WHAT is the relationship between headteacher competences and pupil outcomes? Answer: none. At least that is the conclusion of a large Australian research study which set out to find that elusive elixir - a prescription for headship.

Policy-makers who believe that heroic heads turn schools round and “deliver” outcomes dream of such an elixir. After all, they are often impatient for quick, demonstrable returns.

Pupil achievement is, of course, related to the quality of school leadership, but the relationship tends to follow a circuitous path. The recently-published Australian study by Bill Mulford of the University of Tasmania, points to a critical intermediary - teachers.

No surprises there for those who know their school-effectiveness research - teachers matter. But that is only the beginning of the story. The deep flaw in school-effectiveness methodology is that teachers are treated as single separable units, their individual competences measured against pupil attainment. If it is possible to measure individual teacher, or headteacher, effects there must surely be something seriously amiss in the organisation. Because what we are only now beginning to understand is that the strength, resilience and capability of a school lies in its distributed intelligence, its shared leadership, its communal learning. This is what James Coleman described as “social capital”. It is not a possession or attribute of any individual but is something lying between individuals - in connections and in networks. Organisations with high social capital are characterised by horizontal links, many but weak. Low social capital is marked by vertical links, strong and few.

Imagine a class of 30 pupils. Within that class there are small groups of pupils strongly inter-connected but there are also numerous isolated individuals. There is high reliance on the teacher, the class’s vertical link to learning.

Imagine another class in which everyone enjoys some linkage to someone else. The 30 pupils offer a resource for one another but their alliances are temporary and mainly task-driven. These pupils have built an infrastructure of shared resource and collaborative learning. They are much less reliant on their vertical link with the teacher for acquiring, or creating, knowledge.

Social capital theorists describe the first scenario as “social bonding”, the second as “social bridging” - powerful concepts because they describe an essential difference between the inward-looking exclusive group and the outward-looking inclusive group. If we now apply these concepts to the school as an organisation we can appreciate the extent to which many weak and horizontal links may generate and sustain social capital. Collaborative activity shares and creates knowledge. The sum is greater than the parts and the parts defy easy measurement because the effect lies not in what teachers do individually but what they do collectively.

Researchers are known to complain when the fruits of their labours are published and the tireless researcher appears simply as “et al” while the least alphabetically-challenged individual captures the headline. This is because research reports and books are typically a joint product in which no single hand is discernible. So it may be with thinking, planning, producing, managing and teaching. The truly effective school confounds the reductionist approach of effectiveness and individual competences research.

And so to the leadership effect. Instead of seeing leadership as residing in one individual, we should be talking, says David Green, vice-president of the New American Schools movement, about “leaderful communities”. The measure we should apply is not whether the head is strong, charismatic, visionary or purposeful, but whether there is a “density” of leadership across the school.

The question is “how many people, how many groups, have or assume leadership roles?”. In which contexts can pupils and teachers exercise leadership? Extra-curricular activities, Easter and summer schools, study support, residential experiences and field trips? These offer opportunities for hidden talents to emerge and take a lead.

As government-funded research into study support clearly demonstrates, what happens outside mainstream school life challenges what happens within. With a little imagination these “leaderful” experiences can be transfused into the daily practice of learning and teaching. Building social and learning capital, that is the challenge for 21st-century school leadership.

John MacBeath is professor of education at Cambridge University and chair of Leadership for Learning, an international network of school, local authority and university educators