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Confession.
I’m an English graduate, an English teacher and a Let’s Think English Tutor. Whether by nature or nurture, it is the study of the humanities that has caught my interest and driven my learning. I have come to know that the discipline of geography straddles the divide of the sciences and humanities: to me a powerful relative unknown. We hear that interdisciplinary synthesis is what we will need to solve the complex problems we face in the world like climate change, then I find myself invited onto a project team developing the first small suite of Let’s Think through Primary Geography lessons for Year 5 and 6 pupils.
Before the team of Let’s Think tutors, teachers and geography specialists met, I was invited to read through some early drafts of lessons on maps and scale. A human story had been used to invite children into the journey, scaffold their understanding and their manipulation of variables. Michael Walsh has written with clear insight here on the importance of story to focus and scaffold learning here. But, I have to admit, my mind would not be persuaded that these problems helped me to better understand the human condition. The questions about scale and distance still seemed like maths in disguise.
The question of run-off and relevance
Some of you may have read Stuart Twiss’s blog documenting the birth of our small but perfectly formed Let’s Think through Primary Geography project. I was there for those ‘run-off’ experiments with a watering can: 6 foot plus of Stuart, like the Big Friendly Giant, simulating light, intense and intermittent rain on compacted, aerated and vegetated surfaces; on flat and sloping ground. He asked us to use the same expert language back to him – establishing a shared language code for the model that we would then ask children to think about. Once these concrete variables were established, so enters the weasel question of cognitive conflict:
“How much run off will there be?”
“Well, it depends...”
“On what...?”
And so pupils began to share their awareness and socially construct their understanding of the interplay of variables and complex relationship of rainfall frequency, intensity, gradients and the compaction and saturation of the earth. See – not easy. This was more than fun with a watering can. The cognitive stretch was tangible in the ensuing reach for connectives, ‘and’, ‘also’, ‘as well as’, ‘if’ and ‘when’.
Let’s Think programmes endeavour to be relevant to the curriculum and to pupils, whilst they stimulate that sweet spot of progress in reasoning that we believe as their teachers will be of wider, general benefit to them in life, not only in geography.
Reasoning about the variables leading to run-off is an important step towards understanding what contributes to flood risk and eventually abstract modelling of reduction of those risks.
So we knew it mattered to our educational purpose – did it matter to the pupils?
It seems it did. Our observers fed back that in a lesson busy with activity, small group discussion and props, every single pupil was focused on the task and on their small group dialogue. In a socially and cognitively ‘noisy’ task like this, pupils’ attention could easily drift but it did not. In the bridging discussion at the end of the lesson, when asked if they could think of a situation when there had been too much run-off, the groups did not find it difficult to generalise to incidents of flooding locally and nationally. When pupils then moved to smaller scale models with trays, sponges and jugs of water in class – there was still a clear sense that slowing or reducing the run-off mattered. Moreover, teachers were asked ‘When can we have another Let’s Think Geography lesson? And told ‘That’s the best geography lesson we’ve ever had.’
From collaborative reasoning to action
We had been rigorous in checking relevance not only to the current National Curriculum Programme of Study for Geography but just as/more importantly (select your preferred determiner) the United Nations Sustainable Development Goals (SDGs) and in particular how they have been translated into the SDG Learning Objectives guide for educators developed by UNESCO. UNESCOs objectives for each SDG have three domains: cognitive, socio-emotional and behavioural. Cause and effect reasoning with manipulation of an increased number of variables was clearly cognitive. The Vygotskian social constructivist engine ticking in all Let’s Think lessons to an extent helped us to meet the socio-emotional domains in that learners would collaborate and develop understanding with others. Our Piagetian progression spine would encourage gear shifts over time from a personal, to a group, a local even a global perspective. We did seriously wonder whether this progression would be possible for our age 9-11 year group within just a few lesson episodes. And finally, the behavioural domain. The UNESCO objectives set the challenge that education in each SDG should promote not just thinking, but action. Action in favour of those who are most threatened by climate change. Action through the promotion of climate friendly activity, choices, even policy.
Achieving improved collaborative reasoning, applied to increasingly wider frames of reference with a sense that increased agency would lead to informed action really was demanding more from us as Let’s Think teachers and tutors than before.
Then came the T-shirts.
Supported by the experience and insight of Dr Verity Jones, Associate Professor of Education at the University of the West of England, our next cycle of lessons started with a pile of second-hand t-shirts. We moved from:
- selecting and classifying what makes a ‘good’ T-shirt from the pile (it’s a nice colour, we like the logo, it’s softer);
- to understanding and representing the waste (in energy and materials) in a linear fashion economy;
- to effortfully envisaging how circular processes could be introduced into the t-shirt industry as they have been for paper.
After two intense hours of socially situated mental activity, we asked:
‘What now makes a good T-shirt?’
- It should be made of better material so it can last longer
- It should cost more so that those who make it get paid properly
- It should be made closer to where it is sold
- It needs to be made with different kinds of bleaches and dyes
And finally: ‘To whom does the choice of a t-shirt matter?’
It matters to us and it matters to the planet.
Why does Let’s Think Geography matter?
Throughout this project, we have known that we are standing on the shoulders of the Cognitive Acceleration Pedagogy giant, here. Let’s Think lessons so often do matter to children because they feel safe, they are included: they contribute and are heard. As a group, there is a feeling of connectivity, even when exploring difference and difficulty, because the group (is supported to...) steer through challenge, towards ideas that are gaining traction and are well-reasoned. The creation of new ideas and insights is tangible and builds efficacy.
Indeed, new insights from interdisciplinary research institutes (CANDLE and The Social Brain Institute) – combining neuroscience and social science - are confirming that effective processing in the brain cannot be separated from our social and emotional context. Learners who feel they are socially connected, who are engaged in frequent feedback loops, who feel they have autonomy and who are working with a desirable level of challenge, crucially on matters that are of importance to them, have increased levels of energy fed to the brain. Learning, of a safe, collaborative, dialogic, rigorous well-pitched and affective nature is literally brain sugar.
We are daring to think that our most successful Let’s Think Geography lessons have mattered to pupils because of these very dimensions. At a deep ‘scientific’ layer of the learning river, we have been deepening pupils’ reasoning around complex systems, causal relationships and with the T-shirts lessons, the dimension of moral justice. Just as deep has run the layer of learning about ourselves and our relationship to the world that is both home and resource. Pupils’ frames of reference have moved from themselves, to the group, to society and the wider world. They have begun to construct age-appropriate and hopeful ways in which they can have choice and agency in the face of complex problems. Finally, they have begun to understand how the responsibility for change sits with industry, innovation and legislation, as well as but not only with themselves.
The humanity and science demanded by the vision of the SDGs has been a powerful influence on our existing understanding of CA pedagogy and the extent to which children will think hard together and be moved to act differently, when learning matters.
[post_title] => Finding the humanity in the science: Or the sweet spot of Let’s Think through Primary Geography
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An interesting study was carried out about the effects of what researchers at the MINT Learning Centre in Zürich called cognitively activating instruction in secondary Physics teaching. They worked with a small group of experienced Physics teachers who were teaching in what is known as Gymnasia in German speaking countries.
They are selective state schools which are sometimes referred to in English as grammar schools. A feature of these schools is that all students must attend classes in Biology, Chemistry and Physics that contribute over four years to their school leaving certificate (Matura) at approximately 18 years of age. The Matura is conceived as a broad academic basis for University study that allows a lot of choice in subject specialism. However, despite the fact that Physics is compulsory, the gender outcomes mean that many Swiss University Physical Science courses are male dominated.
These researchers wished to show the ecological validity and effectiveness of their pedagogical concept.
“In a quasi-experimental study, we wanted to determine whether regular in-service teachers are able to implement cognitively activating instructional methods under realistic classroom conditions to the benefit of their students’ conceptual understanding, without hampering their quantitative problem-solving performance.”
The design of our own professional development could well be informed by some of their concerns about how to enhance one thing without minimising some other desirable objective.
They also were concerned with the underachievement of female students and how the nature of Physics traditionally conceived as a highly mathematical problem solving discipline played a role in this.
“The unsatisfactory situation in physics education also becomes obvious in the huge and persisting achievement differences between male and female students, to the disadvantage of the latter….. ongoing difficulties in understanding the concepts of mechanics have been demonstrated …….With our study, we also address the question of whether classroom instruction that focuses more on qualitative conceptual understanding than on quantitative problem solving is especially beneficial for female students.”
The paper also carries out an interesting review of the literature on the idea that successful learning in science is best understood in terms of conceptual change from naive conception to, hopefully, robust understanding.
“In past decades, science educators and psychologists have made good progress in understanding how to foster this type of conceptual change in the classroom: students must become aware of the limits of their everyday concepts and become convinced by the explanations offered during the instruction. This approach requires a classroom culture in which questioning and respect for initially diverse beliefs prevail ...”
I found it particularly interesting that the Zürich researchers developed five key ingredients that they stressed were absolutely essential in their teacher development process.
“generating solutions to novel problems, inventing with contrasting cases, comparing and contrasting, self-explanation prompts, and metacognitive questions.”
I have been wondering how complementary these principles are to the Let's Think Five Pillars (Concrete Preparation, Cognitive Conflict, Social Construction, Metacognition and Bridging) and what we can learn from this study in the ongoing development of bridging lessons from the CASE, CAME and LT English lessons.
A very important methodological point was made in this study about how research must not always be envisaged as large scale RCT type studies.
“With our quasi-experimental study, we wanted to bridge the gap between well-controlled but narrow learning experiments and the implementation of scientifically approved means of instruction by in-service teachers in real classroom contexts.” By making use of parallel classes, we could control for teacher effects and therefore run a controlled intervention study with a relatively small number of classrooms. Although access to parallel classes may not always be as easy as it is in the Swiss system, it should be feasible in other countries as well. Such quasi-experimental intervention studies can be considered an intermediate step between laboratory experiments and large-scale studies.
References
Hofer, S. I., Schumacher, R., Rubin, H., & Stern, E. (2018, March 15). Enhancing Physics Learning With Cognitively Activating Instruction: A Quasi-Experimental Classroom Intervention Study. Journal of Educational Psychology.
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This blog is a tribute to Mundher Al-Adhami, who recently passed away and is a sad loss to the Let’s Think community. Mundher was one of the lead researchers who developed the Let’s Think (Cognitive Acceleration) in Maths approach and has supported the Let’s Think community tirelessly throughout the years.
In this blog, those who knew him share their memories of his life and friendship.
You can read more about Mundher’s life in maths and in Iraqi politics in the Guardian obituary and you might also be interested in reading this tribute issue of Equals magazine, which he founded.
Alan Edmiston
I first met Mundher in 1996 and soon came to view him as a dear friend and trusted mentor. Mundher was the most interesting person I knew, an exiled Iraqi who moved to Russia to study for his PhD before coming to the UK. Initially Mundher spent time at Durham University before working as a maths subject lead in London. He was part of the team led by Margaret Brown that produced the GAIM (Graded Assessment in Mathematics) materials. Following that he paired up with Michael Shayer to work on the CAME (Cognitive Acceleration through Maths) project. This collaboration saw him reside at King’s College for many years resulting in several books, numerous publications and latterly the Let’s Think Maths series of activities. It was just prior to the publication of the CAME or Thinking Maths lessons that I was first introduced to him by Michael Shayer. Little did I know that meeting Mundher would change the course of my career and see me move in a relatively short time from teaching science to someone who would spend most of his time teaching mathematics across all Key Stages and working with maths teachers.
One time with Mundher clearly stands out for me. In 1998 he was kind enough to visit the North of England to spend time with some maths teachers from Sunderland as part of their CAME training. It was a pleasure to host him over that weekend and I clearly remember his joy at visiting Durham Cathedral and his delight as we had tea (Mundher was a great tea drinker) and wandered round the Botanic gardens. At his request we were able to visit his first home in a former coal mining village and Van Mildert College. I distinctly remember him telling me how safe he felt in his university room after fleeing Iraq knowing he would not be arrested and how amazing it was to live without the scrutiny that comes under oppressive regimes.
With Lynda Maple we set up a company called Cognitive Acceleration Associates (CAA) to carry on the CAME CPD when Mundher left King’s College. Early in its history, and soon after the fall of Sadam Hussain, he returned home to Iraq. Mindful of the risks involved in such a journey he left me a gift, which I still have in my possession, of two cheques for £10,000 to be cashed in the event of his getting into trouble so I could carry on the work of CAA.
Thinking back to that gesture brings Mundher’s wisdom into focus for he knew what in life what held true value. Material possessions meant very little to him in comparison to the investment of developing and supporting people to reach their potential. To the frustration of his colleagues he would give resources away including his own time and money. It was lovely to see him carefully and respectfully listen to, and value others without making them feel nervous. He encouraged them to express their anxieties and warmly supported their efforts.
Mundher possessed an intuitive grasp of progression within mathematics and was brilliant at devising activities that enabled children to move towards higher, abstract, levels of thinking within a conceptual strand. For me the lessons he devised stand the test of time and teaching them is a honor to this day. I do not possess the words to fully pay tribute to him and to highlight the impact he had upon my life. It was a pleasure to know him and to spend time in his home and with his family. Those who knew him will miss his warmth, compassion and love deeply.
Sally Howard
I first met Mundher many moons ago when CASE was first branching out from just being a secondary science thing! Mundher’s devotion to quality maths education and helping learners learn and teachers teach more effectively was incredible. Attending any CASE/ CAME sessions he was involved in always bought laughter and great insight into why learners of any age might struggle with maths. It hadn’t crossed my mind that children across the primary age might still not recognise the need to measure from the zero mark rather than the start of the measuring stick, until I took part in one of his early CAME ideas for young children. Only then did the penny drop! Encounters with Mundher as his ideas were always invigorating - keeping up with his pace of thinking, talking and passion for practical experience with cognitive conflict was always an energised affair. He and his ideas will be greatly missed, not just by his family but by all who knew him. Rest in peace dear man.
Shirley Simon
My memory of Mundher goes back to the EARLI conference in Padua Italy in 2003. I had of course already met him at Kings at the end of the 1990s when we started CASE@KS1, but CASE was always quite separate from CAME at that time. I bumped into him in a street in Padua and we had a long conversation ranging from academic stuff to religion and then to his adventures with Michael Shayer in Italy visiting lots of art and culture. He persuaded me to take a day off and visit Venice and it was the best thing I did. That (is a memory) that has stayed in my mind all these years. We will miss him for his kind good humour and his wide range of interests.
Sarah Seleznyov
Mundher was my maths hero and a father figure for me in terms of my professional learning. There was nothing he didn’t know about the development of children’s mathematical thinking and he always had time to answer my questions.
Doing CAME training twenty years ago radically changed my practice and my beliefs about mathematical teaching and learning. I felt as if everything I had learned so far in my teaching career needed to be torn up, reassembled and rethought - it was scary, but it was the best thing that ever happened to me.
I went straight from doing CAME training, to attending a lesson design programme led by Mundher, a replication of the original CAME training for teachers. We wrote a set of lessons which are still used by Year 4 pupils and which were used for a large funded project in London, which achieved effects akin to the original research and were published in a journal article. I then moved straight on to becoming a Let’s Think Tutor, all with the encouragement, support and guidance of Mundher.
He always saw potential in me, and always pushed me to do more. Firstly to read more, advice which led me to get a job at UCL Institute of Education. Then to write more, initially for Equals magazine, but then moving into a Master’s study which became a journal article. I wouldn’t be where I am today - a headteacher, PhD student and published author several times over - without his encouragement and guidance.
We spoke regularly, right up until he passed away. He helped me develop a mathematics progression document for my Reception class, and was working on one for my new Year 1 class. He liked to pick my brains about his latest thinking and projects, and was latterly working on what we affectionately called his ‘world domination’ project with Ian McLaghlan in South Africa. Mundher never stopped fighting for pupils’ rights to a high quality, enjoyable mathematics education.
I will miss him terribly: his grand plans, his eternal optimism, his generosity, and his humour (especially jokes about the Tunisian neighbours). His legacy will live on as we continue to help teachers using the resources and the professional development model he helped us design, and to fight for pupils to have the best mathematics education teachers can provide.
Sue Johnston-Wilder
I remember Mundher as warm, encouraging and fizzing with ideas. He was ageless - there was a time we were worried about him but he got better and came back to work. He seemed to love working with teachers, and building their confidence. He was thoughtful, generous and inclusive.
Lynda Maple
I worked with Mundher for many years; in the main, as joint tutors on Let’s Think maths courses. We trained hundreds of teachers as part of an initiative with the Education Action Zone in North Islington. Although that was over twenty years ago, his enthusiasm and kindness lives on in the schools and the work they do in mathematics.
Mundher was always positive in his dealings with the teachers he met. He was humble and generous and had a way of helping everyone to take on the challenges they faced when introduced to the CA approach.
I will miss him very much and he will always be one of the highlights in my career in education.
Martina Lecky
From the first time I met Mundher at King’s College as part of the CA tutor group that Philip Adey organised in the 1990s, I knew I was in the presence of an ‘intellectual giant’. Every time he spoke, I was struck by his passion for the discourse on students’ cognitive development. My friendship grew with Mundher when I became a member of the Let’s Think Forum (LTF) shortly after Philip’s death. Mundher asked me to be a trustee with him and Michael Shayer in 2014 and some of my fondest memories are sitting in Michael’s garden discussing numerous topics from LTF business to educational pedagogy. Mundher was a bright light in all our lives, leaving an indelible mark on the field of cognitive psychology and mathematics education. We will miss our debates with him and his legacy, cognitive acceleration, will continue to change students’ learning and teachers’ classroom practice.
Mark Dawes
I was extremely fortunate to be part of a secondary CAME training cohort about 20 years ago. Mundher was an extraordinary character, and someone I enjoyed working with over the subsequent years. I didn’t just benefit from his professional wisdom during the course days, but was, as many others have mentioned, mentored by him over a long period of time. Mundher continued to be an enormous influence on my teaching and my professional development in ways that I am consciously aware of, and, undoubtedly, in ways that I do not realise.
One of my abiding memories of Mundher is the way, after listening intently to those of us with vastly less experience and wisdom, he would connect our half-formed ideas to research, to data he had collected, to things that he and others had written, and to lessons he had observed. For me, those discussions were transformative in my thinking about mathematics and about education. His work, and his personality, will continue to influence me and my students in the years to come.
Rosemary Hafeez
I worked very closely with Mundher when he and Michael Shayer were developing Primary CAME. Some years later, I remember him coming to Kingston and teaching a model lesson in one of our tricky boys' schools. He was amazing: able to hold the boys attention, engage and adapt to suit their differing needs, whilst challenging and extending their thinking. He was a great person in the world of mathematics.
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If I had a pound for every time I’d heard the Cognitive Acceleration approaches described as a ‘skills based curriculum’, I could have retired long ago. It is probably something I have been guilty of saying myself over the years, perpetuating a rather limited description of the approach. The risk with any kind of descriptor for anything is it that it oversimplifies the approach to a point that the subtlety and nuance is lost. In this blog, I aim to write a better description that clarifies this point.
The reason for articulating this comes from a conscious educational drive in the UK to consider knowledge. This is exemplified by a speech from 2021 from the Rt Hon Nick Gibb MP, Minister for Education, in which he draws on the work of Professor E. D. Hirsch, articulating that those furthest behind have larger gaps in their knowledge and so over time, the gap tends to grow (the Matthew Effect). He stresses the importance of trying to fill those gaps in all pupils.
This isn’t the only place you might see this referred to. The work of Prof Hirsch as also been referred to in other Department for Education documents. The same thinking about knowledge and the importance of retaining it also appeared in the 2019 Ofsted Inspection Framework and is retained in the most recent (and current) update of the framework. The high stakes around Ofsted inspections for UK schools means that this is something that many schools are considering in their curriculum design.
In discussions that I have with school and curriculum leaders, this topic has come up again and again. The focus of their work is (almost) inevitably designing a well sequenced curriculum that helps build a bank of 'sticky knowledge', along with the favoured techniques of ‘spaced practice’ (spreading the learning out) and ‘retrieval’ (pulling the learning back from the memory of pupils).
So where do the Cognitive Acceleration approaches fit in to this? If you take Cognitive Acceleration through Science Education (CASE) for example, it can appear that it is a series of topics that although connected to each other through the CASE schema, are not designed to be connected to the rest of the curriculum. Does that therefore mess up the curriculum sequence? Also, CASE seems to be very focused on enabling students to become good scientific investigators, rather than learning the important sticky knowledge that is required in science like cells, particles and forces.
I’ve had a few discussions with teachers and leaders that raise these points over the years and here are some of the things I would now say in response.
In science, the curriculum knowledge that is required includes ‘Working Scientifically’ as a key component. You don’t need to take my word for this, this was very much the response of the Department for Education when working with them to establish a school improvement project in 2019. An analysis of the lessons and curriculum at the time indicated that the 30 CASE lessons cover approximately 18% of the UK National Curriculum for Science for Key Stage 3. A typical student will have over 300 science lessons in years 7 to 9 and so CASE would only need to cover around 10% to be ‘pulling its weight’ from a curriculum content perspective. Therefore, CASE teaches important knowledge in an efficient way.
Schools can sometimes struggle to identify a sequence that helps to teach ‘working scientifically’ well. It often presents more of a challenge that the more recognised content of biology, chemistry and physics. CASE is a well-sequenced curriculum for teaching this ‘working scientifically’ and associated knowledge.
CASE lessons are designed to be spread out, with lessons consciously spaced out with perhaps a couple of weeks between them. It also incorporates recapping and retrieval of ideas from previous lessons, as well as the encouragement to apply these ideas outside of lessons. CASE was designed around the principles of ‘spaced learning’ and ‘retrieval practice’ to help embed important knowledge.
The learning processes that take place in CASE lessons help teachers assess the learning that pupils have recalled. Knowledge is tested as students apply existing knowledge to novel contexts during CASE lessons. The focus on metacognition helps also assess the security of this knowledge and identify and resolve unhelpful preconceptions (misconceptions). CASE helps teachers and pupils work diagnostically to identify and fill knowledge gaps.
The lessons learnt from CASE seem particularly ‘sticky’. The idea is that the ‘active ingredient’ of cognitive conflict and the associated techniques of social construction (students building their own mental models) and metacognition (discussions around the process of learning) can help students test a previous unhelpful schema (mental model) to its limits and rebuild a better and more useful mental model. CASE helps teachers and pupils fill those gaps with the correct knowledge, and connect that knowledge in a useful way.
As teachers practice their techniques with classes, both teachers and students become more expert at using them in lessons. They are also likely to begin to transfer this thinking to their other lessons. This can help both teachers apply these approaches with their other lessons on biology, chemistry and physics content and the students with their other subjects, which can increase the chances of them learning more knowledge over time. CASE can help learners get better at retaining more useful knowledge beyond that which is taught in CASE lessons.
The reason I have introduced so many schools to CASE lessons is that time and time again, it has been a key component of school improvement in science, helping pupils attain better outcomes in ways as detailed above. CASE is not simply a skills based curriculum, it is very much a knowledge focused curriculum, using techniques which make sure important knowledge sticks over time and help learners become better at keeping a whole range of knowledge in their heads.
[post_title] => Isn’t Cognitive Acceleration all about skills? Isn’t sticky knowledge more important?
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It’s a cold but sunny afternoon in February, I find myself standing in the school grounds of a Hampshire Junior school, pouring water on different surfaces and at different rates from a watering can. Listening and watching intently are a small group of teachers and the core team of a new Let’s Think project. Can small experiments with a watering can lead eventually to the reasoning pupils will need to inhabit our planet in a sustainable way?
The Primary Let’s Think through Geography (PLTtG) project started up in earnest in February with four teachers from schools in Hampshire meeting up with a team of Let’s Think tutors, a school leader and an Associate Professor from University of the West of England.
The project aims to develop a taxonomy of reasoning applicable to Geography and children at this age, in line with Piaget’s Stages of Cognitive Development. From this taxonomy we have begun to develop lessons that are challenging for children to reason through the content of Geography. Michael Shayer is providing the guidance for this crucial aspect, especially how we develop a taxonomy that is relevant to teachers and appropriately challenging for children.
We also intend to have each lesson contribute to the UN Sustainable Development Goals as they provide an opportunity for a richer curriculum in which children have some agency and can make a difference to issues that will affect their future. This aim resonates with the original CASE development. Thinking about sustainability is complex - more complex than most Primary Geography curriculum journeys. The question as to whether LTtPG renders this complexity accessible echoes the pioneering work of Shayer and Adey setting out to accelerate cognition rather than reduce the curriculum complexity.
A further goal for the team is to understand the experience of developing the lessons so that we would be be able to scale the project up into a larger intervention. Many Let’s Think programmes are over two years with about 30 lessons. It is too early to say whether we could do that.
The project scale is small at the moment with a trial of six or more lessons for Y5 and 6. We are initially seeking evidence that Let’s Think pedagogy and approach is applicable in this subject and for this age of children. The teacher researchers all have experience of using Let’s Think in their classrooms, albeit in a different subject, English, and it is their skill and experience that we will rely upon to bring the challenge to children and to gauge their response.
Some readers may be familiar with David Leat and his publication Thinking Through Geography (1998). David developed the resource for KS3 and we are delighted that he has agreed to be an associate to the team, offering critical advice on the lessons and approach. David has written extensively on cognitive acceleration and argues in a Geography Association paper for the importance of thinking through Geography.
So what is it with the watering can?
Flooding is a consequence of the relationships between infiltration of water and run off which in turn are dependent upon rainfall frequency, duration and intensity and ground conditions. Sustainable solutions to reduce flooding involve Sustainable Drainage Systems (SuDS) that typically slow down run off to allow for infiltration. The complexity of modelling these systems requires deeper reasoning than Piaget would credit children with at this age and hence the challenge necessary in a Let’s Think lesson.
We expect to have some draft lessons for readers to look at in a few months and will keep you updated as we go down that road. Geography is a journey after all!
[post_title] => Primary Let’s Think through Geography
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Leah Crawford is a Let’s Think in English Tutor. From Sept 2020 to July 2021 she was contracted to devise and teach post lockdown English interventions at Amery Hill School, a 11-16 secondary school in Alton, Hampshire. Part of the strategy was to teach Let’s Think lessons and embed the principles in small and whole group teaching. In this blog, she reflects specifically on teaching Let’s Think in English to a Year 7 mixed ability class of 30, as well as their core English curriculum.
From pagan mythology to literature, the moon has become a symbol of constant change, unreliability, even madness.
Conversely, during the past year, as scrolling news reports tried to unravel the impact of the fast-changing pandemic, broadcasters seemed to be more than usually attentive to the lunar calendar as a reassuring constant, drawing attention to unusual full moon manifestations: September’s Harvest Moon, January’s Wolf Moon, April’s Pink Moon, and May’s Supermoon.
Looking back on my 2020-21 year of teaching, perhaps the most ‘lunatic’ year to return to classroom teaching, we had to steel ourselves against inconstancy and ride some rough storms. There were the lower level but necessary pragmatics of desk cleaning, seating plans and hand sanitising; the logistics of zoned year groups that gave birth to a new breed of masked avenger teacher, scurrying between zones, heroically pulling their trolleys of books and papers; then there was the swift-footed response to burst bubbles, managing in-class and remote learning in tandem.
We came to expect the waxing and waning rhythms of pandemic life, the full glow and the shadows. But what we now know that the pagans didn’t, is that the rock of the moon is always reassuringly there. The full moon is always in orbit – its full glory is just not always visible.
As I returned to the classroom, luckily to a school that has embraced Let’s Think in English, the principles of Cognitive Acceleration (CA) became my rock. Those principles were always constant but I felt their enactment in practice wax and wane through the challenges of COVID era education.
Although many reading this blog will be familiar with CA in some form, it does not hurt for me to be clear and transparent about the principles we aimed to enact through Let’s Think in English and why:
- High and equitable involvement: it was likely that what our most vulnerable learners had most missed out on through a period of remote learning was the efficacy that comes from being a valued contributor in a safe community. You matter, you all matter, and it matters what you think and say.
- The social construction of meaning. Reading is not an extraction of meaning from the page but an active, constructive, personal and social process. We needed to test out whether readers were alert, attentive, monitoring and questioning the meaning they were constructing. Could we help them to become more aware of their own process of meaning making by making it shared and social?
- The centrality of challenge. Without challenge, learners are metaphorically treading water. This may build stamina, but it does not take you into new ways of thinking: extending cognitive capacity. Could we help students to move from personal and instinctive responses to texts towards reasoned and critical responses by noticing resonance and dissonance with the thoughts of others?
- The nurturing of metacognition. Becoming more aware of and being able to productively steer one’s thoughts is not a given in our academic or personal lives. Could students over time become more aware of how they were building understanding, whether that understanding was reasoned and tested and become more able to transfer and apply this to new texts and contexts?
Lofty aims. So how much of this did we achieve?
So follows my reflections on the past year’s phases of the moon: teaching Let’s Think in a pandemic.
September’s Full Harvest Moon
In the full glow of the ripe promise of September, my very first lesson with my Year 7 group was a KS2 lesson using Smriti Prasadam Hall’s symbolic picture book ‘Rain Before Rainbows’ which you can access here. It is a story that moves from a place of trauma and loss through struggle, to hope. The message of the text did not present the usual degree of challenge for a Year 7 group but it was deeply pertinent and we took our journey in deliberate stages to establish the routines and rituals of collaborative making meaning:
- Can you repeat that so the whole group can hear?
- Could you share what your group thought?
- Did you have a similar or different idea to this group?
With subtle metacognitive nudges:
- What was it in the text that led you to think that?
- As we continue to read, what will it be helpful to look for?
- Do you know other symbols of hope?
I was clear with the group that they faced an additional challenge to listen and respond to each other’s ideas whilst being seated in rows facing the front. They described what they would need to do to show that they were listening other than through eye contact and body language, based around being able to repeat, respond to and question the contributions of others.
We then moved to the usual Let’s Think induction lessons based on a fable, The Bridge, (lesson available here) which provoke conflict in ethical perspective taking and build on awareness of narrative structures. We began to gain some traction with the power of conflict, working with difference to deepen thinking. As teacher mediator, I felt the power and responsibility to calibrate our climate. Yes, I could request elaboration from a student to explain their group’s response – but I could also create the air-time for students to explain what or who had led them to change their mind as the lesson progressed. I saw that if I made space for and was fascinated by this– the students became so and quite quickly became unafraid, willing even, to share changes in their thinking.
It was heartening to see the cross-fertilisation of ideas and increased confidence was still happening even without the powerful, physical signifier that is students seated in table groups.
Waning Moon...November to December
As the second wave of the pandemic loomed, it became harder to build on our promising start. I was part of a well-run department: a tight ship. As bubbles burst and the usual scheme of work was at times disrupted with students having to self-isolate, I felt the very real tension between programming in Let’s Think lessons and making progress through the scheme of work with its valid common assessment tasks and moderation cycles. A great reminder of the pragmatics of applying research principles in practice.
January New Moon
It is odd that the very absence of a visible moon is heralded as a new moon. The ultimate ‘glass half-full’ philosophy, perhaps. Be patient...it will return.
That’s exactly the position we found ourselves in just a few days into January with the dark days of an extended lock down and a return to remote teaching. Our school policy was to keep to the usual school timetable, teaching alternate synchronous and asynchronous remote lessons. Could we maintain the CA principles we had set and begun to enact through this phase? The attendance of my Year 7 students at live lessons was remarkably good, but only a third or so of students had working microphones to contribute orally, not all initially had access to lap-tops and not all had good broadband connectivity.
To maintain our principles the pace through lesson content slowed down and innovation kicked in:
- To maintain high levels of contribution, I would share a recorded reading of a text and pose a question or questions and capture responses asynchronously on Padlets or Google Jamboards. The beauty of Padlet particularly is that there is the facility for students – and teachers – to respond to each other’s posts, creating chains of thought.
- To encourage elaboration and the shift from thinking to reasoning, I could select student posts to use as springboards in live lessons – inviting students to elaborate on an idea and explore dissonances between student responses.
- To maintain the centrality of challenge for progress, whether teaching Let’s Think lessons or the core scheme of work, we worked towards and through binary choices to slow down thinking and provoke reasoning. Is this Romantic painting/poem frightening or beautiful? Having read these poems, which poet has the greater respect for nature: Wordsworth or Clare?
Waxing towards a full Supermoon
We returned to school in March 2021. Every first lesson I taught with every group was a Let’s Think lesson.
Why? We had not let go of the importance of equitable conversational turns to build self-efficacy, meaning and cognition during lockdown – but it had been more difficult, more stilted and too reliant on each student’s access to hardware and broadband connectivity and their confidence to share ideas in a chat box or on the live microphone. We needed the return to class to be a return to valuing, responding to and enjoying each other. We were unmuted and unlocked – but not unmasked. Masks made smaller, quieter voices hard to hear. Ensuring that all pupils were contributing to and accessing the ensuing discourse of the lesson was even harder. Asking students to discuss and arrive at a small group response, then jot down a phrase or a few bullet points to indicate that response on a white board unlocked the next ‘waxing’ phase of teaching. If I could see each group’s board, I could reflect back to them the common chords and discords from across the group. In this way they could still ‘hear’ and respond to each other, and I could more easily distil themes or productive binary conflicts to inform the next phase of the lesson:
- So I can see many of you think...
- The most common response seems to be...
- However, we also have some groups who think...
- The room seems to be split between those who think...and those who think...
This really was now a phase of waxing growth: I was able to teach lessons with rhythm and regularity across the remaining school term. There were two major developments that became possible in this phase which I feel are central to embedding Let’s Think as an intervention that works in synergy with the broader curriculum.
- The lessons were sequenced and positioned to enable students to bridge concepts from one text to another. Some might call this interleaving. When constructing an English curriculum, we are often used to creating tapestries of texts for study by theme or by genre. So, for example, why would I place the study of a short 1950’s sci-fi story at the end of a unit on Romantic poetry and nature? By the end of the sci-fi lesson, students consider whether a text that contains some outdated notions can still be resonant and relevant in the present. When we bridged to the relevance of Romantic visions of nature in 2021, the students argued passionately that we are just as much in danger of losing touch with the natural world. In the face of the climate crisis, we need humility and respect for the power of nature. And how would we have coped in lockdown without those walks?
- I made the group increasingly accountable to set their own direction and goals for development. We had used dialogic talk reflection tools in the autumn term, but the disruptions to in-class teaching had knocked us off course. We used the tool below, developed through the Assessment Companion for Thinking Skills (ACTS) project (link to this and other tools here) to assess the strengths and areas for development in the group’s dialogic talk behaviours: moving from foundational behaviours of inclusion, politeness and clarity in exchanges, to ones that are fuelled by a desire to question, share differences and reach for the most reasoned, evidenced ideas.
Developing dialogic norms reflection tool
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To improve our group needs.. |
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1 |
Everyone contributes |
Expect to contribute
Take turns
Be polite
Show you are listening |
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2 |
Seek understanding |
Make yourself clear
Elaborate your answer
Track the ideas of others
Ask questions of others |
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3 |
Explore differences and reasons |
Be open to different ideas
Share agreement and disagreement
Ask ‘Why do you think that?’
Ask for evidence & reasons |
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4 |
Pursue the best ideas |
Be open to changing your mind or adapting your ideas
Work towards well reasoned ideas together |
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Let’s Think pandemic teaching has confirmed my belief in the full Supermoon principles mentioned at the start of this blog. It has forced innovation in improved use of white boards, Padlets and binary options as effective dialogic mechanisms. In the final term, it gave me the opportunity to enact the rich possibilities of embedding Let’s Think lessons in wider curriculum sequencing and design. In collaboration with department leaders, we drafted the legacy for a more generative Let’s Think pathway through their rich curriculum. Finally, it has crystallised the importance of inviting students to become co-pilots on their shared educational journeys. To the moon and beyond...
[post_title] => Reflections on a Mad and Moonly year of Teaching English
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How We Learn by Stanislas Dehaene (ISBN: 9780141989303)
I was first introduced to the work of this neuroscientist by Mundher Adhami many years ago. Michael Shayer and Mundher drew upon his work during the development of the Let’s Think Maths lessons for Key Stage 1 and at the time I found his book, The Number Sense to be a revelation. Back then it was helpful to read a book that actually gave real insights into how the growing understanding of the brain could help teachers in the classroom. The impact then was a careful rethinking of my understanding of the development of mathematical thinking during early childhood. The early part of this century saw the educational press awash with books about the brain, many of which made some rather grand claims about the application of neuroscience to the learning process and the actions of the teacher in the classroom. Philip Adey refers to several of these issues in his last publication, Bad Education, which I would strongly recommend you reading for a deeper reflection on the place of Let’s Think within education.
To say I enjoyed How we learn would be an understatement. I found it stimulating, challenging and accessible which is actually quite something given the number of chapters on brain imaging and the multiple references to obscure areas of the brain I think I should know. How We Learn has given me even more to think about for it has made me question my own understanding of the brain and how it impacts the learning taking place in my classroom. For a week after putting down the book I weighed up my classroom practice against the advice in this book which is also titled The New Science of Education and the Brain. Until recently any author claiming to give direct teaching advice based upon brain science was given very little space in my thinking. This is in part due to the spurious science that is often involved when someone claims to tell you how the brain learns and the movement pushing learning styles and other such oversimplifications of science as quick educational fixes.
This book however is among an emerging breed of practical application texts concerning brain science. It seeks to use scientists’ growing understanding of brain development and function to provide clear and simple advice that can transform our classrooms. Dehaene is a very well respected neuroscientist who is both measured and thoughtful in the advice he gives and also one who is mindful of the claims he is making.
What is helpful, is how his understanding of how the brain works can be applied to learning and specifically learning that takes place in school. There is a lovely episode on page 189 where there is an appeal to allow mirth and laughter to have a place in the learning process. This is timely advice for I finished this book on the 8th of March the day when children in England returned to school after lockdown2. I wonder how much laughter was heard after all those months of silence?
Part Three of this book gave me the most food for thought for here he outlines the pedagogical features that need to be present for efficient learning to take place: attention, active engagement, error feedback and consolidation. As a Let’s Think Tutor three of these resonated very strongly with me. His reference to the idea of error feedback contained a really interesting take on cognitive conflict (a key feature of all Let’s Think teaching). The subheading for one section in this chapter was ‘surprise is the driving force of learning’ and to qualify what he means he quotes research that states that: ‘organisms only learn when events violate their expectations’ which helped me to look afresh at this aspect of my teaching and planning. I also found his focus upon attention quite interesting as this referred to what pupils attend to and my own understanding of how to engage pupils. I have now come to see that Let’s Think lessons contain triggers that engage children and to support their talking. Triggers can be part of the lesson or ideas that focus pupils such as in one lesson recently where I used the idea of the r-number to focus pupils on the nature of exponential growth. Active engagement connects with the idea of social construction in Let’s Think and the fact we are supporting pupils to working collaboratively on a shared challenge. Dehaene states that the brain learns efficiently only if it is attentive, focused, and active in generating mental models and in Let’s Think this is best done with other adolescents for the words of a 12 year old are more accessible to another peer of the same age than mine. Consolidation concerns time and the importance of sleep in the learning process. Let’s Think works because it takes time i.e. two years as we seek to enrich and balance our students diet of experiences within the classroom.
Each of the sections above are practical and helpful and serve to lead the reader towards the main aim of the book which is to provide a neuroscience-informed approach to education. The highlight of this section are the thirteen easy applicable action points of which I will relate numbers 6, 7 and 13.
- Keep children active, curious, engaged and autonomous,
- Make every school day enjoyable,
- Let students sleep!
There is much here to support the pupils we are so passionate about and I aim to distil more of the gems contained within How We Learn for the rest of this year and beyond.
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Alex Black a fellow member of the Let's Think Forum, re-introduced me to Annette Karmiloff-Smith and Barbel Inhelder's 1974 paper with the charming title, 'If you want to get ahead, get a theory'.
I had first read it a long time ago as a paper about how young children develop an understanding of balance, seeing how small blocks can be balanced across a steel rod. A second reading gave me much more, and something that has real power for teachers developing their practice.
Please read the paper because I wouldn't want you to miss out on the way the authors create an elegant activity for young children to try: the oddly weighted blocks, the sequence of task demands are all very typical of the Genevan School at the time. And do read the paper because it's aiming to share a much bigger idea about what happens to our theories of the world when we attempt actions in the world based on them.
It's the bigger idea that has captured us and will inform a seminar we are planning about the theories behind cognitive acceleration. It is a paper about how we deal with the clash between our internal world of ideas and the world itself. For example:
A person has a theory about the world, their theory leads them to act in a certain way. Their actions lead to unintended consequences.... what might they do next, what might they be thinking?
A: Keep their theory and act the same way again
'The world is full of chance events; things don't always happen the same way. My theory is a decent one but this time, by chance it didn't work out, I'll give it another go.'
B: Keep their theory but act differently
'I know the world well but the fault was in the way I acted, if I try something different in line with my theory then this time it will be OK'
C: Begin to reject their original theory and act the same way again
'Well, that was a surprise, I must have things wrong about the world. I am going to try it again as before but just look closely at the consequences to see what I need to do to change my ideas.
D: Begin to reject their original theory, but act differently
'Well, that was a surprise, I must have things wrong about the world. A better theory would be this, I'll try something new based on my new theory.
The ideal state for a person is to have their theories about the world 'in equilibrium' with the way the world is so that there are no unintended consequences brought about by their planned actions. That way they can plan ahead, making 'abstract' choices about their path through the 'concrete' world, all the time being aware of the consequences, making the right choices, and not getting any nasty surprises.
'Equilibrium' is however a very hard thing to achieve especially where the world you are acting in is complex and where you have had little time and few learning opportunities in which to build your theories about it. Therefore, we often end up somewhere between A-D in our choices.
I find myself at A, a lot! I'll check my pockets for my keys perhaps 10 times before I can finally agree they are not there!
Sometimes I find I am operating in the realm of C, knowing that I'm wrong but trying to build a new theory by looking closely at the consequences of my actions. I can't get onto Netflix, I thought it was the internet that was down on my Smart TV but the lights are on the router and my phone works, maybe it's the battery in the remote control?'
When Karmiloff-Smith and Inhelder watched children building and balancing blocks on the steel rod they were interested in this, 'the interplay between action sequences and children’s ‘theories-in-action’. They noted that when the child's theories in action were inadequate in the face of action sequences that 'failed' then the child began to focus more closely on the means by which the world was failing their theory. They also noticed that children in this mode were pausing before acting with their attention shifting from just trying to balance a block successfully to understanding how blocks balance; building their theories as they did so. They saw that children, ‘must first form a unifying rule based on regular patterns he has observed' before the shift in thinking could take place.
As teachers we have theories for how thinking may best develop in a child. We set up our classrooms and act on our theories daily. Importantly those theories may not necessarily be explicit, even to ourselves even though we are acting in accordance with them. But do our theories work in the real world and if they don't how do we face the disequilibrium we feel when our attempts to promote thinking fall short of our expectations?
If things don't go as we expect as teachers do we pause, look closely at what is happening and use the new evidence of the world to reflect on our theories? Do we make our theories explicit to ourselves, aiming to unify them to make for a more robust theory based on the observations we have made? These are the hallmarks of reflective practitioners. These are the hallmarks of evidence-based practice.
It's really hard to shift one’s ideas about the world based on what is happening in the world because it can be easier to explain away an unexpected outcome as chance or an aberration than it is to make explicit our theories, undo our mindset, adopt a new theory and as a result new actions. There is risk in this and as a result we can avoid it very, very persistently. Karmiloff-Smith and Inhelder saw children attempt again and again to balance blocks using their current theory of ‘balance it in the middle’ despite the block falling off because the real world rule was ‘find the centre of gravity, by feeling the weight distribution, and balance it there’.
Alex and I are going to look at some of our current theories for the positive effect of cognitive acceleration and some of the action sequences that follow from that. We are going to look at how that differs from some of the practices we see. We’ll consider Piaget and Vygotsky, Dweck, Kahnemann, the relevance of neurological theories, the power of group efficacy after the ideas of Wooley, the learner as apprentice thinker after Rogoff and much more. All great theories but do they explain the impact of cognitive acceleration, are they put into practice by Let’s Think teachers and what do we do if our theories don’t hold up in the real world?
Of course, A-D are only some of the many ways that people deal with the theories in their head not playing out too well in the real world. The way we have evolved has also given us another option, based on our desire for community and the security of the crowd.
E: Keep our original theory and recruit others to the same theory ignoring the consequences of our actions in favour of group think.
'I feel better about my ideas when others share them, this feeling is more powerful than the evidence of my actions which in any case can be accounted for by chance or the recruiting of other ideas and explanations. Let’s conspire to ignore what the real world is really like'
Position E is one of the most challenging aspects for us all because it is a position that actively ignores the real world and as a result real world evidence has little power to bring about change. It is also self-sustaining because the group members aim to support each other in both affirming the theory and rejecting the real-world evidence. All are equally invested in the internal logic of the theory rather than the unfortunate evidence of its falsehood. I remember a time in the 1990’s when theories of ‘Teaching and Learning Styles’ swept through schools and teachers were exhorted to match the curriculum to their children’s preferred styles, and in some cases to test children to ascertain that. Group think to marvel at began to emerge in schools despite the evidence that this popular raising attainment approach had no effect at all on attainment. I see the same evidence avoiding group think today in the anti-vaxxers and global warming deniers and in those convinced that private companies will act for the public good.
We in Let’s Think aim to keep alive the debate about what our theory is and the evidence for it, to be explicit about the current theories and to pause and reflect when they don’t play out in the real world as we had expected. It’s a way of making progress perhaps?
Stuart Twiss
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[post_content] => Stories have special powers. While most of humanity learnt to read and write in recent history – only 12% of the people in the world could read and write in 1820 – narratives have been central to human life for thousands of years. Cave paintings from 30,000 years ago appear to depict scenes that were probably accompanied by oral storytelling. Story dominance in human interaction has rewired the human brain to be predisposed from birth to think in, make sense in and create meaning from stories. Stories predominance is a survival skill; forms of narrative, allowed early humans to learn more about their kind than they could experience at first hand, so they could cooperate and compete better through understanding one another more fully [1]. Story was so crucial to survival that the brain evolved specifically to respond to it.
If you’re reading this your brain is designed by evolution to develop story representations from sensory input. Don’t believe me? Then watch this video and explain what is happening:
https://youtu.be/VTNmLt7QX8E
The animation experiment by Heider and Simmel (1944) revealed that humans have a strong tendency to impose narrative even on displays showing interactions between simple geometric shapes. When watching this animation with three simple shapes, most observers tended to interpret them the shapes as having intentions, desires and beliefs. You might enjoy watching how comedians reacted to watching the animation:
https://youtu.be/ZAnt9II-5Co
As Bruner [2] (1990) explained: “Children produce and comprehend stories long before they are capable of handling the most fundamental Piagetian logical proposition that can be put into linguistic form.’. In the present educational landscape when Ofsted claim learning is “an alteration in long-term memory” and recall and retrieval are valued so highly it strikes me the power of story in supporting the formation of memory is undervalued and frequently overlooked. As Egan [3] (1997) states:
“oral cultures discovered long ago that ideas and values put into rhythmic story form were more easily remembered and more accurately acted upon”.
The power of stories to support learning is quite remarkable with research showing it has impact on comprehension, motivation to learn, language mastery, writing and memory [4].
Let’s Think lessons draw upon the power of story. In Let’s Think in English (LTE) we are fortunate as the focus of the lessons tends to be narratives. It’s a pleasure and privilege to observe pupils following the texts, eager to meet the next page and see if their predictions ring true before engaging in cycles of discussion sharing their views and collectively developing understanding. In Let’s Think we are familiar with the Vygotskian concept of mediation; the act of guiding and supporting pupils to develop higher mental functions as a more knowledgeable other. However, in LTE lessons I see narrative texts as mediators too providing a springboard for thoughts linking to Vygotsky’s role of cultural mediation and supporting internalization.
Let’s Think maths’ and science’ programmes draw upon the power of stories too. As Alan Edmiston, Let’s Think in maths tutor explains:
“All of the maths lessons follow a sequential series of episodes, the first of which is concerned with engagement within a context. From that context comes an exploration of mathematical relationships moving upwards towards the more abstract aspects of the concept that runs throughout each lesson. An example is a Year 5 lesson: Sports League.
The lesson is focused upon how many games a team will play within a league which can be expressed algebraically in an expression as n x (n-1). To begin with however we start with a story of how both my daughters love netball, yet I do not like team sports because of my father who used to embarrass me in team games when I was in Year 5. I mention to the class that they asked if I could organise some games with two other schools but this time the parents and teachers play, and the students watch. The only problem is I have to make sure I can take part in all the games and fit them into my diary so I need to know how many games we will play altogether if everyone plays everyone else and everyone plays at home. Hooked – you bet they are! I find such an approach and the narrative that flows from it acts as a stepping stone towards higher level mathematical thinking.”
While Dr Martina Lecky, executive headteacher of the Vanguard Learning Trust, outlines the influence of stories in Let’s Think science and CASE:
“As an experienced practitioner, I have often found that the use of a narrative can increase students’ engagement in CASE lessons. One of my favourite lessons is activity 20, which focuses on the reasoning pattern of correlation.
I set the scene with the class: we live in a village called Brocklehurst and we are all carrot farmers. The problem is our supermarket buyer, Sainsbury’s, is about to cancel its order because our carrots are not as big as those of other growers. One of the villagers has, however, found a company selling a chemical called ‘grocaro’ which could solve our problem. As the carrot growers of Brocklehurst we need to decide, based on the evidence, whether the treatment, grocaro, has the effect of growing larger carrots compared with a control group.
I give the students different roles – farmers, town mayor, representatives from Sainsbury’s and the company selling grocaro – and the excitement throughout the lesson is palpable. I believe the narrative provides the context for them to have a heightened response as they consider the issue from the perspective of their role. At the end of the lesson, I know that the experience leaves an indelible mark on students as they have not only been challenged cognitively in terms of the lesson’s reasoning pattern, but also they have been on a conscious journey facilitated by the unfolding narrative.”
The narrative framing evident in the LT math and science lessons and rich texts of LTE provide familiar steppingstones to formal thinking and abstract concepts. Once we recognise the power of stories we have to as Egan says: “…reconceive the curriculum as the set of great stories we have to tell our children and recognise… school teachers as the storytellers of our culture.”
In my next blog post I’ll look at another story influence: how a lesson’s sequence can mirror narrative structure.
Footnotes
- Boyd, B. The evolution of stories: from mimesis to language, from fact to fiction. Wiley Interdisciplinary Reviews: Cognitive Science, Volume 9, Issue 1. 2017
- Bruner, J. Acts of Meaning. Cambridge, MA: Harvard University Press, 1990.
- Egan, K. The Educated Mind: How Cognitive Tools Shape Our Understanding. Chicago: University of Chicago Press, 1997.
- Miller S & Pennycuff L. The Power of Story: Using Storytelling to Improve Literacy Learning. Journal of Cross-Disciplinary Perspectives in Education Vol. 1, No. 1 (May 2008) 36 – 43
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Professor David C. Johnson was a pioneer in many aspects of mathematics education and computer education, first in the United States and later in the United Kingdom. He combined rigorous educational research with equally rigorous development of the curriculum, of high quality teaching resources and of teacher professional development, aiming to provide all students with an engaging and relevant education. He worked by forming collaborations with others, including researchers, policymakers and teachers, and acted as a wise research supervisor and adviser to a whole generation of leading researchers in both mathematics and computer education.
David was one of twin brothers born in Minnesota, USA, to Carlton, a retail manager and shop owner, and Dora, a shop worker. He gained a BA from Colgate College (now Colgate University) in Rochester, New York State, and then a PhD from the University of Minnesota, where he taught for 17 years (1961-78), progressing to become Professor of Mathematics Education. This included a 5-year period as the Head of the Mathematics Department in the Laboratory School attached to the university.
David was an active member of the research committee in the National Council of Teachers of Mathematics (NCTM), and was chosen as the founding editor of the Journal for Research in Mathematics Education, first published in 1970. This quickly became, and remains, the leading international mathematics education research journal, reflecting the high standard he set at its inception. In another ground-breaking publication from the NCTM, a 1980 reference book
Research in Mathematics Education, David contributed two key chapters
The research process and
Types of research, and also edited and provided the commentary for an important section of case studies.
Parallel to his leading role as an educational researcher, David was becoming an early enthusiast for the use of computers in the mathematics classroom, not to practise skills but to both support the development of important mathematical concepts and to refocus the curriculum for a computer age by introducing a greater emphasis on the ideas which underpin computer use, especially algorithms and iteration.
He led a team in the production of a school textbook series
Computer Aware Mathematics Project (CAMP) which pointed the way for developments in other countries. One prescient result identified by an independent research study was that this teaching of simple programming (now known as coding) improved attainment in algebra. He also established a much copied innovative graduate programme.
While in Minnesota, David married his first wife, who gave birth to their daughter Pamela. They later divorced and while on sabbatical in Cambridge, working with Robert Harding on the use of computers to teach university mathematics, he re-connected with his future second wife Katie. This led to a move to the UK in 1978, when he was appointed to the Shell Chair in Mathematics Education at Chelsea College, part of London University. This was already becoming a leading centre for mathematics education research, under his predecessor Geoffrey Matthews, and for computer education, with Bob Lewis. David became Deputy Director of the Centre for Science and Mathematics Education at Chelsea under Professor Paul Black, and later after the merger into King’s College London, Deputy Head of the School of Education under Professor Arthur Lucas. He was later also appointed on a part-time basis from 1991-93 to the Research Professorship of Mathematics Education at the University of Louisiana, Baton Rouge, to lead the development of a Centre for Mathematical and Scientific Literacy.
At Chelsea/King’s, David directed a series of major projects in the teaching, learning and assessment of mathematics at primary and secondary level. These included
Concepts in Secondary Mathematics and Science (CSMS),
Strategies and Errors in School Mathematics,
Children’s Mathematical Frameworks, and Graded Assessment in Mathematics (GAIM),
Nuffield A-level Mathematic,
Evaluation of the Implementation of National Curriculum Mathematics,
Cognitive Acceleration in Mathematics Education (CAME),
Effective Teachers of Numeracy and the
Leverhulme Numeracy Research Programme (LNRP). These projects were variously funded by major charities, government and research councils, with the intention of improving classroom learning in mathematics. They included a range of qualitative and quantitative research methods, rigorously employed, and entailed working, with differing emphases, with children, teachers, and professional advisers, sometimes with very large numbers of students involved. The outputs included the identification of conceptual progressions in mathematics learning; comparisons of the effectiveness of innovative teaching methods, themselves informed by earlier research; the devising and implementation across more than 150 schools of an 11-16 and GCSE assessment scheme, and the production and evaluation of a new A-level mathematics curriculum and accompanying set of A-level mathematics textbooks for the computer age. They informed a series of policy initiatives, including The Cockcroft Report, the development of GCSE, the first and subsequent versions of the National Curriculum and its models of assessment, the National Numeracy Strategy and subsequent developments. Yet even so, due to a series of conservative ministers from both parties who valued tradition over the attempt to implement teaching methods, assessment and curricula which were research-based and appropriate to the 21
st century, this vast programme of research has had much less impact than it deserved.
Alongside these projects David maintained his initial enthusiasm for the use of computers in mathematics classrooms, and broadened his interest to include computer education more generally. He became an active member of the Education Committees of the British Computer Society, and of the International Federation for Information Processing, which established his international reputation. Most importantly he gained funding for and co-directed a major project
Computers in the Curriculum which was the most generously funded government computer education project; it unusually gained repeated funding and lasted for 19 years, from 1972-91. Here again the aim was to use computers to improve the teaching of important concepts in existing school subjects, and the development process involved groups of teachers and researchers in each subject discipline working to develop and test activities for pupils. As with David’s mathematics education projects, this work at the time put the UK up among the international leaders in the use of computers in schools.
Following on from this, he also co-directed an influential large-scale government-funded project
Impact of IT on children’s achievements (ImpacT) evaluating the effectiveness in terms of results of computer use in schools.
David’s role in these projects was strategic: setting aims, writing and securing the funding bids, overseeing the management, staffing, research methods, ongoing evaluations and final reports. He was careful to ensure that each project kept on track, finished on time and within budget, with final reports and academic papers written. But in some projects his role was also very hands-on; he enjoyed working with teachers and researchers in professional development sessions and in classrooms. Throughout his career he continued to keep up to date with research and practice, reviewing many journal articles for editors, and to publish frequently, often collaboratively, in journals, books and reports. He communicated clearly to audiences of different types, writing logically and fluently.
Across the 25 year period of this research, David mentored and inspired, and in most cases supervised the doctorates of, a progression of mathematics education and computer education researchers, including ten future professors, many of whom in turn became leaders in these fields:
Kath Hart,
Margaret Brown,
Steve Lerman,
Mike Askew, Dylan Wiliam,
Jeremy Hodgen,
Richard Noss,
Margaret Cox,
Deryn Watson,
David Squires. Many others who worked on the projects also went onto further research or took leading roles in curriculum development and/or policymaking: Alice Onion, Gill Close, Mundher Adhami, Sue Johnson-Wilder, Julia Anghileri. He also successfully supervised many overseas doctoral students (altogether he supervised more than 35 successful doctorates) who went on to make contributions in their own countries. He was an excellent supervisor, always setting ambitious but achievable objectives for students, and a shrewd judge of what type and degree of guidance each student needed.
David was hugely respected as a scholar, researcher, teacher and administrator who was never self-seeking, always acting decisively and with integrity. But above all he was much loved by those to whom he was a generous mentor, friend and collaborator. He was always good company and could converse entertainingly with people of all backgrounds.
David retired from King’s in 2004 to spend more time with his second wife Katie, and with his daughters Ashlie (a barrister) and Sophie (a hospital doctor), and their families. At times in his life David, although apparently very fit, suffered from medical emergencies: he had polio as a child, later a serious heart attack and then a major stroke. From all of these he made amazingly good recoveries, with his family’s (and especially Katie’s) strong support, but on March 17
th 2020, aged 83 he died peacefully of heart failure after a long illness.
[post_title] => A tribute to Professor David Johnson (26th March, 1936 – 17th March, 2020)
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Confession.
I’m an English graduate, an English teacher and a Let’s Think English Tutor. Whether by nature or nurture, it is the study of the humanities that has caught my interest and driven my learning. I have come to know that the discipline of geography straddles the divide of the sciences and humanities: to me a powerful relative unknown. We hear that interdisciplinary synthesis is what we will need to solve the complex problems we face in the world like climate change, then I find myself invited onto a project team developing the first small suite of Let’s Think through Primary Geography lessons for Year 5 and 6 pupils.
Before the team of Let’s Think tutors, teachers and geography specialists met, I was invited to read through some early drafts of lessons on maps and scale. A human story had been used to invite children into the journey, scaffold their understanding and their manipulation of variables. Michael Walsh has written with clear insight here on the importance of story to focus and scaffold learning here. But, I have to admit, my mind would not be persuaded that these problems helped me to better understand the human condition. The questions about scale and distance still seemed like maths in disguise.
The question of run-off and relevance
Some of you may have read Stuart Twiss’s blog documenting the birth of our small but perfectly formed Let’s Think through Primary Geography project. I was there for those ‘run-off’ experiments with a watering can: 6 foot plus of Stuart, like the Big Friendly Giant, simulating light, intense and intermittent rain on compacted, aerated and vegetated surfaces; on flat and sloping ground. He asked us to use the same expert language back to him – establishing a shared language code for the model that we would then ask children to think about. Once these concrete variables were established, so enters the weasel question of cognitive conflict:
“How much run off will there be?”
“Well, it depends...”
“On what...?”
And so pupils began to share their awareness and socially construct their understanding of the interplay of variables and complex relationship of rainfall frequency, intensity, gradients and the compaction and saturation of the earth. See – not easy. This was more than fun with a watering can. The cognitive stretch was tangible in the ensuing reach for connectives, ‘and’, ‘also’, ‘as well as’, ‘if’ and ‘when’.
Let’s Think programmes endeavour to be relevant to the curriculum and to pupils, whilst they stimulate that sweet spot of progress in reasoning that we believe as their teachers will be of wider, general benefit to them in life, not only in geography.
Reasoning about the variables leading to run-off is an important step towards understanding what contributes to flood risk and eventually abstract modelling of reduction of those risks.
So we knew it mattered to our educational purpose – did it matter to the pupils?
It seems it did. Our observers fed back that in a lesson busy with activity, small group discussion and props, every single pupil was focused on the task and on their small group dialogue. In a socially and cognitively ‘noisy’ task like this, pupils’ attention could easily drift but it did not. In the bridging discussion at the end of the lesson, when asked if they could think of a situation when there had been too much run-off, the groups did not find it difficult to generalise to incidents of flooding locally and nationally. When pupils then moved to smaller scale models with trays, sponges and jugs of water in class – there was still a clear sense that slowing or reducing the run-off mattered. Moreover, teachers were asked ‘When can we have another Let’s Think Geography lesson? And told ‘That’s the best geography lesson we’ve ever had.’
From collaborative reasoning to action
We had been rigorous in checking relevance not only to the current National Curriculum Programme of Study for Geography but just as/more importantly (select your preferred determiner) the United Nations Sustainable Development Goals (SDGs) and in particular how they have been translated into the SDG Learning Objectives guide for educators developed by UNESCO. UNESCOs objectives for each SDG have three domains: cognitive, socio-emotional and behavioural. Cause and effect reasoning with manipulation of an increased number of variables was clearly cognitive. The Vygotskian social constructivist engine ticking in all Let’s Think lessons to an extent helped us to meet the socio-emotional domains in that learners would collaborate and develop understanding with others. Our Piagetian progression spine would encourage gear shifts over time from a personal, to a group, a local even a global perspective. We did seriously wonder whether this progression would be possible for our age 9-11 year group within just a few lesson episodes. And finally, the behavioural domain. The UNESCO objectives set the challenge that education in each SDG should promote not just thinking, but action. Action in favour of those who are most threatened by climate change. Action through the promotion of climate friendly activity, choices, even policy.
Achieving improved collaborative reasoning, applied to increasingly wider frames of reference with a sense that increased agency would lead to informed action really was demanding more from us as Let’s Think teachers and tutors than before.
Then came the T-shirts.
Supported by the experience and insight of Dr Verity Jones, Associate Professor of Education at the University of the West of England, our next cycle of lessons started with a pile of second-hand t-shirts. We moved from:
- selecting and classifying what makes a ‘good’ T-shirt from the pile (it’s a nice colour, we like the logo, it’s softer);
- to understanding and representing the waste (in energy and materials) in a linear fashion economy;
- to effortfully envisaging how circular processes could be introduced into the t-shirt industry as they have been for paper.
After two intense hours of socially situated mental activity, we asked:
‘What now makes a good T-shirt?’
- It should be made of better material so it can last longer
- It should cost more so that those who make it get paid properly
- It should be made closer to where it is sold
- It needs to be made with different kinds of bleaches and dyes
And finally: ‘To whom does the choice of a t-shirt matter?’
It matters to us and it matters to the planet.
Why does Let’s Think Geography matter?
Throughout this project, we have known that we are standing on the shoulders of the Cognitive Acceleration Pedagogy giant, here. Let’s Think lessons so often do matter to children because they feel safe, they are included: they contribute and are heard. As a group, there is a feeling of connectivity, even when exploring difference and difficulty, because the group (is supported to...) steer through challenge, towards ideas that are gaining traction and are well-reasoned. The creation of new ideas and insights is tangible and builds efficacy.
Indeed, new insights from interdisciplinary research institutes (CANDLE and The Social Brain Institute) – combining neuroscience and social science - are confirming that effective processing in the brain cannot be separated from our social and emotional context. Learners who feel they are socially connected, who are engaged in frequent feedback loops, who feel they have autonomy and who are working with a desirable level of challenge, crucially on matters that are of importance to them, have increased levels of energy fed to the brain. Learning, of a safe, collaborative, dialogic, rigorous well-pitched and affective nature is literally brain sugar.
We are daring to think that our most successful Let’s Think Geography lessons have mattered to pupils because of these very dimensions. At a deep ‘scientific’ layer of the learning river, we have been deepening pupils’ reasoning around complex systems, causal relationships and with the T-shirts lessons, the dimension of moral justice. Just as deep has run the layer of learning about ourselves and our relationship to the world that is both home and resource. Pupils’ frames of reference have moved from themselves, to the group, to society and the wider world. They have begun to construct age-appropriate and hopeful ways in which they can have choice and agency in the face of complex problems. Finally, they have begun to understand how the responsibility for change sits with industry, innovation and legislation, as well as but not only with themselves.
The humanity and science demanded by the vision of the SDGs has been a powerful influence on our existing understanding of CA pedagogy and the extent to which children will think hard together and be moved to act differently, when learning matters.
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