Nurturing young mathematicians

Ems Lord considers how you can enrich the maths experiences of the children in your classroom or early years setting, whatever curriculum or approach to maths you use. She discusses maths activities from NRICH – a collaboration between the faculties of maths and education at the University of Cambridge and part of the Millennium Mathematics Project.

One of the greatest challenges facing classroom practitioners is engaging children in their learning. When that lesson is mathematics, the level of challenge is easily doubled! In this article, I would like to share a range of mathematical activities which can engage and enthuse even the most reluctant learners, or those facing additional challenges to their learning. Along the way, I’ll share the thinking behind the resources and introduce an exciting new venture which encourages your learners to explore a mathematical landscape and share their ideas with a worldwide audience.

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      string(5403) "curriculum, they also contextualise maths by demonstrating its uses in practical situations. In the game ‘ Ice Ice Maybe’, students hone their estimation and approximation skills to help penguins hop between icebergs and avoid killer whale-patrolled waters. In ‘Pyramid Panic’, players must master the full spectrum of geometry skills to assist in a Mummy’s escape from his tomb. And in the fast-paced action game ‘BIDMAS Blaster’, the use of brackets, indices, division, multiplication, addition and subtraction is key to the destruction of the Roborators that run amok. Mangahigh reinforces skills through repetition, whether the students are blasting meteors or raising flowers. These games are supported by Prodigi®, the world’s first adaptive maths learning engine for key stages three and four. The games can all be used for free on the website. But for about £9 per student per year, teachers can get the ‘school package’ – which includes print out worksheets and statistics of your student’s progress. Marcus du Sautoy has criticized the British maths curriculum for shying away from more challenging concepts. There’s also a problem with how – also allow users to share ideas and resources. All the VIBE software teaches Functional Skills. Learners’ work in the virtual world can be stored – to build a personalised electronic portfolio. The VIBE also comes with an ‘editor’ – a function which allows teachers to upload tasks, resources and content into the VIBE environments. The VIBE software is updated every year to ensure it stays in line with the latest curriculum and technological developments. Government policy is demanding that practitioners become ‘facilitators’ for learning – rather than knowledge gatekeepers. The VIBE encourages this – in the virtual worlds, teachers are guides helping students find their own answers. The VIBE helps students test drive a career- to find out if they like a workplace before joining it, and learning the standards of professionalism expected from them. What’s next? A resource for the diploma in IT is scheduled for release in early 2010. Liz Forrester is the VIBE programme manager at the Specialist Schools and Academies Trust.    e-learning reports 48 Creative Teaching & Learning n Volume 1.1 maths is being presented to students. Primary school maths is adequate in part – because it uses numbers in an exciting way. But the secondary maths curriculum isn’t quite as inspiring – it’s like learning musical scales without being able to play the music. Standard teaching materials are failing to excite children about a subject that deserves their attention and can be fun. Students are bored and disinterested in the maths that will equip them for life. How Mangahigh was started I first thought of Mangahigh when I was at King.com. I watched millions of players sharpen their game-playing skills on the site, and I saw that if this same motivation could be brought to maths education, it could be a game- changer. I approached Marcus, who I had met as a student at Oxford, about finding a way to use the skills developed in playing computer games. Marcus has a track record of making maths accessible to a wider audience, through his weekly newspaper column ‘Sexy Maths’ in the Times. Marcus immediately saw Mangahigh’s potential because, like many parents, he had observed his son’s dedication to games on the internet and on the PS3. Marcus agreed to help us develop games where challenging maths is an integral part of the package. Now the Chairman of Mangahigh’s Board of Advisors, he is an important source of inspiration and thought leadership for the company. We were convinced that a key to getting students excited about maths was to present it in an entertaining way. We knew the game had to be commercial quality. We gave Mangahigh its manga theme in homage to the style of Japanese illustration that is so popular with teenagers at the moment. Case study: Featherstone high school Mangahigh is now beginning to see quantifiable results. At Featherstone high school in Southall, London, a group of 90 year nine pupils of mixed ability recently used Mangahigh over a two-week period. Before the study, the children spent an average of 3.5 hours per week on maths at school and home. Those same students reported studying four hours per week during the case study. Their confidence rose and 85% improved their maths skills using Mangahigh. About 93% said they would enjoy maths more if they regularly played the games on our site. “ T h e r e s p o n s e h a s b e e n overwhelmingly positive,” said Neil Bradford, Featherstone’s deputy head and head of maths. “The blend of gaming technology with the learning and re-enforcement of mathematical skills is quite superb. The product has proved hugely popular with students, many of whom have been lured into answering more mathematical questions than we could ever have hoped with a textbook approach.” As the most diehard gamers at Mangahigh say: the only way to achieve the high score is by doing the maths. Toby Rowland is the CEO and founder of Mangahigh.com, the first curriculum-compliant maths games site for 11-16 year olds.  "
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Creative Teaching & Learning

Technology and learning

5 Apr 2010

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      string(5663) "“Over the past decade there has been virtually no improvement in learning outcomes from students in the western world…”World Class – How to build a 21st-century school system. Andreas Schleicher 2018.The shocking statement made last year by Andreas Schleicher from the Organisation for Economic Co-operation and Development that there has been virutally no improvement in learning outcomes from students in the western world over the past decade must not be ignored, but instead seen as a call to arms. Transforming education to meet contemporary needs means reimagining schools, and reimagining the environments in which learning and teaching take place.   Pioneering Italian educationalist, Louis Malaguzzi, famously described the classroom as the “third teacher”; evidence from around the world establishes the link between the design of the spaces in which young people learn and better learning outcomes.School designs have a great impact on our lives. 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What form should a staff room now take? And, if there is a wider and more diverse range of learning experiences instead of a teacher simply dictating information from the front of a class, what shape should a classroom, studio or learning space be?But this is not a book about pie-in-the-sky design that polishes architects’ egos and leaves teachers wondering why they are delivering a Year 6 maths lesson from a sandpit.Using recent and inspiring real-life examples, the book sets out to show how designers and architects can engage teachers and schools in the design process, to help them meet their educational vision. Importantly, it shows how organisations, for example the West Thornton Primary Academy in London, UK, have accomplished this on a limited budget. Drawing on the latest research, the book looks in depth at the importance of getting the basics right: fresh air, good light, heat and acoustics make the environment optimal for learning.Tackling the whole span of the school experience from preschool to vocational college, the authors also explore how well-designed school environments can create a sense of belonging, engage pupils, encourage new ways of working and foster creativity.Taking inspiration from the ideas of the famous Rosan Bosch Studios in Copenhagen, Denmark, the book looks at how the design of early learning spaces has the potential to change behaviour and encourage interactions, learning, activity and play.The authors also remind architects, designers, teachers and other key decision makers how they can prioritise the integration of indoor and outdoor space, even when that may appear to be a design challenge – in multi-storey buildings, for example.Meanwhile, the importance of the interaction between furniture, technology and the learning space is highlighted. Personalised learning requires an end to traditional desks and tables in a row for a more dynamic and adaptable approach. 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Learning Spaces

Planning Learning Spaces: A New Practical Guide For Architects, Designers And School Leaders

13 Mar 2020

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      string(5731) "The Cultures of Thinking (CoT) framework was developed by the Project Zero team at Harvard University. The framework focuses on eight cultural forces that exist in classrooms: expectations, language, time, opportunities, interactions, environment, routines and modeling. These forces, according to Dr. Ron Ritchhart, the Principal Researcher for the CoT project, exist in every classroom, whether they are given attention or not. The idea is to properly leverage these forces so that classrooms become places where thinking, collaboration, independence and deep-learning rule and become common-place, rather than teacher-centred places that are ruled through stress compliance and work.Harnessing meaningful opportunities is a crucial part to creating a Culture of Thinking in a classroom. As Ritchhart points out, “the opportunities that teachers create are the prime vehicles for propelling learning in classrooms” (p. 144). If planned properly, opportunities can be engaging, thought-provoking, and fun for students. This article will focus on the application of the forces of opportunities in the secondary classroom. Although many of the examples will focus on maths and science, the core principles that are drawn from these examples can be applied to any classroom. In past years, when covering the concept of unit vectors in IB DP Math SL, the lesson would go something like this:Tell the students that a unit vector is a vector of length one, and demonstrate the proper notation.Show them the procedure, or ‘recipe’ to find a unit vector.Have them work independently to find unit vectors given several vectors.Show them how to use unit vectors to create parallel vectors that have the same directions, but different lengths.Show the students the tie-in to motion of objects that have a constant velocity.When covering voltaic cells in IB DP Chemistry 1, the lesson would go as follows:Lecture about the parts of the voltaic cell, how to construct one, and give examples of voltaic cells used in their daily life.Give a lab hand-out and go over the steps to construct a voltaic cell. Have students perform the lab and compare their results to theoretical results.Have students practice drawing voltaic cells, including labeling the parts of cells and predicting electron flow. The maths lesson and the chemistry lessons both went well in terms of test performance. The students could do the maths problems as long as they were scripted exactly like they had been in class, and chemistry students were able to successfully construct voltaic cells.As we began to have discussions about the CoT framework, we really started to think about these lessons and the impact that they had on student thinking. As we reflected on our teaching, we pondered the questions in Table 1 and realised that with a bit more planning, we could provide richer opportunities that provoked deeper thinking. As far as the opportunities, the students had to repeat back very cookbook-like tasks that they completed exactly the way they were shown, as though we were the sages who knew the content better than they did. The tie-in to real life applications in particle motion and batteries was prescribed and told to them. Their thinking was not stretched or pushed, and even though “it is what students are actually doing mentally that matters” (Ritchhart, p. 144), the students were mentally just doing surface-level learning. They demonstrated an ability to perform these skills, but only in familiar situations – and they were only assessed in familiar situations.Table 1: Key questions related to the Opportunities forceOpportunities key questions: 1. How did I ensure that rich thinking opportunities are woven into the fabric of my teaching and that students aren’t just engaged in work or activity? 2. How did I provide students with opportunities to direct their own learning and become independent learners? 3. How did I take pains to select content and stimuli for class consideration in order to provoke thinking? These questions are adapted from Creating Cultures of Thinking: The 8 Forces We Must Master to Truly Transform Our Schools, pp. 324-325What can be changed? The answers to the questions in Table 1 are exciting because there are potentially infinite ways to accomplish deeper thinking. The beauty of implementing a Culture of Thinking in a secondary classroom is that you can decide how much to change at any one time. We decided to use the key questions in Table 1 in order to leverage the opportunities so that the students were doing the critical thinking and driving the lesson. After pondering these questions, and revising and revisiting them for several iterations, here are the ‘new’ lessons:The new maths lesson:1. 	The students reflected quietly for 5 minutes using the the ‘Think-Puzzle-Explore’ routine to start their thinking on naming vectors and how to find the magnitude of vectors. During this time, students used their math resources – textbooks, phones, computers – to look up anything that they couldn’t remember about vectors. Students know that using these resources is encouraged.2. 	After the reflection time, we moved the desks in pairs, and the students then did the MicroLab protocol to discuss their findings from think-puzzle-explore. The MicroLab protocol has one student talk for a set time while the other student listens, then after the set time the roles flip. After both students had a chance to talk, they had a few minutes for open discussion about any remaining questions or ideas.3. 	This led to the guiding"
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Cognition and Intelligence

Cultivating a Culture of Thinking

10 Oct 2018

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      string(5725) "XXVIIWINTER2006BoardGAMESSchools are embracing interactive whiteboards andstudents are reaping the benefits from new software,says DUNCAN MCMILLAN, who looks at how oneaward-winning company is bringing a new dimensionto maths through interactive games designed speciallyfor interactive whiteboard useXXVIII WINTER2006The days of the blackboard arebehind us, and teachers nostalgicfor chalk dust and flying boardrubbers are having to adapt prettyquickly. Interactive whiteboards aretaking over the classroom and softwareis rapidly being developed to make themost of these new tools. With tens ofthousands of UK schools now using them,interactive whiteboards aren’t simplycool classroom gimmicks – they arechanging the way we teach.A TES report in February this yearhighlighted the huge amount of moneybeing spent on ICT resources. Primary andsecondary schools spent over £400 millionbetween 2004 and 2005, dwarfing the£150 million spent on books over thatperiod. The ICT spending figure doesn’teven include computers, so where is themoney being spent?According to technology marketresearch firm Decision Tree Consulting(DTC), much of it goes towardsinteractive whiteboards and projectionequipment for classrooms. Seniorconsultant Colin Messenger describedthat huge growth: “When we startedtracking the market [in 2001], 11,000units were being sold in the year. Lastyear 100,000 units were sold – and no-one just buys a whiteboard, they all buya projector, they’ll all have it installed.The average they pay is £2,200pounds.”This means that over £200 million wasspent last year on electronic whiteboardequipment. In fact, the UK market forinteractive whiteboards is the biggest inthe world. As Colin Messenger says:“We’re way ahead of anywhere else inEurope and we’re ahead of America,even though they’ve got about five timesas many schools.”ApplaudThe enthusiasm of UK schools for thesenew technologies is certainly somethingto applaud, and Britain’s largestproducer of interactive whiteboards,SMART Technologies, has seen globalsales grow by two-thirds since the startof 2005. However, interactivewhiteboards are just expensive wallhangings without good software to runon them – something that educationalsoftware publishers are beginning torealise.Many new companies have sprung upin recent years to cash in on the growthin schools ICT and the money spillingout of the Government’s enthusiasmfor electronic teaching methods. Onesuch company is Whizz Education,which started up at the end of 2003.The company emerged from CreativeDirector, Ron van der Meer’s longbackground in pop-up books. His newdirection took the interactive elementsof those books and applied them tomaths education by using animatedgames. Since 2003, Whizz Educationhas released eight different Maths-Whizz teachers’ resource year packs –all built around the principle, accordingto Ron van der Meer, that the animatedexercises allow the student to ‘learnwithout thinking they are learning’.Earlier this year, Whizz Educationrecently won a prestigious BETT awardin the ‘Maths Key Stage 1 and 2’category, which hints that thistechnique of ‘education by stealth’might well be catching on.Developed in conjunction with leadingeducationalists Steve Mills and Hilary Koll(who were recent Overall ExcellenceAward winners at the Basic Skills BookAwards), the Maths-Whizz teachers’resource follows guidelines set by theNational Numeracy Strategy. Thesoftware combines interesting animatedexercises that enhance learning, with aclear objective based guide for teachersstraight from the National NumeracyStrategy. Each pack contains a documentwhich maps every lesson to an objectivefrom the National Numeracy Strategy. Ithas been designed to make it easy forteachers to see where they can findresources and save time on lessonplanning.Capturing attentionThe interactive exercises work well atcapturing the attention of an entire class,especially when used with an interactivewhiteboard. The software was also thefirst product to get official accreditationfrom the UK distributors of SMARTBoards, Steljes Ltd. Catherine Howard ofSteljes describes the software as: “…idealto use on a SMART Board. Its vividanimation used in conjunction with thefunctionality of the SMART Board toolsenhances the teaching of maths in anyclassroom.”Whizz Education has found thatschools buying their teachers’ resourcesare suddenly finding something to runon their under-used interactivewhiteboards. Jill Green, of CherrywoodCommunity Primary School, says: “Maths-Whizz gets the most out of ourwhiteboard. 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Digital Learning

Board Games

24 Jan 2007

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      string(5641) "As we returned to school and undertook the latest exciting chapter on our journey into pupil focused independent learning, I was left wondering why more schools aren’t engaging with this agenda. At a time when Government and Ofsted are telling schools that there isn’t one formula that they are looking for, surely we should be breaking away from the “delivery of a knowledge based curriculum” to an approach where teachers engineer opportunities for deeper learning and where children lead their own learning and have an investment in their learning. This is an approach, which we have gone for as a leadership team and the transformation for us as a school and for the children has been staggering.If I were to ask whether you would prefer to be involved in something that affects you or have it done to you, then I know how 100% of people would answer. Yet we used to deliver a curriculum to children rather than see them as integral to leading their own learning.At St Nicholas we have given every one of our learners the right to be involved in their own learning and it has seen us go from a Requires Improvement judgement in December 2013 to Outstanding in March 2016. The pupils at St Nicholas arrive in school with the same range of skills, attributes, challenges and backgrounds as most other schools with nearly 10% of the school population coming from the Gypsy, Roma, Traveller community, which enriches our school still further.We made a decision as a staff some time ago, that regardless of the learning challenges that children face, all children can learn and we set ourselves a target of 100% 2 levels progress in all three subjects. In 2015 we achieved this and went on to achieve at least 50% in each of reading, writing and maths for more than expected progress. Our children’s baseline in Reception has traditionally been low and therefore progress is the currency which we work in. If we can make enough progress, attainment will look after itself!In the depths of despair as most RI schools will know, we looked for someone to help us to build on the progress that we knew we were making and decided to work with Bill Thompson. Bill has a wealth of experience and set up the highly successful Tipton Learning Trust in the West Midlands. He’s keen to reference the work of Dylan Wiliam, Paul Black, Carol Dweck and Shirley Clark as people who have strongly influenced his philosophy for effective learning. Having worked as a School Improvement Adviser in Birmingham and Sandwell, as well as regularly conducting training for senior leaders and Ofsted Inspectors regarding school improvement, he’s keen to stress in all his training that leaders should run schools according to what they believe in, doing what they think is important and not just for Ofsted. He is also very different in that he goes into class and team-teaches, showing teachers and school leaders what he talks about, in practice, in the classroom, with the children. He has real credibility.Our first task was to set about developing a growth mind-set in our pupils and move away from the fear of failure and the fear of making mistakes, which the children often imposed on themselves. We developed a language of incremental growth in learning and the use of the word YET. “I don’t know how to do this YET!” In fact the children often chime this to each other if they say, “I can’t do this.” But it is also about building a growth mindset within the staff and giving the staff the ability to be open an honest about their mistakes and what they can do to improve. We decided that those who failed to be open about their errors, who saw them as private barriers, who lived in a culture preoccupied with blame – will NOT see mistakes as learning opportunities. It was clear that their effectiveness, both with pupils and staff, will slowly, imperceptively, become severely impaired. The children now proudly display “My best mistakes – and what I’ve learnt from it!” on the classroom wall. There is no failure only learning opportunities.This approach, combined with an understanding of James Nottingham’s Learning Pit (http://www.jamesnottingham.co.uk/learning-pit/) means that children know that learning is a process and takes time and for deep learning, there will be struggle.  However they also know that the struggle is worth the effort and that their learning will benefit from the greater challenge. Lane Clark (http://www.laneclark.ca/) has a lovely phrase as she talks about children going from “strength to struggle!” If we want deep learning we have to develop the resilience in our children, to fight for it and for many children, particularly in challenging contexts, the development of resilience is a platform, which has to be in place before learning can be built. Bill Thompson also refers to the work of Daniel Willingham, Professor of Psychology, University of Virginia, by saying that pupils remember what they have been thinking about, so if you make the learning too easy, pupils don’t have to work too hard to make sense of what they are learning and, as a result, forget it quickly. Unless pupils are put in positions where they are struggling to make sense of what they are learning, little knowledge is likely to be retained in the long term.  With an understanding of a growth mind-set in place, we asked the children to become more active in lessons. 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Family

Giving pupils the green light! Improving outcomes for all pupils through independent learning

16 Oct 2017

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