Advancing all learners. ‘It can be achieved. It has been achieved.’ (Part 1)
This is the first of a two-part series summarising the discussions that took place during our annual conference.
Late in November, Maths — No Problem! held its 2022 Annual Conference, the first in-person gathering in three years. The theme was Maths Mastery in the Post-Pandemic World.
About 140 delegates filled the Great Cumberland Meeting Spaces at the Hard Rock Hotel in London to hear prominent speakers including Dr Yeap Ban Har and Dr Sue Gifford talk about the lessons learned during the lockdowns and why the maths mastery approach was more important than ever.
The event was a great success and many delegates told us they felt inspired and renewed after attending. Feedback included comments such as this one from Heidi Andrews, a Year 1 teacher: “The overall experience was fantastic and highly informative. I have taken so much on board to be able to take back and share with my colleagues. I left feeling truly invigorated.”
Expert-led sessions on topics such as assessment and advancing all learners generated a lot of buzz, as did the case studies from accredited schools.
Many delegates said Ban Har’s session was one of their favourites. The world renowned maths mastery expert gave a concrete demonstration of the concept of advancing all learners — a cornerstone of the mastery approach.
“Advancing all learners is not a mystery,” he said. “It’s not a fantasy. It can be achieved. It has been achieved.”
He used an example of a Year 1 exploration lesson that involved finding the sum of three numbers — 7, 3 and 2.
Ban Har explained that Year 1 beginners will be able find the sum of the three numbers by counting all or counting on. They’ll be successful because:
- The teacher provides time to figure out the problem
- The teacher provides appropriate concrete objects like counters and ten frames
- The pupils receive collaborative help from their friends
Some of the more advanced pupils will be able to make 10 because of the choice of numbers. They will see 7, 3 and 2 is the same as 10 and 2, which is 12.
Ban Har explains, “The choice of numbers — 7, 3 and 2 — coupled with the provision of 10 frames and counters will accelerate the process of being able to see making 10.”
Still other pupils may try to make all the containers contain the same number of items, or three sets of four. Others may notice that 7, 3 and 2 is the same as 7 and 5, which is double 6.
“So the more able learners will attend to multiplicative structures,” says Ban Har. “Those who are more ready will get their challenges to do multiplicative thinking. Those who are not ready, it’s fine. We’re not doing multiplication anyway. We’re doing finding a sum.”
The Goldbach Conjecture and prime numbers
In a very small number of cases — maybe one out of every one hundred classrooms he visits — Ban Har says he encounters a “minor genius” who would point out that the three numbers — 7, 3 and 2 — are prime numbers.
A teacher could then say, “I heard this rumour that a number like 12 can be written as a sum of three prime numbers. I wonder if that rumour is true.” They could test to see if the rumour was true for other numbers like 13 and 14.
The Goldbach conjecture — that every number greater than 2 is an aggregate of three prime numbers — was proposed by Russian mathematician Christian Goldbach in 1742.
In summary, says Ban Har, there’s no need for a teacher to provide different problems to different children. Beginners will successfully add by counting. If other pupils find counting too easy, they can begin thinking about multiplication.
“And for the really small number who for some reason are too advanced for Primary 1, they can also be challenged by the Goldbach Conjecture.”
Rushing through the curriculum won’t help
Rabia Ahmed’s presentation was about creating ‘thinkers not calculators.’ The Assistant Headteacher and Curriculum Lead at West Twyford Primary spoke about the crucial roles of journalling and investing in teachers.
West Twyford is an accredited school that began using the Maths — No Problem! Programme in 2015. Rabia said the switch involved a ‘radical change’ of how maths was taught in the school and a deep overhaul of “what we want the children to be and what we want the teachers to do.”
“I know it’s cliché but we do believe in every child and we have a mindset among our teachers that every child has maths potential,” Rabia said. “There are no labels. That leads to confidence within the children and the teachers that every child can succeed.”
Insights that leave the class in awe
There have been many occasions at West Twyford when a child who may have been labelled as ‘lower ability’ provided an insight that left the whole class in awe, she said.
Another pillar of West Twyford’s approach is the willingness of the staff to take as much time as they need to make sure pupils understand the material.
“I hear a lot of teachers talking about how behind the pupils are,” says Rabia. “This is not going to get fixed by rushing through the curriculum.”
She tells teachers that if one hour isn’t enough, they should take two hours, and she urges them not just to teach each topic discreetly, but to seek to make connections with other topics and concepts.
Teachers should figure out what pupils know and what they don’t know by asking questions like:
- What do you see here?
- How do you know that?
- Does this link to another lesson?
- What other concepts have you learned that this links to
This approach and this mentality “really helps embed understanding, and what you’ll witness as a teacher and a school is that children will be making connections effortlessly, naturally,” she says.
A firm foundation in number sense is the beginning of success
Dr Sue Gifford, Emeritus Fellow, University of Roehampton began her presentation with a question: What does research into Early Years maths tell us about the predictors of success, and what are the things we should be doing?
There are a couple of predictors that we can’t do much about, including home background and an autumn birthday, she says. However, a firm foundation in number sense also makes an enormous difference.
“It makes so much difference, that if you start with a firm foundation in number sense, then you will tend to learn quickly and do well,” says Sue. “If you start with a weak foundation in number sense, you will tend to be on a back foot, not catch up and actually make slow progress.”
To make matters worse, the gap tends to get wider from the beginning, which is why establishing a firm foundation in number sense in the Early Years will make the biggest difference to the lives of children.
What does that mean?
“It isn’t rocket science,” she says. It’s about:
- Knowing the values of numbers to 10
- Knowing number symbols in order
- Linking those together
“What really makes a difference is that secure understanding of number symbols and the links between counting and number values,” she says.
Letting go of maths anxiety
According to Dr Gifford, the good news is that there’s still time. Looking around the world, many children start school in Year 2 and do better, probably because they’ve had time to embed that early understanding of number and counting.
And more than just being confident with numbers, children will ideally “see themselves positively as learners of mathematics,” she says.
“We don’t want to tell them they’re in the ‘red group,’ and therefore they’re not very good. We know what a self-fulfilling prophecy that can be.”
One result of the pandemic is that more children have maths anxiety. And many adults have maths anxiety from damaging experiences in school. In fact, many teachers choose the Early Years to avoid maths. Yet, these are the people who can make the biggest difference.
“So we really need to support Early Years teachers,” she says.
Maths education shouldn’t be about public humiliation because you got the answer wrong or you need to do it quickly. In fact, research has proven that anxiety blocks working memory, which prevents learning.
“We don’t want to put pressure on children to accelerate their learning,” says Dr Gifford. “We want them to have firm, confident and enjoyable experiences with maths.”
‘We don’t have those invisible children anymore’
Emma Potter, Director of Mathematics at Leo Academy Trust and self-described Maths — No Problem! superfan, says her approach to teaching maths during and after the pandemic has been guided by the following motto:
‘Keep up, not catch up’
“We want our learners to constantly be keeping up with each other, and we have to be the facilitators of that learning so that they can move forward,” she says.
That’s because waiting until assessments at the end of Key Stages to determine whether or not learners have fallen behind is leaving it too late. The pandemic has required a change in the way teachers do their jobs: they now need to take the ‘important bits’ of the curriculum and keep moving their learners forward.
Precise, deliberate learning
Emma says everything she and her colleagues teach now must have a reason, which often means doing without unnecessary elements and activities. That’s one of the reasons she appreciates Maths — No Problem! resources, “because we can trust in the scheme.”
She knows that the research has been done by experts, and the questions will be linked to something worthwhile and to real-life maths, so teachers can focus on making sure every single learner in the class is keeping up.
“We don’t have those invisible children anymore,” she says, adding that she herself was an invisible child — well-behaved, quite clever, got on with it, didn’t cause a fuss, a top achiever at the end of primary school who became a low achiever at GCSE time “because I’d peaked, and I was invisible, and nobody saw me in the classroom.”
She says she now looks for those children who are just getting on with it and making sure they’re not only keeping up but also excelling. A big part of that is explaining why pupils are learning certain topics, for example, perhaps it will help them if they want to get a particular job.
Using technology not to replicate but to enhance maths education
Being precise and deliberate extends to the decisions Leo Academy makes around technology, Emma says. Investments in technology are made not to replicate learning methods but to enhance learning and move pupils forward.
In particular, the trust uses assistive technology to keep learners keeping up with everybody else. She cites the example of downloading a piece of software called OrbitNote onto every child’s Chromebook. Any pupil can now download a pdf file off the school website and the software will read it to them. This was a big help for some of the pupils who could do the maths, who could talk about it, but when it came to sitting down and reading a question, they would switch off.
Technology has empowered many learners because it allows them to help themselves, which leads to a more positive attitude towards the material, Emma says.
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