Four Lessons from Shanghai

Blog: Nirva Bohdjalian, Primary Development Lead

Four Lessons from Shanghai

Posted: 17/04/15

Working at Mathematics Mastery we had heard a lot about the Shanghai approach to teaching mathematics, but hadn’t been fortunate enough to see it in practice until a couple of weeks ago.

A fantastic opportunity arose through the National Maths Hubs to observe a teacher from Shanghai teaching a lesson about unit fractions to a class of Year 3 pupils at Fox Primary School, London. As Shanghai is currently the top performer in Mathematics according to the Programme for International Student Assessment (PISA), we were excited to see their approach.

The Shanghai Approach

We have summarised four of the principles we observed in the Shanghai approach.
1)    Repetition of language and correct terminology
The Shanghai teacher repeated the key mathematical vocabulary and sentence structures throughout the lesson. Pupils were always expected to respond in full sentences and it was an embedded routine that the whole class repeated sentences in unison after the teacher. 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.
2)     Conceptual Understanding
Teaching focused on conceptual understanding and learning was linked to the part- whole model previously encountered by pupils. Unit fractions were compared by representing the fractions as part of a whole. There was a clear emphasis on equal parts and a pictorial representation was displayed clearly on the board. Pupils could visualise why 1/10 is smaller than 1/5 by comparing the lengths of the parts in the diagram below:


When pupils were confident with using the pictorial representations to compare fractions, they were able to successfully move into the abstract to identify the smaller and larger fractions without using pictures to support them. The importance and value of visualisation through images was clearly reflected in the pupils’ understanding.
3)     A clear goal!
The teacher was very clear about the aim of the lesson and did not deviate from it even when pupils asked questions about other aspects of fractions. The lesson aim was to teach pupils that, when comparing unit fractions, if the denominator is a larger number, the value of the fraction is smaller. During the lesson a child recognised the relationship between 1/5 and 2/10 and, to our surprise, the teacher did not acknowledge this finding and continued talking about unit fractions. We later found out that the teacher did not want to move away from the purpose of the lesson and start teaching about equivalent fractions as she knew that this would be covered in another lesson in the planned sequence of learning. With a clear picture of the lesson aim, and an overview of the planned progression in learning, the teacher was able to ensure all pupils achieved the key learning.
4)     Sound subject knowledge
The teacher displayed excellent subject knowledge and this was evident in her confident, effective questioning. She was clear about potential misconceptions related to fractions, for example emphasising the necessity of ‘equal parts’ and the fact that a larger number for the denominator does not mean that the size of the fraction is larger. At Mathematics Mastery our [download id=”4192″ template=”misconceptions”] include possible misconceptions that pupils may have so that teachers are aware of this when teaching the lessons. During our conversation with the teacher after the lesson, she told us that Shanghai Primary teachers like herself specialise in the subject for five years. This struck us as a complete contrast to the number of days, not years, teachers in the UK receive training on the subject of maths in their PGCE year! Although the UK currently do not replicate the numerous hours of training in maths for Primary teachers like Shanghai, a lesson we can certainly take is the importance of being knowledgeable about the maths we are teaching. At Mathematics Mastery, we provide ‘[download id=”4205″]’, further reading and additional guidance for every unit to support teachers in developing their subject knowledge.


Our programme, Mathematics Mastery, combines research and good practice from the UK and other leading countries in maths education, and as such we had anticipated that elements of the Shanghai approach would be reflected in our programme. For example, the emphasis on mathematical language and developing a deep conceptual understanding of maths that underpins the resources and professional development we provide.  This experience reignited our commitment to continuing to learn from Shanghai and other high performing education systems.

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