextualising them in the scope of your original questions and sceptically verifying them. Take another turn to fix or refine.</p> </div> <div class="lime-down-arrow"></div> </li> </ul> </div> </div> </div> <p class="sub-text">Download the poster here for <a href="/computational-thinking-process-poster/">free</a>.</p> </div> </div> <div> <h3 class="fix-header"><span>Fix 2</span><span>The right outcomes</span></h3> <div class="fix"> <p>Our curriculum follows an 11-category draft set of outcomes to reflect the needs of modern society (see the full set of outcomes <a href="/materials/math-education-outcomes.php#detailed-view-ct">here</a>):</p> <div class="cbm-nodes"> <a href="#detailed-view-cp" class="subtab">CP<span class="tooltip bottom">Confidence to tackle new problems</span></a> <a href="#detailed-view-if" class="subtab">IF<span class="tooltip bottom">Instinctive feel for computational thinking</span></a> <a href="#detailed-view-cv" class="subtab">CV<span class="tooltip bottom">Critiquing and verifying</span></a> <a href="#detailed-view-gm" class="subtab">GM<span class="tooltip bottom">Generalising a model/theory/approach</span></a> <a href="#detailed-view-cc" class="subtab">CC<span class="tooltip bottom">Communicating and collaborating</span></a> </div> <h4>Thinking Outcomes</h4> <div class="cbm-nodes"> <a href="#detailed-view-dq" class="subtab yellow">DQ<span class="tooltip bottom">Defining the question</span></a> <a href="#detailed-view-ac" class="subtab cbm-red">AC<span class="tooltip bottom">Abstracting to computable form</span></a> <a href="#detailed-view-c" class="subtab cbm-red">C <span class="squares-wrapper"><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span></span> <span class="tooltip bottom">Concepts</span> </a> <a href="#detailed-view-t" class="subtab cbm-red">T <span class="squares-wrapper"><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span></span> <span class="tooltip bottom">Tools</span> </a> <a href="#detailed-view-mc" class="subtab magenta">MC<span class="tooltip bottom">Managing computations</span></a> <a href="#detailed-view-in" class="subtab green">IN<span class="tooltip bottom">Interpreting</span></a> </div> <h4>Step Outcomes</h4> <p>Our outcomes follow four core principles:</p> <div class="fix-list-header">1. They cover “thinking”</div> <p>Outcomes should explicitly abstract out the thinking skills needed to tackle real-world problems using real-world technology. Skills like the ability to critique and verify a solution, or to generalise a model.</p> <div class="fix-list-header">2. They fit to the Computational Thinking Process</div> <p>Outcomes come in varying levels of granularity. One outcome might be about the whole process; another might be about one step of it; another might be about just one small part within a step.</p> <div class="fix-list-header">3. They scope beyond individual toolsets</div> <p>The Computational Thinking Process is iterative, multi-layered and complex. Outcomes should be broad, not limited to the concepts and tools of a specific problem.</p> <div class="fix-list-header">4. They are not dependent upon assessment</div> <p>If current assessment methodology cannot measure an outcome, that should not be a reason to remove it from the curriculum.</p> <div class="fix-list-inline"> <div class="cbm-nodes-inline"> <a href="#detailed-view-c" class="subtab cbm-red">C <span class="squares-wrapper"><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span></span> <span class="tooltip bottom">Concepts</span> </a> <a href="#detailed-view-t" class="subtab cbm-red">T <span class="squares-wrapper"><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span><span class="square"></span></span> <span class="tooltip bottom">Tools</span> </a> </div> <span class="fix-list-header">Two key outcomes: Concepts and Tools—the Computation Outcomes. </span> Being computer based, the computational toolset vastly increases in depth and complexity. Levels of "knowing" are substantially different to hand-calculation toolsets. When we think about which actual concepts and tools we should include, we start with actual problems that students need to solve, working back to the concepts and tools they need to solve them. </div> </div> </div> <div> <h3 class="fix-header"><span>Fix 3</span><span>A New Curriculum Based on Real-World Contexts</span></h3> <div class="fix"> <p>Our curriculum falls into five broad sectors (although these are by no means strict divisions):</p> <img src="/img/case-categories-of-math.png" alt="" width="521"> <p>Traditional curricula are built upon outdated collections of mathematical concepts, making them poor representations of the problems people face in the world today.</p> <p>We have taken the reverse approach: carefully choosing a selection of modern, real-world problems, then seeing how they map across mathematical concepts. By doing this, only concepts useful in the real world make the cut.</p> <div class="split"> <img src="/img/case-cbm-pisa.png" alt="" class="right"> <p>Our curriculum goes beyond the innovations required in the <a href="/pisa/">PISA 2025 Mathematics Framework</a>.</p> <img src="/img/case-cbm-pisa.png" alt="" class="right__600"> </div> </div> </div> <div> <h3 class="fix-header"><span>Fix 4</span><span>Ready-to-Go Deliverables</span></h3> <div class="fix"> <p>Rather than separately specifying the curriculum and then building deliverables, building deliverables is part of our curriculum specification. Each deliverable, or module, is problem-centred, with students focusing on an overarching question that they can understand.</p> <p>Modules can be delivered with the <a href="/inside-module/">CBM Teacher Platform</a> or as <a href="/self-study-resources/">self-study</a> versions, both leading learners through the Computational Thinking Process to solve a problem.</p> <img src="/img/case-modules.png" alt="" width="569"> <p>Within the compute step, students learn to drive the computer, so coding is integral to our approach. The Wolfram Language has the advantages of being easily understandable and having real-world knowledge built in.</p> <img src="/img/case-module-code.png" alt="" width="423" class="img-border"> <p>At the end of each module, there is a final project where students independently transfer their skills and knowledge to another related context.</p> <img src="/img/case-module-project-image.png" alt="" width="423" class="img-border"> <p>Each module comes with a certificate of completion and opportunities for assessment of the CBM outcomes.</p> <img src="/img/case-cbm-certificate.png" alt="" width="357"> </div> </div> </div> </section> <section id="the-summary"> <div class="inner"> <h1>The Fix: 1-Minute Summary</h1> <h2>The Computational Thinking Room</h2> <p>Using the metaphor of a computational thinking room, we can put the fixes together: the four-step process, outcomes (across the whole process and within the process), concept learning stages, toolsets, categorisation areas and contexts. Different rooms may be customised to represent different contexts and the appropriate thinking, computation and outcomes that best apply.</p> <iframe src="//player.vimeo.com/video/452331267?badge=0&byline=0&portrait=0&title=0&player_id=vimeo_vid3106&api=1" webkitallowfullscreen="" mozallowfullscreen="" allowfullscreen="" width="100%" height="300" frameborder="0"></iframe> </div> </section> <section id="the-change"> <div class="inner"> <h1>Start the Change</h1> <h2>What can I do now?</h2> <h3>Read <span class="slide-quote">The Maths(s) Fix</span></h3> <p>The groundbreaking book that exposes why maths education is in crisis worldwide and how the only fix is a fundamentally new mainstream subject.</p> <a href="http://themathsfix.org/" class="button">Buy now</a> <h3>Campaign for change</h3> <p>Do you agree with our five main principles for core computational curriculum change (MFC5)?</p> <a href="/take-action/" class="button">Find out more</a> <h3>Role by role: Action for you</h3> <p>Whether you are a student, policymaker, parent or educator, you'll find a list of ideas to get you started on the change to modern computational thinking.</p> <a href="/take-action/#Students" class="button">Get started</a> </div> </section> </main>  <footer class="footer"> <div class="inner"> <div class="left">© 2024 computerbasedmath.org</div> <div class="right"> <a class="mail-icon" href="/form/">Get Involved or Contact Us</a>   | <a class="linkedin-icon" href="https://www.linkedin.com/groups/9083995/" target="_blank"></a> </div> </div> </footer>   <script src="/common/framework/js/body.en.js"></script> <div id ="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "WebSite", "name": "Computer-Based Maths: How to Fix Maths Education", "description": "Maths does not equal calculating. 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Making the Case for Computer-Based Maths Education