Is a sea of correct answers a positive sign?

Our decision to change our teaching and delivery of maths has been driven by the desire to find a child-centred approach to teaching that was progressive and flexible to fit the needs of all our pupils. Maths is a subject that still polarises opinions and it can often still be socially acceptable to be weak at the subject. You certainly hear less parents and adults proclaiming quite so vocally that they are unable to read for example!

We also wanted our curriculum to be fun, engaging and accessible for all – maximising progress without hot-housing. Maths is a subject that children can get quite competitive and anxious about and where the fun can be easily lost. It elicits a strong emotional response for many at every age. Excessive repetition, a lack of physical resources, minimal discussion and a lack of application to the real world and other subjects can lead to poor outcomes.

This contributes to its sometimes negative reputation and can be source of worry and low confidence. We wanted a system that promoted keeping up with curriculum content, not catching up, and that supported and encouraged group work and problem solving. Providing personalised provision with a focus on a growth mindset is at the heart of our educational ethos at Hatherop.

Ensuring forward momentum

What we have chosen builds students’ mathematical fluency without the need for excessive rote learning. It introduces new concepts using Bruner’s Concrete Pictorial Abstract (CPA) approach, which is very inclusive for all abilities but is also used as a standard teaching practice for those with dyscalculic tendencies. Most importantly, it strengthens pupils’ ability to think mathematically as opposed to reciting formulas they don’t really understand. I’m sure there are many parents and teachers out there who find that with some of their less confident children, that they have a ‘soup’ of mathematical understanding. This consists of fragments of concepts of how to perform certain operations – but no firm foundations on which to build their knowledge.

Some children learn to cope with this quite readily, following a set procedure and thriving on the repetition of similarly pitched questions and amassing lots of ticks on a page as positive reinforcement of their mathematical worth. But when a mistake occurs the emotional reaction, particularly in high-achieving children, is often extreme and unsettling. They become averse to challenge. A sea of correct answers should only indicate that the challenge level was not high enough. All this style of lesson can conclude is a confirmation of material already understood. There is no forward momentum. Progress stands still. The content having not been mastered, regardless of the number of ticks they have collected, shows an understanding that is shallow and their progress is capped.

For pupils who already weren’t coping with their early years and KS1 curriculum the gap can only continue to grow with incorrect answers reinforcing the negative view of their ability in the subject.  This can come to light quite early in their primary education or only become apparent in KS3 when there is little time for ‘gap filling’ – particularly when there are many years to pick back through and so much confidence lost.  

The importance of making mistakes

A teaching method that does not solely repeat reams of questions – albeit at different levels – until a mistake is made but that actually targets misconceptions in the first 2 or 3 questions is not only a more efficient teaching and learning style but also one that positively reinforces the importance of mistakes for learning. Everyone beginning with the same question and content allows students an equal chance in each lesson to access the curriculum at their level, at their ‘depth’, with the skill of the teacher demonstrated in extending or supporting each pupil based on their responses allowing them to be able to make links across mathematical concepts. A child who is struggling with abstract multiplication may flourish with tessellating and repeating shapes.

Finding the relationships between these two subjects, for example, builds a network of connections that in turn encourages confidence and creativity, positive participation and most importantly – engagement. Ticks and crosses should become less emotive and it is the questioning and explanations, exploring different ways of reaching the same answer and the comparison and discussion that makes the capacity to communicate the indicator of ability and understanding. It is these skills that are assessed and not just the right answer. Discussion becomes celebratory in a lesson as opposed to being interpreted as criticism or a spotlight on what went ‘wrong’ for those less self-assured.

Although there are many examples in other countries of highly successful educational systems beginning when children are much older, in the current UK system additive reasoning ideally needs to be mastered by end of Year 1 and multiplicative reasoning by end of Year 2. These benchmarks coupled with times tables skills and an understanding place value, are the fundamentals needed for a highly successful KS2. Choosing a cyclical curriculum that covers these foundations every year at an ever greater depth was a key consideration.

Getting everyone on board

As a general rule, few enjoy the process of change. No one can dispute that schools have to make curriculum and organisational changes when the education system and external obligations demand them. But these changes can often be negatively interpreted as a reflection of teachers’ capabilities, prompting reticence and a natural inclination to fall back on the ‘but we’ve always done it this way’ response and avoidance of innovation.

The fact is, schools have to adapt and it is not only teachers who often push back on change. What is wonderful about the staff at Hatherop, and part of the many qualities that make it such a special school, is how open and responsive the staff are to professional development and trying something new. The best outcomes for our pupils are always at the centre of what we do and this has been particularly evident as we start this new term, embracing the change with confidence that the children will be the direct beneficiaries.