Climbing The Hill
Deepening Thinking in Mathematics Part 2: by Jonathan Owen @mrowenedu
In Autumn this year, after exhaustive research, the Greater Depth prompts were introduced across Foxfield Primary School. Along with Mr Satnam Bansal and Mr Patrick Adekoya, I led a PDM and gave over our books for scrutiny, asking the staff to pull out how, when, where and why the prompts were being used. We asked
- Which prompts have been used?
- At what point in the lesson were they used?
- What sort of responses do they elicit?
- How could they be adapted to be suitable for your phase / year group?
There had been some calls for a crib sheet on how these should be used, and I started to make one, but within this session teachers helped to create rules and requirements for each sticker using an example provided. This has ultimately led to teachers adapting the use of the stickers to be effective in all phases across the school.
Before, and especially since this session, I have been amazed at how much the children love using these stickers to drive their own learning. In using them, the children are a far cry from the unconfident child I was at the same age – the motivation and pride that the children show when using these are the reason I do this job. Some of the links the children have made, prompted by these simple images, are incredible; moreover, they are often connections that my colleagues and I would not have made. Quite humbling. In using the prompts, I believe we are well on the way to developing learners who are ‘able to recognise when they are learning and explain how they are learning.’ They are analytical, evaluative and proud.
I am also humbled by the effort of all teachers across Foxfield Primary School to evaluate the effectiveness of this approach to deepening thinking and their willingness to adapt the use of these prompts in their own classes. As teachers take the extra time to save examples of the prompts in action, it’s clear that children in Early Years are just as confident and independent in reasoning and problem solving as children in KS2 – perhaps even more so! Also, and most importantly, it is not only high attainers who are using the prompts: their universal simplicity and accessibility mean that all children, whatever their barriers or current attainment level may be, can think more deeply than they previously did because of research, careful planning and some small, yet beautiful formed images.
This week, the prompts will be introduced to all schools in the partnership. They are currently being used in four main ways.
- On our flip charts and smart boards
The image above shows, the prompts that the children have been trained to use are included on our lesson slides, including our mental oral starters, to extend thinking and reasoning. This not only provides an opportunity for reasoning, noticing patterns, making connections etc, but also develops children’s independence and allows them to make choices on where to take their learning. We believe the prompts make what could be a restrictive task into a low threshold but high ceiling activity. Some responses in this Year 4 lesson included:
- If I said 2 more numbers, I would say 175. I know this is correct because the ones don’t change when you are adding 10.
- I disagree that the last one is the odd one out because it’s going in 10s too – ten tenths at a time.
Within collaborative Kagan Structures the prompts also elicit analytical and evaluative responses from children. They provide an a dditional opportunity for assessment for learning, which is not present when children simply compete a calculation. Tasks such as these are routinely supported by sentence stems.
Children in Year 4 noted:
- They are the same because you add the ones, tens and then the hundreds in each method.
- It’s different because It’s really clear how many ones, tens and hundreds you have in the expanded method.
- In both of them you have to make sure you say 70 add 80 instead of 7 add 8 and 50 add 70 instead of 5 add 7.
This example from Year 4 is taken from the book of a learner who is currently working below Age Related Expectations. The visual nature of the prompt means that the child was able to understand the task with very little support and their reasoning gave the teacher further opportunity to assess understanding and address misconceptions.
3. In Feedback Marking
Teachers’ time is precious. Quality feedback marking should not require half a page of green ink to elicit in-depth responses from children. And it does not. Just use the prompt stickers!
The same sticker can elicit a whole range of responses from children and it can be scaffolded as much or as little as necessary. The example above – where a Year 6 child linked ______ to percentages showed a child making connections that a more traditional closed task would not have enabled. This was then used by the class teacher to strengthen the understanding of all learners.
4. Independently to Direct Own Learning and Deepen Thinking
The above example shows how many children (in Key Stage Two largely at the moment) independently take stickers at any point in the lesson. The advantages of this, which have all been mentioned in some other sphere of the project already, are:
- It develops confidence and enables children to take responsibility for their learning. As Tom Sherrington refers to in The Learning Rainforest, one of the greatest joys of teaching is seeing where children go with something.
- Explanations and reasoning about the mathematical process actually serve to clarify understanding for the learners themselves.
- Explanations and reasoning about the mathematical process give chance for teachers to assess exactly where a child is making an error – an answer, a number alone cannot do this.
The reasoning prompts ask children to look at what they have done from a different perspective, consolidating and deepening understanding on a topic they may have ‘got’ already.
A Few Words of Warning and Disclaimers
Although the examples above show that spontaneous reasoning, independent problem solving and child-led greater depth learning can and do occur, this is the end goal of a journey of which we are much nearer to the start than the end. We are aware that children will not see a sticker and become great mathematicians, without careful planning, training, reflection and adjustment. However, they have made a massive impact in the school and children clamour to use them.
It was our expectation for this term, that:
- Six children independently using the prompts at least once a week until Christmas.
- Flipcharts and worksheets to have a reasoning prompt evident at least once a week and for all adults to model responses to these.
- Feedback mark six children using the stickers where appropriate.
- You do not have to stick to any rules rigidly – we would appreciate feedback on how you have adapted them
Finally, In reality, teachers and children are using the prompts over and above what is expected, but our training session also made clear that these are not the only way to evidence greater depth or challenge. My key message to my staff and anyone reading would be that these stickers supplement and in no way replace careful and considered task design, effective questioning, thorough assessment for learning or individual feedback.
I mentioned in part one of this blog that my vision included A simple, supportive approach that works for any area of mathematics and any age group or attainment level. A child with SEND asked me last term, ‘Why can’t I use a sticker yet? My adding is different but I might understand my adding better if I have to explain it, or prove it, or find the error.’ He instantly became one of the first wave of children in my class to use the stickers independently. I believe that Maths is a curriculum area still mistakenly obsessed with correct answers. To my mind, our success with these stickers, and the way were are using them, emphasise that ‘greater depth’ in Maths, as with any other subject, is as much a learning process, equally based in the affective and cognitive domains, not an outcome.