Professor Valsa Koshy “ Enriching and Developing Mathematical Promise of Children within the National Curriculum

Aims of the National Curriculum Students should: become fluent in the fundamentals of mathematics, complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content

The purpose of studying mathematics in The National Curriculum Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

Mathematics is a creative discipline. It can stimulate moments of pleasure and wonder when a pupil solves a problem for the first time, discovers a more elegant solution to that problem, or suddenly sees hidden connections. The Mathematics National Curriculum 2000

Nationally The recent Ofsted report (March 2015) noted that too many gifted students were insufficiently challenged and failing to reach their full potential. In addition to this, a review of pupil premium expenditure, (Ofsted, 2014) showed that ‘disadvantaged students continue to lag behind others’.

What does research tell us about children’s mathematical learning? ‘Mathematics lessons lack depth – it is a mile wide and an inch deep’ Children already know 55 % of what is taught The student most neglected, in terms of realizing full potential, is the gifted student in mathematics. USA Sir Peter Williams (2008) highlighted that gifted and talented children were not stretched enough (after repeated calls for action) we need to consider 4 factors which will determine both the display and fulfillment of high ability in mathematics. Ability Motivation Belief Experience Reflective journals and discussions raise confidence and achievement. Brain function research suggests that we can enhance children’s ability and learning capacity through problem solving.

Base-line data Questionnaires What is mathematics? 84% said it was about numbers, adding up and ‘stuff’ What do you think of mathematics lessons? 54% found it very easy, with 21% saying they were bored.

Able More able Exceptionally able  It is best to view ability as a continuum  Strategies for effective provision for the most able/ gifted and talented is essentially about good practice in teaching and learning. ‘A rising tide lifts all ships’ Establishing principles

Need : a 3-dimensional model of curriculum for enhancing mathematical learning

Need : Zone of proximal development – through challenge and scaffolding

Attributes of a mathematically promising students 1. Learns new ideas quickly. 2. Finds the work set for the class easy. 3. Understands challenging and abstract concepts with ease (e.g. decimals, negative numbers etc). 4. Shows curiosity and asks many questions (usually reflective in nature). 5. Is able to estimate accurately. 6. Is able to spot patterns and make connections between mathematical Concepts 7. Shows ability to analyze, reason and make some generalizations. 8. Is a fast information processor. 9. Enjoys learning mathematics. 10. Shows stamina and persistence. 11. Has the ability to be engaged in carrying out extended investigations. 12. Is able to transfer previous knowledge to new situations. 13. Produces unique and elegant solutions. 14. Enjoys solving problems and puzzles. 15. Recognizes similar structures and solutions from what was previously learnt.

Strategies for enriched provision Motivating contexts – interest and challenge Advanced Content built into the tasks Develop ‘big’ ideas Training in mathematical ‘processes’ – using and applying, problem solving Multi - levels of differentiation Asking Higher-Order questions Meta-cognition /reflection – purposeful recording, journals, personalised glossaries Opportunities for generalisation and proof Discussions and debates

Which is the odd one out? Why? A B C

Questions for differentiation What or what if? What patterns do I see? What is the best answer, the best method of solution, the best strategy to Begin with … ? What if I change one or more parts of the problem? Who? Who has another answer? Who solved this another way? Who agrees or disagrees? When? When does this work? When does this not work? Where? Where did that come from? Where should I start? Where might I go for help? Why or why not? Why does that work? If it does not work, why not? How? How is this like other problems or patterns that I have seen? How does it differ? How does this relate to "real-life“ situations or models? How many solutions are possible? Linda Sheffield 17