Day 7: Today in Shanghai, noticed that…
It was another thought provoking day in Shanghai. We watched the next Grade 5 (aged 10-11) lesson in the sequence on algebraic equations and then saw a Grade 1 (aged 6-7) lesson on subtracting using partitioning.
Again, in the Grade 5 lesson, it was clear that the teacher was able to have a really specific learning point and stick to it. The misconception he correctly anticipated was that the children wouldn’t write the conclusion to the equations that they solved. For example:
A Dad uses ¥80 to buy five children’s cinema tickets. He has ¥5 remaining. How much does one ticket cost?
x = each child’s ticket.
¥80 – 5x = ¥5
5x = ¥80 - ¥5
5x = ¥75
x = ¥75 ÷ 5
x = ¥15
The learning he valued was the sentence at the top, which he rightly predicted would be the children’s misconception. He expertly picked apart the children’s responses, which had all correctly found that x = ¥15, under the visualiser.
X = tickets (wrong)
X = children’s tickets (wrong)
X = each child’s ticket
Again, nothing revolutionary, and something we would do - but done really clearly and precisely by ensuring that children pay attention to what the teacher wants them to so that the maths is clear. While the children have done some practise of solving equations this week, all the learning has been about giving the equation meaning.
At the end of the lesson, the learning was put into context of where it would be used in the real world - an electric bill. The maths was too complex for the children to solve but that wasn’t the point. Due to the focus that the teacher had put on writing equations in the correct order and not just the simplest to solve, they could write an equation to solve it and apply their learning. What we liked about it was that it wasn’t shoe horned into the lesson to detract from the maths, it was shown at the end to support the learning. Everything is meticulously planned out here.
The second lesson was fascinating but not for its content - which was very similar to a year 1 lesson you’d experience in the UK - but for the comparisons of the children in both countries.
Firstly, it was explained to us that Grade 1 is particularly difficult to teach in Shanghai because the gap between the most and least able children is the biggest in the school. Some children have been tutored and already know it and some are coming across it for the first time. By Grade 5, the gap is much smaller. I don’t think I can think of a more damning comparison between our two systems than that.
Secondly, at Grade 1, we saw our first behaviour chart – where the children can earn stars for their rows for good learning. The mentality is very much that the children are taught how to learn at the start of their school journey and then, supported by parental reinforcement, the responsibility to engage is on them. It is against the law to “punish” children by making them miss their play time, or stand up on a time out.
The lesson itself was well thought through, precise and packed with learning. Noticeably, having seen the world of difference between the content taught to our Year 6 and their Grade 5 this week, the content at this age was no different.
The teacher started with a problem solving task, matching up eight equations into pairs (e.g. 2+3 and 12+3) but she wasted little time in getting them to solve it. She quickly gave them the answer and drew their attention to what she wanted them to notice – 12+3 has one more ten than 2+3 – before unpicking this relationship using concrete resources.
One child, who’d clearly been highly tutored, solved 12+8 by converting it to decimals but this was dismissed as irrelevant as it wasn’t the focus. When the children independently solved the equations, the focus was first on writing out the whole process before giving them a chance to solve the problems mentally.
Later on in the lesson, the teacher gave the children a chance to use the same structure of partitioning to solve subtraction equations. To further empathise the point that we’ve previously made about Shanghai teachers understanding their curriculum, our host teacher explained to us where the Year 1 sequence of lessons on subtraction fitted into supporting children with regrouping to divide in Grade 3. At their desks, today’s link from addition to subtraction was no problem for the children as the image used to support their understanding was so clear. The teacher was able to focus the discussion around why we add when we subtract using partitioning.
This leads me onto my final comparison. The fluency of the children was incredible. There were no children counting on or back as we would see in the UK. There were no children using their fingers to add. There were no children who had the barrier of not being able to add a single digit number without regrouping. The mistake they made was not to use today’s structure – the answer was easy and irrelevant.
This was the 19th maths lesson of these children’s lives – although they would have experienced numbers at Kindergarten and at home prior to this. The first 15 lessons were all about the numbers 1-10 and they’d only been introduced to the numbers 11-20 after that. This isn’t too dissimilar to our Year 1 classrooms back home, so why are they so far ahead? The easiest answer is to bemoan the obvious barriers: additional parental support out here (or lack of for us), additional tutoring, starting school later when they’re ready to hold facts and focus longer, us having a broader and less precise curriculum etc. but a lot of those things are out of our control.
We need to think about the provision that we do offer. Our children, by the same age, would have had over fifty maths lessons of one hour, compared to 15 of 35 minutes in China, as well as our early year’s provision. How are we using this time? What can we do that we’re not doing already? We have made great strides in improving the use of resources, teaching more mathematical structures, teaching things for longer and slower, etc. but we must do more. Do our Early Years and KS1 teachers know where the maths is leading or are they rushing them towards the fastest method for SATS? Do we spend enough time on each number in EYFS? Is our EYFS environment rich enough? Do we allow the children to solve 13 + 5 by counting on when we should be forcing their attention to the structure of 10 + (3 + 2)? Can we spend more time learning number bonds to 6, to 7, to 8, etc? If we don’t teach children to be flexible with number at this age, when will they learn?