What Next?

This week I was lucky enough to sit down with the Headteacher of the fantastic Central Primary in Watford, John Mynott, and discuss all things Lesson Study. I explained to John how I felt Lesson Study had been fundamental to the development of my teaching practice and had been a key element in creating a culture of collaboration at the school I work at. John asked if had to choose one cycle of Lesson Study which was particularly memorable which would it be.
One Lesson Study cycle which really stands out to me and one I often reflect back on was when the great Ban Har came into our school and acted as the ‘knowledgeable other’ in our interrogation of Singapore maths. This obviously was a unique situation – a once in a pedagogical life time experience – and has been the single greatest CPD I have ever been involved in. I explained to John that after the 3 day cycle came a feeling of energy and a personal buzz around teaching that up until that moment I had not felt in such a vivid way. I went on to say that the outcomes and professional learning from the Lesson Study are still shaping my practice to this day – I often frame what I teach and how I teach it in reference to my professional learning on that day. John then asked what have I done with these outcomes and who/ how I have shared them.
Great question.
Well immediately after the Lesson Study we (the research team) created a learning poster and shared the outcomes with our staff in a meeting and the learning has also had an influence on the numerous Open Days we host across the year. But the truth is I hadn’t really reflected in sufficient depth just how influential the learning from the 3 days had been. I always felt there was a sense that I knew at the time the outcomes of the learning were groundbreaking to my practice but I hadn’t yet fully understood the implications and how I could apply it to my own context going forward.
So I’m writing this for a number of reasons:
1) I find writing helps me understand my own thinking as I have to be really clear when putting my thoughts down onto the page and this allows me to gain an appreciation of whether I do understand something.
2) I hope this makes me a little bit more accountable for the sharing of the learning. I had this incredible professional learning and on reflection have I utilised and made the most of? Not yet. So hopefully this will force me to make the learning a stronger foundation to the pedagogy in our school.
3) It’s not every day you get the opportunity to have such an experienced and knowledgeable guru in your classroom. So I feel it is now my responsibility to share it with as many people as possible, with the hope that others can benefit in the same way I did.
So what did I learn?
(Just to give you a bit of context this was a Year 6 class of 20 pupils in a mixed setting and the focus was on challenge for all.)

  1. Time

The first thing I learnt was the importance of allowing enough time for children to interrogate a problem within a group without any teacher input. Piaget calls this ‘exploration’ and Ban Har ‘ample processing time’ where children are allowed to explore, make mistakes and get their head around a problem in their own reality. This exploration phase of a lesson should be a sufficient amount of time but the key is it needs to be in a low stakes environment where pupils are allowed to make mistakes, look at a problem informally and in a number of different ways before any teacher interjection or formal teaching. (Zoltan Dienes – Six-stage theory of learning mathematics).
What I found what I was doing was that I was allowing time for exploration but nowhere near enough. It would only be 2/3 minutes before I would start to interject with questions scaffolding or enriching a problem before pupils had time to really explore and make ³sense of the problem deeply.
It was suggested that the exploration phase should be longer – 8-10 minutes (which can seem like a lifetime). The role of the teacher going around and ‘eavesdropping’ on the pupils learning- carefully beginning to consider how they were going to select and sequence the class discussion that would follow the exploration, also keeping an eye out for any unanticipated misconceptions. Just allowing those extra few minutes meant more pupils had time to answer the problem in a way that suited them – which meant more methods – which meant more points of connection making – which meant better discussions. Ban Har wisely said afterwards that sometimes ‘you need to waste time to save time.’

  1. The Five Domains of Challenge:

Ban Har suggested that there are 5 domains in which teachers can consider when planning for ‘challenge for all’.
Ban Har offered that there are many layers of challenge within a maths lesson and these can provide different challenges for pupils far beyond just the actual maths.

Cognitive – the actual maths. Students being able to solve the problem using any method. The movement between concrete, pictorial and abstract.

Metacognitive – pupils being able to spot mistakes, recognising and selecting the most effective methods, being able to make generalisations and adding a new perspective to a previous response.

Mindsets – having a productive set of beliefs, developing an understanding of how they work best and the ability to challenge themselves.

Social collaboration – contributing to the learning of others and developing themselves through this, seeking help and questioning of their partner.

Affective – showing perseverance, restraint and enjoyment within the lessons, understanding that it is okay to struggle with a task or problem.
🤯 – this was me at the time
I think naturally as teachers we provide sufficient challenge through both cognitive and metacognitive domains even if we don’t frame it using those terms, but I guess thinking on my own teaching I’m less conscious about the way I provide challenge through mindsets, social collaboration and affective domains.
But I’ll give it a go:

Cognitive – using MNP I don’t struggle to provide a challenge cognitively due to how well the textbooks have been written. I am aware of making sure that pupils aren’t coasting during a lesson and make sure I’m providing some kind of learning turbulence (learning pit) during the lesson. I’m aware that it’s not better to accelerate a pupil to ‘harder’ maths but rather enrich deeper (that’s where the next domain comes in). This is also where our ‘descriptive’ journalling would fall.

Metacognitive – this is where in some capacity children are required to make a judgement. Identifying a misconception/ Selecting a sophisticated method/ reframing others thinking/ ABC (agreeing/ building/ challenging). This is probably best used once children have a secure understanding of the cognitive element of the lesson/ learning.

Social collaboration – as we all know with partner talk to can be variable on many different levels. Our school uses talk excellently but this has grown naturally and we can’t rest on our laurels so seeking ways to improve it: I joined the Oracy Pioneers Programme which has begun to shape how I differentiate and challenge through talk. This is still a work in progress and an area I hope to write about more extensively over the next year.

Mindsets/ Affective – now this is one that I find it quite hard to conceptualise about how this happens. It does happen and I do try to incorporate it, but without consistency and without a framework… I use reflection questions inspired by Jo Boaler (see previous blog) and the time to work for the time being. These are the next to explore fully.
3) Self Efficacy
Teachers are inherently overly self critical and I am too. The truth is you are doing a better job than you think you are and the fact you doubt that will probably make you a better teacher in the long term.
Anyway hope this was helpful and please contact with any questions. These ideas aren’t fully formed yet and I would love to discuss and reflect further.

Anyway, cheers,

Dave 🖖

Wait. What? Writing in maths?

Maybe some of you, like me, had this reaction when you first heard about journal writing in mathematics. How can I do that? They struggle with the maths itself let alone writing about it. These thoughts screamed across my head 5 years ago when I started my journey using journals and I continue to hear these when supporting colleagues new to the approach. And, to be completely honest, it’s a good question. What is the point?

The Point(s)

Gemma Meharg in her blog post ‘4 reasons why your maths students should be journaling’ https://mathsnoproblem.com/4-reasons-why-maths-students-should-be-journaling/ outlined the main benefits of a maths journal: student engagement, student self assessment, develop higher level thinking skills and formative assessment for teachers. Adding to this I would specifically like to draw attention to the positve benefits of writing in mathematics. If you’re anything like me you may find writing difficult. I sometimes sit and redraft a 2 or 3 sentence email multiple times. During my studies, sometimes it only came to me when essay writing that I didn’t have a secure understanding of the concept I was writing about, and I would hit the books again. My point being that writing to convey a message or to communicate understanding takes organisation, consolidation and clarity of thought (with a bit of reflection in there too). I would love to develop these skills in my students.

The Backlash

Now, the next backlash my brain provided me 5 years ago was: well that all sounds brilliant, but it will take too much time and maths is maths and English is English. Yes and No. Developing writing in skills in mathematics will take on a similar process to your approach in English. Analysing good (and bad) examples, creating a toolkit of skills, shared writing led by the teacher, drafting, feedback, reflection. – the writing cycle. The great Ban Har once said, ‘you have to waste time to save time’. Maybe this process isn’t a waste but rather an investment in deepening students’ understanding. Okay but what about the kids that can’t write? Sentence stems. Teacher modelling. Paired journals. Verbal reasoning being scribed. Yeah but when do I fit in the lesson? On an average day we may spend 10 – 15 minutes on a journal task after exploring the ‘In Focus’ problem (often now, without prompting, the children will often go back and add to their journals after completing their workbooks).

The Journal Task

Initially, all our journal tasks were very similar. We would slightly alter the ‘In Focus’ problem changing the numbers (careful not to change the underlying maths concept) or the ‘nouns’ (sweets to coins, fish to birds). These journals came with a framework; the inclusions of multiple methods and an explanation of at least one (often to a friend who is absent or in another class). However, the approach to journaling evolved after a recent Lesson Study which focused on ‘challenge for all’, where some of our teachers had the privilege to work collaboratively with Dr Yeap Ban Har acting as ‘koshi’ or ‘knowledgeable other’. From this research, and the support of MNP accredited schools days, we have begun to explore 4 different types of journaling. Which we now call DICE journaling.

Descriptive, where students explain the different ways to answer a problem.

Investigative, where students may be required to explore in a method will always work.

Creative, where students create their own problem for a friend to answer.

Explorative, where students are asked to make a judgement on method efficiency or preference.

Finally, after recently reading ‘Mathematical Mindsets’ by Jo Boaler – I’ve adopted the use of reflection questions in class. These are still a work in progress but I have found them useful for prompts to spark some interest taking discussions.

Would love to hear how you have been using journaling, feel free to magpie any ideas or questions from here! Hope this was of use.




The Process of Growth

Under the leadership of Jeremy Hannay our school has shifted away from ‘traditional’ school philosophies of observation and high stakes to one that promotes support, growth and development of all staff. For example ‘Performance Management’ meetings have been replaced with an ‘Annual Learning Plan’ where teachers are paired up with a member of SLT to develop two/three lines of enquiry to focus on for that year. A sample question may be: ‘What reading strategies can be implemented to support emerging readings in KS1?’ or ‘To what extent does writing in mathematics support learners and, considering the law of diminishing returns, how much time of the lesson should be dedicated to this?’ Under this approach I have witnessed teacher autonomy, confidence and well-being increase dramatically.

Yes, teaching is a hard job, we all knew that when we went in (didn’t we?), but these conditions have allowed teachers to flourish as professionals, collaborators and individuals. My point is that, without the requisite conditions it would have been extremely hard for our SLT to develop an approach to journal writing, reading or (hopefully shortly) Oracy effectively. These conditions are intentional, they are an investment and they have formed the foundation of our school. As we expect our pupils to, teachers are encouraged to collaborate, research, explore, make mistakes, reflect and go again.

Therefore, after a year of whole school dialogue and action research a framework for writing in mathematics is beginning to emerge in our school. It has been, and will continue to be, an ongoing process. We are in no way a perfect example, but with each day I can feel us taking a step closer and its liberating to know that if we fall there are so many dedicated people to pick you up, dust you off and guide you back to the path.

With that said – here are a series of journal tasks from our Year 6’s unit on fractions. I love this part of the lesson and it’s always good to here the whispers of ‘Yes!’ from the pupils when it’s time to journal.

Would love to see how your school has been journaling.


Maths Journals

For the last 4 years our school has adopted a Singaporean approach to teaching mathematics which is centred on student collaborative exploration when problem solving.  Since embracing this approach we have seen our students’ mathematical reasoning and understanding flourish tremendously. Our results in both KS1 and KS2 being consistently above national expectations with over 40% of our students being considered ‘greater depth’ by the end of Year 6.

A key element to this pedagogical approach is the concept of ‘maths journaling’. After an initial ‘anchor’ problem, students are required to complete a journal task based upon the mathematical concept that is the focus of the lesson. We often alter the anchor problem slightly allowing students the opportunity to record their thinking, which reinforces learning but also acts as a way for children to think metacognitively about their learning. This is a valuable tool for formative assessment as well as an opportunity for the teacher to see the students ‘thinking’.

When first exploring maths journaling we encouraged a framework for pupils; including multiple methods in their journal with an explanation of at least one (often to a friend who is absent or in another class). However, our approach to journaling is beginning to evolve after our recent Lesson Study which focused on ‘challenge for all’, where some of our teachers had the privilege to work collaboratively with Dr Yeap Ban Har, a leading expert in Singapore maths. From this research we have begun to explore 4 different types of journaling: descriptive, where students explain the different ways to answer a problem; explorative, where students are asked to make a judgement on method efficiency or preference; investigative, where students may be required to explore in a method will always work; creative, where students create their own problem for a friend to answer.

This has, and continues to be, an ongoing journey of professional collaboration, dialogue and reflection. We teachers work together to generate journal problems and share reflections with each other, as we would expect our students to do.