Professor of Education and Director of Brunel Able Children’s Education Centre, Valsa Koshy, writes for us on Nurturing Mathematical Promise. Prof Koshy is co-founder and director of the Brunel Able Children’s Education (BACE) Centre which supports Talent Development. The centre’s work is based on a broadened conception of talents and gifts rather than on labelling children, it focuses on the uniqueness of a child’s special strengths and interests. The centre team aims to empower teachers with strategies for effective curriculum provision, so that they can provide enriching and enjoyable learning experiences of all pupils.
In the past few months a range of issues relating to nurturing mathematical promise of children was highlighted for me in various forms. First, I have had a large number of e-mails from primary school teachers asking me if I could suggest how they can support individual children who display amazing capabilities and aptitudes in mathematics. For example, 4 and 5 year old children who arrive at sophisticated generalisations and mathematical proofs and 9-year olds who had mastered the curriculum for the whole primary school. A second experience was during a PhD viva I was examining in which the author provided evidence from schools where children who were in the top set for mathematics lessons were selected purely on the basis of their skills to do number operations fast and most of these children had private tutoring at home. This meant a whole section of the children from poorer families were not included in the top sets. My third experience involved requests from schools where they were concerned that the teachers had no professional development in aspects of how to both identify and develop children’s high ability or giftedness in mathematics. We are not referring to a small minority of children but many children nationally, who show higher achievement or have the potential to excel in mathematics.
As a Professor of Education at Brunel University for the past few years, my two research experiences are in Mathematics Education and Nurturing Giftedness. I know here has been a growing recognition, over the past few decades, that more needs to be done to support both the identification and development of mathematically very able or gifted learners. A common view still held by many is that mathematically gifted and talented students were not an educational issue or ‘problem’, because through their talents they could take care of themselves. More than three decades ago, in 1982, the authors of the very influential Cockcroft Report felt the need to explicitly refute this view. At around the same time, Anita Straker who was to be the director of the National Numeracy Strategy in the UK in 2000, told us that gifted pupils have a great deal to contribute to the future well-being of the society, provided their talents are developed to the full during their formal education. The launch of the ‘Gifted and Talented’ initiative by the government in 1999, gave a new impetus to the area of provision for more able mathematicians in our schools. Within mathematics, several support documents were issued for teachers to help them address the needs of children who display special abilities in mathematics; most of these these documents are now in archives.The challenge of making appropriate provision for children with high ability or aptitude in mathematics still remains and several school inspection reports have stressed the need for more challenge in mathematics lessons. Professional development needs to be in place for teachers to support them.
The most recent National Curriculum for England (2013) provides clear programmes of study and states that the majority of pupils will move through the programme of study at broadly the same pace. Further, the recommendation is that pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems. ‘Mastery Mathematics’ has been introduced in many schools which promotes the building of ‘strong conceptual and deep understanding’ which is welcomed by all. However, many teachers have concerns about the lack of professional development to explore effective teaching strategies for differentiation within the whole class of mixed ability pupils. Addressing the needs of very able children who enjoy spending time figuring things out and who have the stamina to keep going with investigations and of those children who already know what is going to be taught who switch off out of frustration remains a challenge.
How do we nurture mathematical giftedness or potential for high achievement? I have been involved in a number of research initiatives and, as I have discussed in my publications, there are some children who exhibit key attributes – a strong memory, the ability to reason and the capacity to generalise a solution – who show mathematical promise. But there are many other children who can become ‘more able’ and achieve highly, given the right level of opportunities and experiences. This viewpoint is supported by research which has pointed out that ability and intelligence can grow with effort and practice.
There is a set of ‘gifted and talented mathematical behaviours’ that one can observe in mathematically able pupils, according to Linda Sheffield, who was the Chairperson for the Mathematically Promising network in the USA. She told us at one of our national conferences that the attributes of mathematically promising children include:
- early and keen awareness, curiosity, and understanding of quantitative information
- the ability to perceive, visualise and generalise patterns and relationships
- the ability to reason analytically, deductively and inductively
- the ability to work with mathematical concepts in fluent, flexible and creative ways
- energy and persistence in solving difficult problems
- a tendency to formulate mathematical questions, not just answer them
- make some hypotheses, conjecture and generalise and establish proofs.
In order to develop these attributes, I believe we need to provide children with:
- motivating learning experiences
- specially designed activities which support children, as well as teachers with their subject knowledge to use them confidently.
The question I ask myself is: ‘are we providing our most able mathematicians with opportunities to demonstrate these attributes?’ A mathematics curriculum which relies heavily on text-book based exercises and worksheets, which are mostly designed for the average child in a classroom, may not provide a fertile soil for the development of mathematical talent. So, with teachers, I designed a set of activities for primary school children, which provide opportunities for children to both demonstrate and develop their mathematical talent. The 3 Enrichment Activity Packs are for use with 4-7, 7- 9 and 9-11 year groups. They provide multilevels of outcomes so that they extend the most able children whilst enriching all children’s mathematical learning. Potential Plus UK believes that these three 2 year courses should help schools to take on the challenge of making mathematical learning a pleasure.
Valsa has authored several books/courses, some of which are available in our shop area: