Do we need more maths at 16 or a closer look at our approach from the early years?
When mathematical concepts are introduced early and in a developmentally appropriate way, most children love and can succeed at maths explains our Head of Training Louise Livingston as she responds to the Prime Minister’s plan in our latest blog.
The recent announcement that all young people in the UK will be required to study some form of maths until age 18 received a mixed response from educators, students and parents around the country and perhaps a few exclamations of “thank goodness that didn’t happen in my time”.
The “more more more maths” approach – we’ll keep teaching until they “get it” could be missing the point. If children haven’t gained basic numeracy in the early years, at primary school or secondary school, will they really be motivated and successful when required to study Maths beyond age 16? Research shows that learning is most successful when young people are happy and when motivation is high.
Both the French mathematician Pascal and Maria Montessori observed that the human mind is mathematical in the way that it learns from experience, so it seems logical that maths should not be as challenging as it seems to be to so many. The magic of maths should be experienced long before children reach secondary school.
Like every aspect of education, maths is much more successfully learnt when delivered in a way that appeals to children’s natural tendencies and interests. My many years of experience working with children and as a Montessori teacher trainer has shown me that when mathematical concepts are introduced early, in a developmentally appropriate way, most children love maths. Making maths relevant, engaging, and purposeful is also key.
Being able to use your mind to calculate, classify and make predictions is like “milk and honey” to a young mathematical mind in the process of building mental capacity. So rather than maths being a drudgery that many have to endure, it should be a delight. Not only is it helping children to build brain networks that can be utilised in other academic domains, such as learning to read and write, it is also enabling the many different paths that children may choose in the future from accountant to zoologist – or any, as yet unimagined, career.
A huge body of research suggests that early mathematical skills are good predictors of later mathematical ability, pointing to the benefits of starting early. But how can we start so early when abstract concepts are difficult for younger children to grasp?
One key aspect of a successful approach to maths in the early years is a focus on representing abstract concepts in concrete form, making them more accessible to children who have a natural propensity to explore with their senses during this stage of life.
For example, in the Montessori Children’s House (3-6 years), the decimal system is introduced with golden beads – units of beads are grouped together in bars of ten, which are in turn grouped in tens to represent a hundred and then a thousand. Children can see and feel the concrete difference between a unit, a ten, a hundred and a thousand – and this is done before they are shown how these quantities are represented in writing. Understanding the meaning of an abstract number is therefore built on a concrete understanding of what those numbers represent. Operations and the memorisation of number facts are done similarly – concrete representations are explored before linking to symbols and then we gradually withdraw the concrete materials from the child’s experiences, as they are ready, so that only the symbol is left – a symbol which now carries real meaning for them.
Later, in Montessori Elementary (6-12 years) similar approaches are used for learning about the squaring and cubing of numbers of quadratic equations and beyond.
Another important point to bear in mind is that children are rarely ready to learn the same concepts at the same time: they are human beings with unique developmental trajectories yet are frequently expected to work on the same topics or at the same level regardless of their actual level of skill or knowledge. In Montessori education, children are encouraged to take on new concepts as they have mastered previous ones, starting new challenges when they are individually ready and therefore building on their own personal foundation of knowledge, rather than a wing and a prayer that they “got it” when they did it yesterday. This may be a safe assumption for children who learn quickly, but for most of us who take a little longer, the foundation may feel as if it is built on quicksand! On the other hand, in Montessori education when children have already mastered a topic, they don’t have to keep laboriously repeating it because everyone else has not yet “got it” – this quickly leads to boredom and disengages children from the subject; motivation is empowering but it can easily be destroyed if we don’t respond to it.
A recent review by Basargekar and Lillard, at the University of Virginia, suggests that in authentic Montessori schools maths learning is good or better than in conventional schools. This may be due to the specific Montessori materials used for maths, but it may also be because Montessori schools are enablers of two key aspects of development that are associated with later mathematical ability. One of these aspects of development is the focus on motor sensory perception, which is nurtured in the hands-on learning approach in Montessori. The other is executive function (the ability to focus on goals, remember ideas and think creatively about solutions) which is nurtured in Montessori by the child’s opportunity to choose activities that appeal to their interest and abilities and the freedom to engage in them until they have found out what they are interested in knowing. Research shows that both motor skills and executive function are predictors of mathematical ability further down the line.
There is no doubt that good maths skills are needed in life. The Prime Minister’s ideas for increasing understanding of personal finance, mortgages and so on is certainly to be welcomed, though I would question why this can’t be incorporated at GCSE as it is clear young people are interested in money exchange and related topics much earlier than 16-18 years.
As a firm believer that education must support development from birth to adulthood – and must not be something that we DO to our children, it worries me that young people may be required to continuing studying maths when they wouldn’t choose to do so at a time when they should be making their own choices about what will serve their life goals as they transition from adolescence into adulthood. In a society where mental health referrals are at an all-time high, there is also the danger that the scheme could make education a more stressful experience, which is the very last thing our young people need.
When mathematical concepts are introduced early and in a developmentally appropriate way, most children love and can succeed at maths explains our Head of 
