The end of our trip and the beginning of our journey

It seems hard to believe that that we are almost at the end of our exchange to Shanghai.  2 weeks have flown by and we have learnt so much and seen many lessons across the 4 schools in (2 x primary, 2 x secondary).

We could spend weeks recalling everything that we have seen, but perhaps it is more important to share some of the key learning points that we will be sharing with our schools and hub.

  • If you are learning something new, model it using the inverse at the same time in order to show the connections.
  • Precise use of language and questioning to move children on
  • The use of TRGs to develop, change and challenge your thinking.
  •   Use students work more regularly to create a positive environment for learning (both misconceptions and correct ideas).  Learning is to be celebrated.

  • Identify the key learning point- design the lesson to enlighten children to this whilst revealing the structure of mathematics at the same time.


So what happens next?

All of us (both Primary and Secondary representatives) return to school next week.  It’s then time to process the information carefully so that we can share some of the above ideas and more in a careful manner so as not to overload our colleagues and schools.

It is important  to share what we have learnt, practice, define, teach and help our teachers to develop their pedagogical knowledge with mathematics to support our students.

And then of course, our Shanghai teachers return in March to teach our students here in the UK and as teachers, we can carry on learning.

The journey begins tomorrow………..

Technology and mathematics

We are now into our second week in Shanghai and are settling into our second school.  There have been many key features of a maths lesson that we knew about before we arrived in Shanghai and have now seen in action.

One key feature that we were not so familiar with was the use of technology to help draw attention to key points in a maths lesson. All teachers have at least one phone (often they have 2 mobile phones, a personal phone and a work phone).  Parents can contact their teacher using WeChat (an app similar to WhatsApp) and they use the phones as a visual tool in the classroom (similar to Apple TV).  Teachers often taking photos of the children and their work to model on the whiteboard.  This is much quicker than using a visualiser and children can compare a variety of methods in one viewing.

Comparing two methods with the teacher model on the whiteboard.

This way of working quickly allows the teacher (we observed many classes with 48 students in each class) to quickly assess the children’s learning and share any misconceptions.

We also noticed that the Shanghai teachers use the interactive whiteboard well.  They use PPT to create many of their visuals and the use of animation is beyond compare to many teachers I have seen in the UK.  To be clear, it is not the use of multiple slides but the skilled use of creating 1 slide with to highlight and draw attention to key points.


Grade 3 class looking at square numbers. 48 children were in this class.




Happy Learning, Fond of Learning.

This week we moved to The Primary School attached to Shanghai No. 1 Normal School. During our tour of the school it became apparent that the education of children is paramount. All children should be given the opportunity to be athletes, scientists, great writers, artists, dancers, mathematicians…

The primary school was built last century in the 1980s, I found it interesting that they referred to the last century and I shouldn’t have really. How often do we forget the detail. Many British schools were build last century but I wondered if this is how we would talk about the school. With 1700 children and 45 classes the school needs structure and routine for the children – it’s everywhere.

As you walk into a classroom it’s obvious what the topic is, science rooms offer high quality resources to inspire, music rooms have enough instruments for each child – nearly all children in Shanghai learn the piano. Walking into room after room of high quality resource it is so clear that children are valued greatly in society.

Every child can follow their dreams; the provision is there for them to do so.

The school’s branding is “Happy Learning, Fond of Learning”, the thinking behind this is Every Child has a Happy Childhood and gets the Best Development. The school sets the goal to cultivate children to have beautiful souls, good intelligence, strong bodies and positive personalities.

While we are here to experience maths we can’t look at maths on its own to understand why there are so many great mathematicians in Shanghai. We must also understand the value of the whole curriculum and the approach that ‘Every Child Can’.

It will be exciting this week to embrace and experiencing teacher in another school whilst also have the opportunity to develop our mathematical practice as we start to teach children in Shanghai.

A small change makes a big difference

During our first week at the schools in Shanghai, we have been privileged to see some fantastic mathematics lessons.  One thing that we have been drawn to, is the importance of variation and how carefully chosen questions ensure children progress and deepen their learning of a key point.

We are often asked what variation really means and having seen it used to great effect, we thought we would share it within the context of a lesson.

Children have already studied the types of angles in Grade 3 (Acute, Obtuse, and Right Angle).

At the beginning of the lesson, the children were asked ‘What do you know already? What is an angle?  Children responded with 2 lines meet at a point. There are 3 types of angle.

Children were then asked, what do you want to know? One child asked’ I know some angles and their size, how can I measure angles that I don’t know?’  Children were then given a slide with an angle and a ruler.  Can I use a ruler to measure the angle?  Children were asked to see what they could measure? Children measured the lines, the distance between different points of the angle lines.

Then the children were introduced to a protractor and its relationship to a circle.  They looked at each quarter and finally the whole circle- 360 degrees.  Children were then given the opportunity to look at the protractor to explore.  Can you find 1 degree?  Can you measure 1 degree?

Children were then asked to share their thinking.  They went up to the board and shared both examples.  To be clear, the teacher reminded them that they must find the fixed point first.  The children then shared how they measured 1 degree.  They looked at the protractor and some children measured L to R, others in the reverse.

The children were then asked ‘What do you notice about the protractor?’  There are numbers 1-180 L to R and 1-180 R to L.

Children were then asked to measure 10 degrees and show how they did this.   They were then asked to look inside the angle.  10 degrees is 10 lots of 1 degree. The children came up with ‘The fixed point – part of the angle where 2 lines meet- should be at the centre point of the protractor.  First, find where the 2 lines meet. This will then become the centre point, and then you can measure the angles.

A child then said ‘I’ve found another way to measure an angle.’


The child then placed the angle within the protractor.  The fixed point remained at the centre.  The child then found the difference between the two angle measurements (60 degrees and 180 degrees for example. Angle size was 120 degrees).  There are 2 numbers that I can read. Which one should I use to measure?  Children then began to generalise using what they knew already.  Could the angle measure 80 degrees or 100 degrees?  It is only possible to be 80 degrees as the angle is not larger than a right angle which is 90 degrees.

The teacher then said ‘You can estimate the size of an angle using what you know.  You can then use a protractor to check it.’  Example 2 on the worksheet.  Is it near 100?  Estimate and check.  Children then looked at Task 2- real life examples.  Which one will be nearest to 100?  Check and measure.  Some children did measure all of the angles, though some used the ‘What I know’ procedure to help them.

The teacher then drew attention to – Which ones are near to 100 degrees?  Which are possible?  Which ones are impossible?  90 is close to 10

No. 2, this is an acute angle.  This is impossible to be close to 100 degrees as an acute angle is less than 100 degrees. You can then check the protractor.  There are 2 numbers on your protractor, 40 and 140.  It is impossible to be 140 degrees.

No. 3 the method could be right (find the difference as detailed above) but the calculation is incorrect.  The answer is wrong.

In the final example, children had to find the measurement of the reflex angle.  Children had not explicitly been told how to do this.

  1. Here, some children partitioned the angle into 2 parts, or they measure the internal angle and subtracted from 360 degrees (this was the initial teaching point).

 What did variation look like?

  • The children were taught how to measure an angle – using a protractor but also what they knew already.
  • They were then asked to measure 3 angles using what they knew and a protractor.
  • The children then used this knowledge to measure objects from the real world.  This time the visuals had changed slightly.  Variation 1
  • The children then had a picture of the protractor with angles underneath the image.   The children had to say if the angle noted underneath could be true or not and explain why.  Variation 2
Worksheet from the lesson showing the variation.

Finally, the children had some angles that that had to be measured.  These were rotated differently and one angle that had to be measured was a reflex angle.  The children had not been taught about reflex angles, however could use their knowledge of angles in a circle or split this angle into 2 or more parts.  Variation 3

Across the whole lesson, variation was minimal however each carefully chosen example made a big impact on the deepening of the children’s learning.

What to teach, not how to teach

Part of our work here in Shanghai is to reflect and share our observations and thoughts as a whole cohort of English teachers.  We have met every evening and we have noticed that teachers are seeing similar lessons across the Shanghai district.  All Shanghai schools purchase the same textbook and don’t use any other book to teach from.  However, what we have discovered is that teachers in Shanghai do adapt their lessons according to the classes they are teaching.  For example, in one lesson we observed the teacher taught a lesson with averages to answer the question: What will be the weight of this box of oranges?  The children had to think about what they knew already about averages and how this might link to this lesson.

They had to discuss,plan, review their plan, experiment and share their findings and ultimately generate a possible solution to the question.  This lesson was more about the problem solving process and at regular opportunities, children were given the opportunity to evaluate and adapt their strategy accordingly.

During the TRG, we asked the teacher what the plan had been in the textbook.  He advised that the problem was only 1 question from the text book and he wanted to give the children a real life example of how to use ‘finding an average to solve a problem’.  He purchased the oranges, added in the scales, all to add interest and purpose to the lesson.  He even went as far as to contact the vendor to find out the weight of the oranges as the weight was not noted anywhere on the box!

Real life contexts. 

As mastery is developing in our schools, we are lucky enough to have access to many ready prepared materials designed for general school use.  This helps with the sequence of lessons and the small steps we need to guide our students.  These last few days have showed us how these can be adapted for a real purpose and that they should be altered to suit the needs of the children we work with.

Textbooks and written schemes tell us what to teach, not how to teach. 

What’s the same? What’s different?

We had the opportunity to work with our secondary colleagues today to share our experiences thus far with a focus being: What’s the Same? What’s different?

Our secondary colleagues were given the opportunity to visit a primary school for a day. This helped us unpick similarities in lesson structure between the two phases.

The key points identified were:


  • The level of detail in lessons.
  • Expectation that the children to have prior knowledge in order to move on.
  • Every opportunity includes using inverse operations, it’s the norm and expectation.
  • Exploration of learning to be completed at home.
  • Encouragement of the beauty of mathematics.
  • Intervention happens same day.
  • TRGs are held within school on a regular basis (weekly).
  • Generalisations, key terms, mathematical vocabulary are in all lessons, if any relate to previous learning it is encouraged and expected that the children refer to these within their explanations.
  • Drawing out key language from the children to give explanations.
  • Sequencing of carefully chosen questions which deepen understanding through variation.
  • Real life examples.
  • Expectation to observe colleagues as well as be observed – (less experiences teachers are expected to observe more)
  • Text book is used but all teachers are personalising their teaching – the book is the guide – however some parts must be explicitly taught.
  • Similar resources used to make links to previous learning.
  • Give children time to explore and find different methods then focus on the most efficient way.
  • Same maths teacher guiding through.
  • Cross curricular observation. It is encouraged to watch colleagues from different subjects teach.


  • Some setting in secondary school
  • There is provision in primary schools to complete independent work at school.
  • Primary lessons tend to have quick plenaries to ensure children are able to explain their learning.
  • The key learning point of the lesson is highlighted visually as well as verbally and regularly in primary.
  • Although CPA is used in both primary and secondary it is more evident in primary.
  • Senior schools don’t use as many representations because children should have already have a secure understanding of key skills.

On reflection, in would benefit our children’s mathematical journey significantly if Primary and Secondary schools worked more closely with each other, be it from Year 2 – Year 3 (Infant – Junior) , Year 6 – Year 7 (Primary – Secondary), Year 8 – Year 9 (Middle – Upper schools).  We need to know what teaching and learning is happening and what it looks like across the whole journey, using representations which are familiar to students to support their mathematical understanding.

Having closer working relationships with our Primary / Secondary teachers could have a significant impact on the progression of our students.


Collaboration is the Key to Unlocking Good Professional Development

We were fortunate enough to observe two maths lessons today with NCETM and Shanghai University representatives.

We spent the sessions observing key elements of Mastery Mathematics.  Today, we would like to share our thoughts on the importance of the TRG process and reflection.

In this school the teachers have the opportunity to observe their peers twice weekly, as well as the chance to visit another school in Shanghai every two weeks.

This process allows the teachers to continually develop their craft, they are use to receiving critical feedback on regular occasions and adapting their teaching accordingly.  All teachers take part in this process. Often there are multiple observers within the lesson both teachers and pupils see this as the norm.

Whilst we are developing the use of TRG within Maths Mastery work groups we can the benefits of this process becoming a regular of our school practice.

I am a mathematician!

Whilst we have only observed two 45 minute lessons, we have already identified some key aspects that we can use to develop Maths Mastery for both our teachers and our students.

A key point that struck us throughout both lessons is how much the children own their learning.  They are mathematicians who are guided along their journey by key questions with the teacher drawing attention to the key point of the learning.

In addition to this, we noticed how far the children’s learning came along in such a short space of time.  This was aided by the use of small carefully orchestrated steps, opportunities for exploration of these steps with regular problem solving throughout.  Again, the children were not told how to solve the problem.  They used what they knew already and applied it to new situations.


Throughout the lesson there was the opportunity to see variation through action which helped to minimise misconception the children may have had.


In both the lessons, the children were focused, engaged and excited about their learning.  They were eager to share their thinking and challenge each other’s as they developed a deeper understanding of the concept taught. This became clear when children’s attention was drawn to a keep point and a loud gasp of amazement was heard.  It was a joy to witness!

Teachers are the engineers of the human soul


We were welcomed to Shanghai Pingnan Primary School today.  The school is an Arts and Technology specialist school. Proudly displaying the incredible works of its students in every corner of the school.

There are 28 classes and 1247 students attending the school.  The school is passionate about developing students’ knowledge and giving them incredible opportunities.  The school’s ethos is for students to grow up with good character, embrace unity, be persistent and never be afraid of difficulty.

The Golden Age is in front of us, not behind us!

An incredible welcome was given to us from Shanghai Normal University at the opening ceremony of England-Shanghai Mathematics Teacher Exchange.

The 2019-2020 was formally opened which was followed by a passionate lecture by Professor Gu.

It was an honour to have an insight into his 50 years of development and research studies around the area of mathematics and in particular, teaching for mastery.

His key reflections focused on:

The core element of the logical analysis of the teaching of content which links to fluency in the 5 Big Ideas of TfM

An arranged sequence of learning – Coherence (5 Big Ideas)

Highlighting key points to deepen learning (Mathematical Thinking and Representation and Structure)

Problem Solving – at this point Professor Gu explained that children get smarter by teachers letting them solve problems by themselves.

Whilst only our first day, we have been given plenty to consider and look forward to seeing more of this in action over the coming weeks.