There is a concern that school mathematics is not equipping young people for life in an age where the ability to think with mathematics is increasingly important. Everyday life involves mathematics and there are many areas where thinking with mathematics is essential for understanding a situation and for making good decisions. In addition, employers complain that new recruits cannot do “simple jobs” that involve quantitative reasoning.

Planning the use of money is one example, but there are many others. For example, perceptions of risk, fed by dramatic stories in the media, are very different from reality, a misunderstanding that affects peoples' lives – they feel that life should be risk-free, but have a grossly exaggerated fear both of specific risks and of risks in general.

Equally, it is worrying that the sentiment “Of course, I’m no good at maths”, remains a socially acceptable, even fashionable, confession among many otherwise-well-educated people; the equivalent of “Of course, I’m no good at reading” is less acceptable.

If these concerns are to be met, the disjunction between “school maths” and the outside world needs to be bridged. The Government has been taking some action, notably in the revision of the Programmes of Study for Key Stages 3 and 4 and the recognition of the need for “functional mathematics”. However, these ‘new' goals were part of the intended National Curriculum since its inception – but were not realised in its implementation.

To make them a reality in every classroom remains a challenge. Bowland Maths will help teachers and their pupils respond to this challenge, successfully as well as enjoyably.

To succeed requires a deeper understanding of why we have not succeeded in the past. One feature of the past has been the focus on “basics” – the mathematical skills and concepts that form the ‘toolkit' for mathematics.

But effective performance in mathematics depends on four interacting components:

1.	Knowledge and skills: a mathematical toolkit, including procedural skills with knowledge of the concepts that underpin them;
2.	Strategies and tactics: for using these tools to tackle new problems, knowing what each tool is good for;
3.	Meta-cognition: teachers report to each other on what happened in their lesson, reflect on a set of pedagogical questions, and consider further related issues;
4.	Attitude: an analytical approach to problems that includes mathematical reasoning.

When faced with a new problem, an individual needs confidence (from 4 above) to work out how to tackle it (2), to start carrying through a plan (using 1), regularly reviewing progress or lack of it, and changing the plan in the light of this (3).

This is done in thinking about any problem in life – or when writing an essay in English. Mathematical performance has the same features. Yet school maths has focused on the first point above, with little attention to the other components. This needs to change.

Bowland Maths is designed to support that change, addressing all four aspects in a coherent and effective way.

The implication of this diagnosis for what should be taught in school suggests that there are three neglected elements that need to be added.

1.	Non-routine problems : Much school mathematics is currently about learning, remembering and then reproducing what has been taught. But problems are rarely routine, so recall is not enough; to be effective requires thinking with mathematics. In the classroom, this suggests that pupils should tackle a variety of problems that they have not been shown how to solve, together with some explicit teaching of the approaches that help solve such problems.
2.	Substantial problems : Most important problems involve chains of reasoning that take much longer than the minute or two characteristic of most current maths tasks – again, there is a parallel with the reasoning used for an essay. In the classroom, this suggests that pupils should tackle substantial, more complex problems, perhaps taking a whole lesson or more.
3.	Multiple connections : Effective performance depends on building multiple connections, between different parts of maths and with practical situations that can be modelled. For example, pupils need to be able to represent situations in words, numbers, graphs and algebraic symbols – and to move freely between these representations, looking for the clearest way to find and express meaning. In the classroom, the time-sequence of teaching often uses a logical sequence of topics, each just linked to the one before. The multiple links that are required for robust understanding do not arise in such simple ways; they have to be built in. Solving non-routine problems depends on such links, and is the key to developing them.

Bowland Maths provides materials that enable teachers to address all three of these areas and so reinforce the mathematical knowledge and skills of pupils.

Might problems like these be too difficult for pupils? After all, many pupils have trouble doing even straightforward exercises. Surprisingly, the answer is no; there is plenty of evidence – which the trials of the case studies have reinforced - that pupils can cope with richer, more complex problems, provided they have the appropriate range of learning experiences in the classroom.

Bowland Maths is designed to address another important challenge. Whenever attitudes to school maths are surveyed, a depressing picture emerges. Maths has a high profile. Successful pupils are proud of their achievements in maths, usually expressed in terms of conquering a challenge. The less successful tend to regard mathematics as an obstacle they have to overcome in order to get on with what they want to do in life. It is clear that the activities that pupils pursue in school maths do not motivate them.

Motivation is a vital factor in learning; if it can be improved for school mathematics, there will be gains in performance. The types of problem that pupils are asked to tackle is a key factor in their motivation. There can be a great variety of problems – not only real world examples, but fantasy worlds too can develop the same processes and motivate pupils .

Mathematics is a subject whose power lies in the range of problems to which it can be applied. Enabling pupils to make explicit connections enhances both their motivation and their mathematical power. There is substantial research experience that this approach can be successful and enjoyable for pupils, and for their teachers: thinking with mathematics about substantial problems – real or fantasy - can be taught, learned and assessed.

These are some of the reasons that the Bowland Trust decided on the concepts of this initiative – larger scale, interesting and open problems, using examples in forms that enable teachers to develop their pupils' skills across the four aspects of performance listed above. The Bowland Trust decided that the initiative should be aimed at Key Stage 3 pupils because that is the point in a pupil's school career which seems to be critical in developing an attitude to maths which can last for life.