Leigh Primary School

Principles of Problem Solving

The whole point of learning maths is to be able solve problems. Learning rules and facts is of course important, but they are the tools with which we learn to do maths fluently, they aren’t maths itself. It’s similar to the way that learning scales is an important part of learning to playing music fluently – but there’s far more to making music than playing scales.

The National Curriculum says:

Purpose of study: 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.

Reading further:

'The national curriculum for mathematics aims to ensure that all pupils.....become fluent......reason mathematically..... and can solve problems.'

Quoted from an Article by Lynne McClure (Problem solving and the New Curriculum)

At Leigh we understand the importance of applied Mathematics and are beginning to implement SPEAR Maths.

What is SPEAR Maths?

SPEAR Maths is a simple but effective framework which promotes the development of primary Maths problem solving and investigational skills and helps pupils to become independent learners. Based on a brain-friendly philosophy of education, SPEAR will help pupils to become effective and enthusiastic Maths problem-solvers.


SPEAR Maths:

•promotes independence

•supports creative thinking

•encourages the application of Maths concepts

•provides a flexible programme for pupils of all abilities

• meets all the requirements of the 2014 curriculum


How does it work?


SPEAR Maths uses a five-step framework:




Each stage is supported by a range of pupil and teacher materials to ensure that children develop the problem-solving skills they need to succeed.  There are main different types of problems children need to learn how to approach.


  • Diagram and Visual Puzzles
  • Word Problems
  • Finding all Possibilities
  • Finding Rules and Decribing Patterns
  • Logic Problems


SPEAR Maths is based on the educational philosophy of Sternberg and Vygostky. Sternberg maintains that ‘intelligence’ is not fixed in any individual but is fundamentally the ability to solve problems. This ability can be improved by giving learners appropriate experiential learning, by embedding the learning in relevant contexts and by explicitly teaching tools and strategies for solving problems. In teaching our pupils problem solving, we have the opportunity to increase their intelligence.

We can dynamically improve learners’ capacities for ‘learning how to learn’ by presenting aspects of the curriculum as problems to be solved, rather than (simply) bodies of knowledge to be learned.

In Vygotsky's 'zone of proximal development' the role of the teacher is to structure learning opportunities to enable learners to acquire new knowledge and understanding for themselves.