Can our maths help Stratford decide if 3 new concrete factories are too dirty?

Jeremy Judge and I have just reached the end of our project exploring the inquiry question ‘can our maths help Stratford decide if 3 new concrete factories are too dirty?’ The answer, it transpires is yes, yes it can! 14 weeks of risky, challenging and exciting exploration later, with multiple dead-ends, some serious writing graft and one powerful algebraic model, and the big news is that the LLDC have asked the concrete company to withdraw their application!

The Evening Standard letter that sparked the whole project.

This project was, as written about in my first blog, in part, an experiment in truly authentic learning. We took a real world problem that was yet to be solved (hitting the top of our self-styled authenticity hierarchy) and set about solving it live, in real time with our students, together as one 16-strong team.

As I reflect on this project and its successes and limitations, I’m thinking about the lessons we have learnt from it that should inform our future practice. They seem to fall under 5 key learnings:

  1. that planning = patience;
  2. that we should embrace uncertainty but control the controllables;
  3. that we must get comfortable in the uncomfortable (and why we should all teach maths…!);
  4. that meaningful assessment is about the future not the past;
  5. and that true purpose can kill a checklist of project ingredients.

If you want to see our full project reflection, feel free to have a read here.

1. Planning = patience

The whole process, start to finish went through what School21 colleague Mark Blundell calls the ‘double diamond’, a 4 stage of process that goes through two rounds of divergent and convergent thinking as it moves from initial ideas to delivery.

Mark Blundell’s ‘Double Diamond’ of PBL planning.

The equal weighting of these sections on this diagram is somewhat misleading; they are certainly not equally chunked sections of the planning process, or indeed necessarily linear.  For me, the ‘discover’ and ‘define’ elements are a constant ongoing exploration (I literally bank ideas, products, opportunities etc and then wait for the perfect storm of learning, authenticity and purpose) and for Jeremy and I with this project, this was around 3 months of patient waiting and spirited arguing.

Once we defined our idea, the sudden flurry of action kicked off with the ‘develop’ phase in the half term leading up to the project launch.  It was here that we focused around the project design and put in the serious planning. Here you can see the outcome of this stage, the planning overview behind our project – this original plan was tuned by a group of school staff initially and then by the class themselves before the project began. To get to this though, it was certainly worth the slow, lengthy ‘fishing’ process of the first 2 sections – the sort of ‘waiting by the pond’ for the perfect bite.

2. Embrace uncertainty but control the controllables

Our timeline document gives the very false impression that this project was clearly structured from the off.  It was in truth a constantly changing beast with shifting goalposts beyond our control, constant dead-ends and false starts, and the document as it stands was created very much by the day.

Our mathematical problem solving process; the very real attempts at problem solving meant several complete cycles of this process before reaching any success, which in turn meant a very flexible medium term plan…

In fact, this project’s authenticity meant a required flexibility of timeline and direction of learning that I haven’t dealt with before (as I blogged about in December). Despite the unknowns, Jeremy and I wanted real rigour of significant content and assessment, and had to very much hold each other to account throughout for our subject ‘non-negotiables’ that we had pre-identified. The changing nature of the planning process, client vs teacher rub and open problem threw numerous challenges against this and at times we were pulled or tempted away from our desired line of learning. However, we assessed each challenge under our clear design principle of being true to our subject content; if it didn’t develop non-fiction writing, algebraic skills or graph interpretation, we (mostly) didn’t do it.

So for all the things out of our control, we had to focus on what we could control: to control the controllables. For us, the controllables were mainly defined by a narrow, clear product and project brief; we were working to create a mathematical report into the impact of the proposed factories on air pollution in Newham. This product wouldn’t display all the learning that had taken place, but all the learning would be designed to create and improve the product.  This I believe is a key design principle of good PBL. For me as the English teacher in real terms this meant:

  • Rigorous development of voice and purpose in non-fiction writing and sentence control through mastery exercises (as written about in my most recent blog) and the use of shared writing as a norm.
  • Constant building of the skills required to comprehend challenging non-fiction. For this we used a range of newspaper articles on the project and the project’s grounding text, picked for it for its value as a model and for significant content and as a style/tone guide.
  • Growth of tier 2 vocabulary via weekly robust vocabulary sessions to benefit students for this project and beyond.

The other thing that helped with our control amidst the uncertainty was ensuring absolute clarity of role; we were purely the report generators, exploring the facts, analysing the data and interpreting and explaining it clearly. It also helped that we were working as a parts of a much wider edifice of people, each with a specific and genuine role in the project. For example, James Durrant of the OPCRD was our client spokesperson, Terry Paul our voice in the local council, Elsa Aristodemou our mathematician providing advanced models, Emilia Papadopoulos the BBC presenter reporting on our work; all of these people were not brought in inauthentically to help out, but were carrying out their actual jobs and roles around us, meaning we could be entirely, authentically, air pollution impact report writers. This importance of clarity of role is something that I think we must take forward into future projects.

Mathematician Elsa Aristodemou introducing the Gaussian Plume model to students in a seminar in December

3. Get comfortable in the uncomfortable: we should all teach maths

One of the things Jeremy and I have done throughout this project to ensure support, accountability and growth is to team teach/observe and feedback on one lesson a week each – so every other Wednesday Jeremy joined an English session and each other Thursday I joined his maths class. This began as observations, with feedback on our chosen students or craft area given in our weekly meeting, but over time morphed into team teaching, which brilliantly blurred the lines between our content.

We reflected the other week on how we had maintained this routine throughout the project with (genuinely!) no sense of loss of time or feeling we had other things to do – in reality it means the removal of between 2 and 3 free periods a week each. I think this is due to our genuine investment in each other’s practice and growth.  It really matters to Jeremy that my practice around robust vocabulary teaching for example is improving as we need students to thoroughly understand mathematical words like ‘assume’ or ‘vary’, and it seriously matters to me that Jeremy is thinking about the most effective ways to use talk in his lessons to ensure students are adept at verbalising what their graphs show.

Interestingly, aside of the obvious advantages of team teaching,  with feedback and learning through osmosis, there are also a powerful side benefit in being forced into the discomfort of teaching another subject. It was in attempting to teach maths that I suddenly found myself completely out of my comfort zone with my pedagogy. I think (though I am as yet unable to clearly articulate the what and why of this thought…) that there is something in this for our teaching. I suddenly couldn’t rely on my subject knowledge to be able to teach something and instead had to wrestle more deeply with the why behind students’ misunderstandings or confusion. I started noticing links between missing skills or misunderstandings in student’s conceptual understanding and really thinking about the barriers and blocks that stood in the way of progress.

4. Assess for the future, not the past

Of course,  it is not the final product in a project that provides any form of useful assessment; in this case, it’s a group created outcome, which has gone through 5 drafts and is not (and should not be) reflective of all the learning or all the assessable skills/content. I see it instead as a narrow slice of the learning, useful to the world as it’s genuine purpose intended, but useful to us purely as a teaching tool (much of the writing learning for example, came through critique and redraft of this document).

Instead, we assessed with a triangulated combination of ongoing class assessment, cold assessment of reading and writing at the end of the term and verbal viva style ‘story of learning’ assessments. This leaves us with a combination of narrative assessment comments and hard data, and a forensic understanding of their learning. These verbal assessments are my favourite part of each project – a 10 minute one-on-one conversation which reveals so much truth behind each student’s feeling and progress, which data alone cannot reveal.  In the past these have uncovered shaky understanding where the data implied solid growth, unexpected misconceptions, and sometimes progress that has gone unnoticed elsewhere. As we hone this practice, I think we now need to decide a) when is the ideal time to have these assessments so that we can identify and respond to gaps early  b) what are the right questions to ask in this viva assessments to inform future practice and c) how do we ensure this knowledge is fully used for future planning/future teachers of the group.

5. True purpose can kill

Fascinatingly, the huge real world success of our project also led to the death of certain elements of ‘gold standard’ PBL, most notably exhibition.  I haven’t yet decided if this matters or not. Our intended ‘exhibition’ was the presentation of the report at the LLDC’s planning committee meeting, however, this was swiftly cancelled when the students’ TV appearance and power of the public campaign led the LLDC to withdraw the plans before the meeting.

The abrupt end of the project left us with an interesting uncertainty; do we plough on and provide some form of exhibition for the students or end it there? We sort of chose both and neither, leaving an odd sense of loss for all involved! But its interesting to step back and notice the complete loss of purpose for both staff and students once the true purpose had been achieved – perhaps we didn’t need the exhibition because we didn’t need the motivation. The question that I feel remains is without public exhibition, how do we achieve the student accountability and testimony that this provides, and does this matter? Certainly something to consider.

Overall, the resonating impact for me (other than that on their writing) was on our students’ sense of self-efficacy and pride, and this is what the authentic purpose of this project brought about. This was put most succinctly by one student who is her story of learning assessment said: ‘I am proud of the fact that we are not having the concrete factories in Stratford. That makes me feel like I have had a good impact on the area I am living in.’

Students grappling with some tricky maths in an English lesson.


Mastery for a purpose

In my previous blog post I referenced the weekly ‘grammar gym’ mastery sessions that I have been doing with my concrete project group in year 9.  This developed out of watching primary teachers in my old school teaching sentence forms and then practicing them repeatedly. It was something I stole at the time and used with a year 11 group as practice, and have been playing with strategies of grammar mastery since then.

When I first taught the concrete project group in year 7, I began to use this strategy to teach the group some of the sentence structures and connectives that were missing from their toolkit of language at that time. It’s not something I’ve needed to do so explicitly before as a secondary teacher.  Yes, I’ve reviewed grammar rules, and taught the use of more complex sentence structures, but I’d never previously had to explicitly teach students to use more than simple unconnected sentences, and the very basics of connectives/constructing a sentence.  As time has gone on with this group, the skills we learn and repeat in the grammar gym (always within context of the project we are working on) have become increasingly sophisticated.

It’s been really interesting watching the impact of this weekly practice and instant feedback/instruction on students individual writing and shared writing.  See for example a selection of one student’s grammar gym work from across year 9 so far as he has got to grips with using  who or which to add more information into a sentence.

An early Grammar Gym from the term before the concrete project, when we first attempted these sentences. It’s clear that the purpose of this sentence structure is not understood at this point.


A heavily supported Grammar Gym from the same student early in the concrete project.
His independent attempt in this Grammar Gym displays his growing understanding of the purpose of this sentence structure and interestingly shows him punctuating accurately too.  He has taken on a really complex sentence in this, a significant growth in his control of language.
Completely independent from a few weeks ago! This doesn’t just show a memorising of a language form, but a conceptual growth.

His competence using complete sentences, commas to control subordinate clauses and his understanding of the function of such sentence structures have grown significantly from initial heavily supported attempts to completely independent craft.  And this competence is vital to the progress of these students; I’m actually not necessarily a huge fan of repeated grammar practice and drill but for these students, all of whom arrived at School 21 lacking some key skills for accurate and flexible communication and with gaps in language development, this internalising of language forms and structures is incredibly liberating and vital.

However, I’d argue that the increasing levels of competence of these students relate to the want and need they have for these skills: the purpose that the authentic project has provided. They need to be able to describe their maths accurately and fluently (an early foray out into Stratford to speak to the public about the factory proposal brought the group to the realisation that “we need to be really clear about what we mean – people don’t all understand maths…”). They want the LLDC to take them seriously and understand the findings their report has exposed. They need written fluency, eloquence and control. This brings me back to the interlinked need for competence, autonomy and relatedness in the project.  You can of course teach English from a competence alone stance, but when taking the importance of relatedness into account, there is suddenly a real purpose for these skills, a need for the competence to increase and a desire to graft away in order to do so.


The tip of the iceberg

I’ve just watched our year 9s on BBC London’s evening news talking about their project to create a report modelling the potential impact of three proposed new concrete factories on air pollution in our local area. It was brilliant to see them speaking eloquently, enthusiastically and earnestly about the project and the very real threat to our community that the plans pose. Excitingly, this amazing opportunity stemmed from the very scary uncontrollable authenticity I wrote about in my previous blog; it arose from an unexpected curve ball thrown at us in the client meeting with OPCRD member James Durrant at the start of this project. He asked, ‘how can you use the power of your youth voice to spread the word about these concrete factories?’  This was not part of our project plan.  We were writing a mathematical report. We sat on his question for some time, and it wasn’t until a sticking point in the maths that we returned to act on it.

A not so dead end

Three weeks before the Christmas holiday, we realised we had spent several weeks exploring an avenue for data collection that slowly revealed itself to be unhelpful. The obvious frustration of this for both us and the students also led to an issue in English; with no data coming through, we ran out of things to write up.  I felt really strongly that we should not engineer purposeless, inauthentic writing, and so in the 3 week gap that presented itself we turned out attention back to our parked thoughts on James’s challenge; how could we, 14 students and 2 teachers, spread the word to the thousands of people across London needed to meet the petition requirements?

Start spreading the news

One of the group’s initial ideas involved harnessing the power of national media to share our message. And, inspired by some of the article we had been reading in our reciprocal teaching sessions to learn about the project, they named the Guardian, BBC, Evening Standard and Newham Recorder as their targets. Achieving this however would require something outside of all our experience; what do you actually need to do to get serious press to cover your work?!

Some light googling revealed we needed to write a killer press release, so we set our sites on the start of the new year and began a 3 week process achieve this goal. This consisted of:

The first 2 drafts of our group written press release.

– Reciprocal teaching sessions a ‘how to write a press release’ article from the guardian which was formed into a checklist.

– A series of structured debates around what our news actually was and what we needed to get across.

– 4 drafts of a press release created through shared writing sessions with the whole group and mini teams within the group. The focus shifted on each critique and redraft from mimicking a newspaper tone (and writing in the 3rd person) through improving vocabulary with high level connectives to a formalising session. Students were editors, nit picking for commas around subordinate clauses or the correct usage of a semi-colon, and creators, arguing over the merits of one word over another for reader interest.

– Throughout, a continuation of our weekly contextualised ‘mastery’ sessions – from our ‘grammar gym’, practicing challenging new sentence forms to our ‘word of the week’, where new tier 2 vocabulary is learnt robustly.

One student’s grammar gym work focusing on using subordinating connectives.

Loosening the reins

The final press release was typed up and sent to the news agencies identified earlier in the term this Monday (we decided to wait for the January return to work so as to not get caught in a Christmas lull). In 24 hours we had a call from the BBC, and then another 24 hours on they were in filming the students. But the real success here for me is the rigourous teaching of authentic non-fiction writing that led up to this. It may have been an unplanned extra outcome, but the learning and mastery behind this product was what we have been working for and building to all term.

As I write this, the over-planned, control-hungry side of me still feels a niggling discomfort with the lack of pre-planning that this exposes. I still ask myself if this swerve is allowing anything to slip through the gaps or if this unplanned change of direction mid project damages continuity of learning. But I feel fairly confident that this is not the case. In fact, in the final outcome and the future writing of these students, I feel we will see significant benefits for this.

The tip of the iceberg?

It’s interesting though as when looking at a project, and particularly the moments of outcome, that much criticism is levelled at the learning that has taken place. Where is the rigour, people ask? What significant content have they actually explored?  How much did students actually do? And actually I think often this ‘product’ or outcome hides the wealth of work and craft that led up to this moment – it is the tip of the iceberg of the stuff we’re really grappling with; and the stuff we’re really proud of.

When nothing is concrete: planning for uncertainty

Maths teacher Jeremy Judge and I are currently 4 weeks into our new authentic learning project.  As mentioned in my previous post, our primary goal was to hit the ‘top’ of our authentic learning hierarchy and plan a project which is a real problem that students can meaningfully help to solve, making a difference to the world.

The problem? We have no problem!

Around June we set about looking for the perfect project opportunity but, acutely aware that we couldn’t force it, nothing quite right surfaced.  When Jeremy and I were about to  part ways for the summer holiday (him to South America and me pottering around the UK), we were both anxious about the looming reality that we might have set our sights too high. And then, on the Jubilee Line, somewhere between Stratford and Southwark, (with thanks to the Evening Standard) the ideal opportunity was right in front of me:


Problem solved?

Right on our doorstep, in the Olympic Park, the LLDC are proposing to build 3 concrete factories and one asphalt factory. Right now! Some light digging by Jeremy led us to a group of local residents fighting the plans, the Olympic Park Coalition for Responsible Development (OPCRD) and we contacted three of their team to see if there was anything we could do for them.

The meeting that followed was a brilliant mix of exciting and terrifying.  Here was a group of motivated people at the start of a live and very challenging fight. Here was a campaign reliant on knowledge that they didn’t yet have. Here was a vast problem yet to be solved. Here was a team with the very real question of how to stop the LLDC going ahead with the building of the concrete factories.

Their enthusiasm for commissioning the student group to work on part of this problem for them got things off the ground and we talked through the areas that they currently needed evidence for but didn’t have. The trio talked passionately about the very topical issue of air pollution and how this could be a significant factor in whether the plans get the go-ahead or not. This became our problem, and the OPCRD tasked us to produce a report as part of their pack of evidence that illustrates the impact of the proposed factories on air pollution in the area. We left that meeting with a wealth of enthusiasm and the guiding inquiry can our Maths help Stratford decide if concrete factories are too dirty?

Planning for uncertainty

The question that remains now, 4 weeks in, is how we plan for a problem that we as yet have no clear idea how to solve.  What do you do when a project is so authentic that you don’t know what the content of the outcome will be before you begin? You start with the things you do know: we know we need to write a report, and we know that at some point the LLDC will call a planning meeting where the report will be used; we know we need to find out how much impact the proposed factories will have on Stratford’s air and we know that we can use algebra to do this; we also know that our students can’t yet use algebra to mathematically model (a pre-requisite of the report) and have never written, or read, an environmental impact report.

This truly authentic project management schedule, with inflexible deadlines but no clear solutions (yet!) flies against the teacher’s reliance on being carefully planned in the short, medium and long term. The shifting goalposts of the LLDC’s moving meetings, and the prospect of dead ends in the problems solving are uncontrollable variables that we just have to work around. Our solution? Be completely up front about these threats with the students.  We are very much in this together – after all, sixteen minds are way better than two – and it is very much our project.

img_3150Back to this week, and we shared our progress so far in a client meeting with the OPCRD’s James Durrant. He spoke for 50 minutes and our students listened, engaged and focused, to every word.  They asked probing, thoughtful questions, and built a strong mental map of what we know and need to know. They were professional, inquisitive and serious.

They are driven, not demotivated, by the uncertainty ahead.  They know the risks, the threat of failure and the very real impact on their community and their lives that the factories could have.  But they also know that they could be a cog in the dissenting wheel against the LLDC’s might; they could change the face of Stratford forever.  Now we just need to work out how.

Not PBL, but authentic learning

When the EEF released their report on the Innovation Unit‘s PBL trials earlier this month, Twitter lit up with the loud anti-PBL brigade’s gleeful celebration of the ‘proof’ they have been waiting for. PBL doesn’t work.

As I sifted through hundreds of angry, righteous and indignant tweets, I felt sad. And as I sit here, trying to eloquently explain why I felt sad, on what basis I’d challenge the arguments, the research, the response and what I’d promote in their place, I realise that this is relatively irrelevant. For a load of reasons, that it would be relatively irrelevant to go into.

So instead, I’m going to blog about my current project: my next step in ‘PBL’, or as I’d rather call it ‘authentic learning’, and the developments in my craft as I take the biggest leap into the unknown of literacy education that I have attempted to date. This blog will reflect on our thinking, planning and processes as they happen. Here we go…

Chasing authenticity 

Over my past 3 years’ explorations with authentic learning and reflection, I’ve stumbled into the belief that authenticity is the key driving factor behind a great project. At School21, we rest on the phrase ‘today matters’ to summarise this; school shouldn’t be a holding pen for a child while they wait for the future. It is the now, the present, and it should be embraced and used accordingly. So why then shouldn’t a 13 year old be working on things that change the world around them, that leave a permanent mark and that alter the environment forever?

As an English teacher, I’ve become somewhat fixated in the past 4 years by the idea of using writing (in particular non-fiction writing) only for authentic purposes and investing time in pursuing genuine authentic needs for student writing to plan learning around. My early, clumsy-ish efforts at authentic learning led to a first draft of this idea – the ‘Words for Wildlife’ project which I created with science teacher Pippa Sadgrove and fourteen year 7s. Fast forward 9 months, and I met maths teacher Jeremy Judge, who was keen to co-create a project with one proviso; it has to solve a real world problem, using maths, authentically. Perfect.

We spent around 4 months scoping out problems waiting to be solved, talking to people from a variety of industries and having (sometimes slightly fraught) meetings bashing around ideas. We were stuck in a cycle of getting excited about an idea and then finding it being undermined by its lack of authenticity; either it had already been solved, it didn’t really need to be solved, or it didn’t need to be solved using maths/English. And then we came to a moment of clarity on our understanding of authenticity in learning whist talking to an app designer from Salesforce about a possible collaboration. Authenticity in schools it would seem broadly falls into 3 categories:

1) An artificial problem that experts in the field would not solve (example: using algebra to plan what you would buy in a supermarket).

2) A real problem, but one that experts have already solved well enough (example: using algebra to predict how well a product will sell in the future).

3) A real problem that students can meaningfully help to solve, making a difference to the world (example: using algebra to ???).

If we can hit the third of these categories, we can use our literacy, numeracy, oracy, collaboration, critique (the list goes on) for genuine, real world output. The drive generated by the risk for teachers and students pushes real grit and motivation, the genuine need to unite, both with each other and with external agencies and experts, drives collaboration and the spark required for flexible, mistake-guided genuine problem solving is huge. And above all, students genuinely need control of literacy and numeracy to be successful. Suddenly, the stakes are raised for learning these basics.

Suddenly, we have a project…