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The Power of Stories in Learning Mathematics

14/12/2020

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by Ioanna Georgiou 
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As a maths teacher of more than fifteen years or so, I have been encountered with the questions “why do we do this?” and “how is this useful?” a few too many times to ignore.


The questions are more than fair: the mathematics taught in school was discovered (or invented, depending on your philosophical inclination) several centuries ago. The mathematics used behind the scenes in our increasingly technologically advanced lives are nowhere to be seen in school. So indeed, why and how?
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School mathematics forms the basis of more advanced concepts and of course without the fundamentals it is impossible to go any further. Hence it is out of necessity that this is what is taught in school (in terms of content — not approach). This fundamental part of mathematics, albeit now very old and simplistic in a sense, was of course once the cutting edge of what was going on.
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Many years ago, as an undergraduate student of mathematics, I came across a most wonderful novel called “The Parrot’s Theorem” by the French author Denis Guedj. In this seemingly ordinary novel that starts with a fire at a house and a subsequent death of its (mathematician) owner, the reader does not know whether the fire was an accident, a murder or even a suicide. The mathematician had incidentally shipped his entire library of maths books to his friend in Paris; devastated by the loss of his friend, and determined to find out whether there was a connection between the death and the shipment of books he had received, he summons his extended family and together they go through the books. That’s where the author essentially embarks the reader on a journey through maths.


Seeing mathematical ideas emerging in their local societies through practical needs as well as intellectual curiosity was eye-opening. Everything suddenly started falling into place for me, an adult undergraduate maths student. And then it occurred to me: if this is helpful for me, a person already quite into maths, maybe it’ll help people who feel alienated by the strict and abstract symbolic form. A form lacking any sentiment — apart from maybe fear and anxiety.
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I took modules on the history of maths, expanded my own readings, and during my MSc and MPhil studies I continued to look into educational approaches through the history and local practices such as ethnomathematics. As a practitioner, I use those stories in my teaching. I have also been presenting masterclasses and workshops on “stories from maths” for the Royal Institution of Great Britain and also independently. It is highly satisfying to see the students’ faces lit up when they realise the reason why calculating in fives and tens is so easy: it has always been with them, their own personal abacus — their fingers! Or that the peculiar number 360, (who would have chosen that number to describe the degrees in a circle!) is nothing but a nicely (albeit strictly speaking wrong) rounded version of the days in a year.
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This experience has culminated in the writing of my first nonfiction book for children, entitled “Mathematical Adventures!” Through this book I aspire to give learners a glimpse of how it all started, and how it progressed, making some stops to times and events that were rather seminal. Tarquin Group, a publisher that specialises in educational and recreational mathematics books was supportive from the beginning and showed real faith in the book.
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The content has been thoroughly trialled for many years. The students’ answers to my questions and their own questions have given shape to the stories that made it through; distilled, concise and relevant, there are lots of connections with what they see in school, alongside some more recent maths that did not make it through the curriculum such as Euler’s graph theory or Cantor’s mind-bending multiple infinities. Euclid’s postulates leading to all the school geometry are fascinating and could not have imagined them coming more alive than in Asuka Young’s illustrations. Her amazing interpretation of these stories from maths have made the book a colourful adventure which I hope many students, parents and teachers alike will enjoy to embark upon!
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Ioanna Georgiou is the Head of Mathematics & Head of Academic Enrichment at St James Senior Girls’ School, London. She is also a Masterclass Presenter
at The Royal Institution of Great Britain.

Buy Mathematical Adventures here: https://www.tarquingroup.com/mathematical-adventures.html
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Improving Educational Outcomes through Publishing Young People’s Work

10/12/2020

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Jude Williams, Chief Executive of The Literacy Pirates shares how they make a transformative impact on the literacy, confidence and perseverance of young people so that they can achieve both at school and in the world beyond.
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The Literacy Pirates works exclusively with young people who are both falling behind at school and have fewer advantages in their personal circumstances. Did you know that in the UK your socioeconomic background is still the greatest determinant of your educational success? In fact, two in three children living in low-income households in the UK fall below the expected levels in reading and writing by the age of 11. This attainment gap widens further as children transition from primary to secondary school. This results in low self-confidence, slower progress, and a bleak long-term outlook.

This intractable social challenge lies at the heart of The Literacy Pirates reading and writing intervention.
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The Literacy Pirates learning programme is a year-long, after-school learning programme devised and led by teachers. During the weekly session children aged 9 to 12 years old work to improve their reading and writing skills, as well as increase their confidence as learners and ability to persevere and keep on going when things get tough in the classroom. We work exclusively with children referred by their school, who identify children who are both falling behind in their educational attainment and they know have fewer opportunities outside of school. By working with teachers, we access children we couldn’t otherwise reach and we are assured they are the right ones who really need our help.
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We have embraced being a venue based, out of school and intense programme by setting the learning programme in a fantastical environment with murals, decking, a Pirate’s cat and secret passageways. The children are given adult volunteer support while a qualified and experience teacher leads the session. And importantly, we know children learn best when working towards tangible, published projects, so each term the young people create high quality published books, films and apps.

Established in 2010, we have worked with 720 children on our intense programme offered in Dalston, Hackney. We are confident in the difference we can make because we have an excellent track record. On joining us at age 9, children are on average 13 months behind their peers; and 24 months behind when they join at age 11. We close this gap by improving their reading age over 50% faster than age-related expectations. Furthermore, 100% of Young Pirates who say they don’t enjoy reading for pleasure at the start of the programme have changed their minds by the end. 95% of parents saw an increase in confidence; and 78% of teachers saw an increase in perseverance in the classroom.
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As an organisation we have now decided to replicate that success in other London boroughs and are working to reach 800 children annually by opening an additional three learning centres or Ships. The first of which opened in January this year in Tottenham, Haringey Pirates. It is an exciting phase of growth in which to reflect on what makes the difference; through all the joy and fun of a learning programme on a Pirate's Ship what actually drives the impact that we see happening through the learning programme?
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Our founder was a teacher and the programme devised by teachers. It was designed to align with schools’ goals, working to compliment teachers work in classroom, but not duplicate. We thought carefully about the different elements that we believe drive our impact. One of the central aspects of our Learning Programme is the creation of published projects; books, films and apps that showcase the creative writing of the children.
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Publishing the children’s written work is both motivating and confidence building.

We work for a full year with children, it’s an intense two-and-half hour weekly session. Every term they will produce just two pieces of writing that they have worked really hard to refine. The theme is always close to home, building on who and what they know and love. The learning comes in the process of writing a piece that requires drafting and redrafting. As you can imagine the fatigue can be real for children to go back over their work again and again. That is where the carrot of publishing their work comes in. ‘Let’s work hard on this, because in a month you are going to have that piece of work published in a book and show it off to your Headteacher’ or ‘Keep going, it will be worth it when you hear yourself speak those words on the big screen at the cinema next month’. School often works on delayed gratification, where the reward for hard work comes at the end of the year as a single result or even exam results at the end of a school career. Publishing children’s work, in our experience, gives them immense motivation in the here and now to put in greater effort.

Publishing the children’s writing also boost confidence. Receiving a copy of a high-quality printed book, with your work, name and this year we included photo is massive! How many of us can boast at being published authors or film screen stars! To make the most of this confidence boost, we put on a celebration event every time we publish their work. We invite parents and carers, teachers and Heads as well as local community leaders and funders. These events are a chance to mark the hard work and achievement of the children. In our spirit of being relentlessly positive, the children perform and speak about their achievement, we have our teachers reflect the journey to date and because we are Pirates, we always play a game or two.

The overachieving sentiment at The Literacy Pirates is relentless positivity. We are not much into failure. Though as teachers we know it has a place in education, we are working with children who are not experiencing success in school as other children might. When you have experienced success regularly, finding the energy to keep going and handling set-backs comes more easily. For those that do not experience success regularly at school, it’s much harder to find the confidence and grit to give it ago. That’s why published projects are a key part of learning programme; they allow the children to experience being motivated, achieving success and being appreciated in a genuine way for that achievement.
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There is another element to publishing the children’s work which is that it gives us an opportunity to talk about the full cycle of learning and how it feels to succeed. Talking about how we learn, metacognition, is increasingly understood as key to improving outcomes for children at school. The extended time taken over writing projects at The Literacy Pirates means the children experience planning, drafting, redrafting and experiencing success over a term rather than squeezed into a lesson, day or maybe a week. It gives them time to actually experience and reflect on each aspect as it takes place — the excitement at having an idea, the confusion at planning a story, to surprise at creating an interesting character, the exhaustion of working hard at redrafting, the delight and satisfaction at seeing your own work published. We use a Pirates Log at the end of each session to write down What Went Well and what could be Even Better If’s. We challenge the children to think about the extent of their effort over the session, asking them to be honest and reiterating what normal effort looks like compared to intensive effort or at the other end of the spectrum, ‘just showing up’.

Key things to consider with published projects:

  1. Quality needs to be really good. Investing in good design and expensive production is important to create something to be treasured for a lifetime.
  2. Taking your time. Allow the process of creation as well and the moment of accomplishment to be given time and space it deserves.
  3. Make it relevant. Using a recording studio, putting a film on at the cinema plays into popular dreams of success. Making the themes relevant to children’s lives also adds a dimension of ownership and pride.
  4. Co-create. Give the children an opportunity to input into the production process — decide on the name, maybe even design elements. Let them write the introduction to the book, give the blurb for the film or write the instructions for an app.
  5. Celebrate, celebrate, celebrate. Make sure the ‘published’ part means getting exposure as far and wide as possible and that the accolades pour in.

Like all educational programmes we are complex in nature; weaving together different physical aspects, pedagogical instruments and psychological processes. It took two years to create the focused programme we know today and another two years to develop a Theory of Change and the right measurement tools to monitor the outcomes. No doubt the next two years of replicating our success, will teach us a lot about ourselves too. And we are looking forward to learning those lessons.

A Case Study

Tayo was referred at age 10 to the programme to give him a boost in literacy as he was attaining below age-related expectations. Although he was engaged in the programme right from the start, in sessions he was often very shy and did not like speaking in a group or performing.

By the end of the year, Tayo’s session leader reported an “explosion in confidence”, which was backed up by his teacher and parents. His teacher said “Tayo has really come out of his shell this year and is a visibly more confident boy”. Both Tayo and his parents mentioned that he was no longer afraid to talk in front of a crowd.

During the programme Tayo’s reading age increased over two times faster than age-related expectations giving him a reading age of well over 12 years old. His teacher told us that he was “back on track” at school.
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Tayo told us that before Hackney Pirates “I wasn’t really doing really well. But now I am confident and better at reading and writing.”
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Website: www.literacypirates.org
Twitter: @LiteracyPirates
Instagram: literacypirates
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Strategic planning is dead, long live strategic agility!

1/12/2020

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How can we bring about whole school improvement using agile strategy? Tim Logan reports

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​Nonna Nerina is the world’s first agile grandmother! In the stunning Italian countryside, Nerina used to run pasta-making workshops from the kitchen of her villa. When lockdown hit, she had to cancel all of her classes. However, with the help of her granddaughter Chiara, Nerina took her pasta making online to keep her business going, and now uses the proceeds to provide meals for children in need! https://nonnalive.com/

Whether it’s companies pivoting suddenly to start making PPE, businesses like Nerina’s adapting to new ways of engaging with customers, or multi-disciplinary teams collaborating to deliver new products or services (such as vaccines) in previously unimaginable timeframes, the language of agility is everywhere. So many people around the world now understand “agility” in visceral ways — the energy, stress or emotion of responding quickly to rapidly changing circumstances. Whether this is the loss of a job or business, new restrictions on our movement or, for so many, the tragic death of a loved one.

What less people realise is that for more than two decades, there has been a growing community of Agile professionals for whom personal, team or organisational agility is their daily concern, and their bread and butter! People who know deeply that ‘the work of change, is the work of changing’ (Steve Peha). And furthermore, they have learned through thousands of transformative successes and spectacular failures that, to create lasting adaptive change in organisations, we need to build rapid learning and deep collaboration into the DNA of the way we work.
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And the evidence speaks for itself. The reality for companies that have embraced this new way of working is that they have not only survived the challenges of the pandemic but thrived. As Jeff Sutherland highlighted in a recent keynote, while thousands of non-agile companies faced bankruptcy in the first half of 2020, agile companies such as Pegasystems, Amazon and Tesla prospered. MIT Sloan Management Review also predicts that only 17% of today’s leading companies will be leaders 5 years from now. The companies that will remain leaders ‘including organisations like Apple and Alphabet continually find new sources of competitive advantage by reinventing their businesses and adapting to evolving market conditions.’ (MIT Sloan Management Review Research Highlight January 09, 2020)
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But what does this all have to do with schools? Well, certainly our schools, leaders, teachers, parents and students have had their fair share of recent and radical changes to which they have had to adapt! But also, learning is our business (isn’t it?!). So surely schools should be some of the most agile organisations in our societies! Hmmm…?

Unfortunately, too often our schools have been governed and structured by the idea that learning is what the students do (if we’re lucky!). And although many schools have increasingly embedded professional learning into their systems, the fact that the organisation itself should be given its own opportunity to learn through regular cycles of action, reflection and adaptation still sounds like an idea from another century!

And yet our schools have learned and adapted at unprecedented speeds in recent times, many incredibly successfully. So, as we take a moment between crises to pause and reflect, we should ask what can schools learn from recent experiences that will help us to be more agile in future? What will help our communities — our students, staff, parents and leaders — to be resilient and well-prepared to thrive in a post-pandemic world of no normal?

“There is no such thing as a new idea… We simply take a lot of old ideas and put them into a sort of mental kaleidoscope. We give them a turn and they make new and curious combinations.” — Mark Twain

One thing that we have learned as school leaders is clear. Old ideas like the ‘5yr strategic plan’ became largely irrelevant overnight! The glossy 50-page brochure of good intentions has been thrown from the window of the speeding bus, as we swerve and struggle to stay on the right road (not even completely sure which is the right road!).

Even before the challenges of the pandemic, school leaders had already begun to question the traditional strategic planning process. Setting themselves a barrage of carefully-worded whole school improvement targets for years into the future, after a six-month process of community consultation seemed for some like a lot of work for not a lot of added value. As Ewan MacIntosh has highlighted, school directors know full-well that barely 20% of such targets are ever fully achieved. Even the yearly school improvement plan, written too often in detached senior leadership offices, was beginning to feel like an annual administrative obligation rather than the authentic collaborative work of changing!

So, when our systems no longer make sense, (as Will Richardson loves to ask) why do we persist with them? Instead, perhaps we need a ‘new and curious combination’ of ideas, connecting our very real need and desire to improve (or perhaps transform!) our schools, with what we’ve learned about successful agile strategy in other sectors.
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According to McKinsey & Company (2018) among the most important characteristics of an agile organisation are:
  • A shared purpose and vision — having a clear “North Star”?
  • Opportunities for continuous learning and igniting people’s passion.
  • Networks of empowered teams with opportunities to shift roles, rather than rigid hierarchies of fixed positions.
  • Experimentation and entrepreneurial drive is actively encouraged.
  • Systems and processes are characterised by visible work-in-progress, action-oriented decision-making and rapid learning cycles.
  • Active partnerships are encouraged with the wider eco-system.
  • Shared and servant leadership across the organisation.

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In fact, this isn’t so far away from ideas that have been around since the 1990s of the school as a ‘learning organisation’ (Senge, 1990). Just looking at the OECD’s work on this in 2016, shows very clear alignment with these attributes. Such a school would have:
  • A shared vision centred on the learning of all students.
  • Opportunities for all staff to engage in continuous learning.
  • Team learning and collaboration among all staff.
  • A culture of inquiry, innovation and exploration.
  • Systems for collecting and exchanging knowledge and learning.
  • Opportunities to learn with and from the external network and partners.
  • Learning leadership growing throughout the organisation.

This certainly sounds like the kind of school that most of us would love to work, learn and grow in! But the million-dollar question is, how do we get there?


We can certainly learn from the successes and challenges of others charting courses into this new territory already. There are some fantastic and innovative educators and entrepreneurs around the world making these connections real already in classrooms (with EduScrum, Leysin American School’s Edge Program and L-EAF) and whole schools (Blueprint, Agora, Learnlife).


But what we have also learned from ‘agile transformations’ in other sectors is that if you’re waiting until you think you’re fully ready to make as start, it’s already too late! The agile mindset encourages precisely the kind of attitude we have needed to ride the recent turbulence of the pandemic — plan, act, reflect, adapt in short cycles. So here are a few ideas that you can consider testing out in your school:
  • Start small with a Kanban board up in your team workspace or classroom. This can be used to identify your “To-Dos” to meet your team or class learning goals (in the left column — of three), what you’re working on together right now (middle column) and what’s met your ‘Definition of Done’ — agreements of quality and completeness (right column). Key aspects of this are that the work becomes visible, team members are held accountable by regular check-ins on progress (called ‘Stand-ups’) and adaptation is enabled by the frequent reflections on progress and close collaboration.
  • Ready for something bigger? Look for ways you can encourage more cross-functional teaming across your school. Grade level teams or subject department teams may be commonplace — though the depth and quality of collaboration within them will certainly vary! But what about trying to gather people’s energies around cross-cutting ‘projects’ — such as, redesigning the way a particular space is used, or developing specific aspects of teaching and learning? Again, these are not necessarily new ideas (remember the PLC?) but keep them agile by building in visibility, accountability and intentional cycles of reflection and adaptation.
  • You really want to go for it in a big way?! Replace your outdated strategic planning process with cycles of ‘Strategic Doing’. This is a very well-structured and dynamic process designed to help to address strategic (but complex) opportunities — such as, school improvement. Ed Morrison and his team at the Agile Strategy Lab have developed it in partnership with many universities across the US and have seen it have a huge impact on enlivening and re-energising communities and organisations to overcome significant barriers to progress through ‘action-oriented collaboration’.

There are lots more ways to get and stay agile as we look forward to a post-pandemic world. So do get in touch if you would like to know more. There is also a growing ‘Community of Practice’ around Agile in Education on LinkedIn (and other social media platforms) that I would very much encourage you to investigate further. Lastly, do check out the Agile Research Consortium (https://www.arc-for-schools.org), who are gathering resources as they emerge to support these positive transformations.
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Tim Logan is a consultant and principal supporting schools around the world to drive improvement and evidence-based innovation through advisory, change management and training services.
Website: www.futurelearningdesign.com
Email: [email protected]


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