Since becoming Maths Coordinator, I’ve taken the opportunity to align our school with our local Maths Hub. I feel this is a valuable link as not only does it mean we can learn from other school’s and their good practice but we are given the chance to observe and learn about current advances in Maths education.
Two of these unique experiences have taken place in the past couple of weeks. One was an opportunity to observe a lesson from an educator from Shanghai. This was an incredible experience. Shanghai is one of the top performers in Mathematics according to the Programme for International Student Assessment (PISA) and I was fascinated to see what all the fuss was about!
Me and my colleague entered the school hall and found around 70 chairs set out for teachers to observe and sets of tables set out in a classroom layout. This surprised me already. I had heard of lesson studies and observation opportunities like this but had never seen one. I was very intrigued to see how this would work. As the lesson commenced there were clear differences between this approach and the usual starter-main-plenary approach that we have become used to in the UK, with plenty of differentiation and limited teacher-talk. This is what I noticed:
1) Use of language and vocabulary
I was particularly pleased to notice this straight away. The Shanghai teacher repeated the key mathematical vocabulary and sentence structures throughout the lesson. Whenever a question was asked, the children were always expected to answer in full sentences and in clear response. The class that I was observing were trained in this style of instruction for almost 4 years so they were very adept at this. However, it does not necessarily take that long to implement. I mentioned I was pleased because we have begun to implement the same value of mathematical talk and vocabulary in our school using our TalkMaths approach. It also encourages staff to use stem sentences, similar to the Shanghai lesson that I saw. Interestingly, the teacher deliberately chose a higher attaining pupil to model the correct use of vocabulary in full sentences. This provided a good role model and other pupils then followed suit. This practice therefore requires a mixed ability class. The practice of setting or streaming Maths classes would frustrate the efficacy of this approach.
2) Conceptual Understanding
I was watching a lesson where the objective was to compare fractions with the same numerator to a class of Year 5 children. The progression from previous lessons was laid out for us by the Shanghai teacher and they had been using a fraction wall to enable the children to work through the concepts step by step.
Although the children did not move completely into the abstract without the pictorial representation in the majority, they were beginning to solve problems at the end of the lesson without the pictorial aid.
3) Focus on the objective
In this lesson I observed the objective was to compare fractions with the same numerator. The children had previously learnt about comparing fractions with different denominators but, after a brief review of that objective at the beginning, this wasn’t mentioned again. This was not the only thing though that showed a complete focus on the learning objective. The teacher planned a game at the end where the children had to create the largest fraction when given a numerator. For example, they were given the numerator ‘5’ and had to make the largest fraction. Now, me and my competitive self, wondered how long it would be before some clever child realised all they had to do was write the number ‘1’ as the denominator and win every time. However, one child tried ‘4’ and the teacher simply addressed this by requesting the denominator be greater than or equal to the numerator to create a proper fraction. Evidently this year group had not yet dealt with improper fractions and they were required to focus on the objective at hand. If any of my children had done this I would have applauded them and said they had indeed found the larger fraction. This made me question which was the better approach.
However, on reflection, I realised the genius behind staying on the objective. If the Shanghai teacher had gone in a different direction to explain the improper fraction concept then some children would have become confused and question their understanding of the concept at hand.
4) Differentiation and Teacher Talk
This was a stark difference, noticeable instantly as the lesson progressed. The teacher spoke to the class, modelling language and demonstrating concept knowledge, for the majority of the lesson. This is where external watchdogs and validators such as Ofsted have had a real influence on teaching practice. Around 10 years ago it wouldn’t be uncommon to see, where teaching had been graded as less than outstanding, that there may have been too much talk by the teacher. This led to a wave of dislike over too much teacher talk in internal observations and a culture of no teacher talk ensued for many years. However, in the past few years Ofsted have shifted and have stated that they will favour no particular teaching style, so long as there is progress in the lesson. As such, this means that teaching approaches, such as Shanghai Maths, are now becoming more accepted in the classroom.
The other noticeable difference was the distinct lack of differentiation. All children in the class engaged, all children in the class aimed for the same goal and all children in the class completed the same activities. This again would be condemned by the previous Ofsted regimes. It still would be frowned upon in most schools. However, if the approach is to work this is clear, all must take part in the same language and same learning opportunities. From the staff that I spoke to who had taken this approach on board at the school this observation took place, they felt very strongly that the Shanghai approach had contributed to the gap between the lower ability and the higher ability reducing, whilst still pushing on the higher ability children. This was a question that came up, how are the gifted and talented stretched and challenged if they encounter the same challenges as their peers. There were many responses: peer coaching, finding more methods to solve the problems, creating their own similar problems and explaining their methods in numerous ways.
For me, the week later I was able to network with a number of schools that had implemented the Singapore Maths approach to their schools through the ‘Maths – No Problem!’ textbook and principles. These principles of the Singapore Maths I found to be very similar to Shanghai – teacher-led, no differentiation, subject knowledge focused, focus on small steps and specific learning objectives. And of course, the ‘Maths – No Problem!’ textbook is the only textbook approved by the DfE. All of this has definitely caught my interest…
As Maths Lead my focus is the well-being of Maths at the school and so far I see two issues to be addressed: subject knowledge of staff and the workload on our staff to plan sessions. We follow the White Rose scheme which breaks down the content well and has good questions to use with the children but not really enough activities to deepen understanding fully. As such, staff are required to look in different places such as nRich, NCETM and other sites. These are sufficient however it is a huge drain on staff time when they could be sharpening up subject knowledge on what they will be teaching instead.
There is a long way to go but all of this is food for thought for the weeks, months and years to come…