This article aims to clarify the effects of conflicts on the task performance of supervisory boards in education. Management studies on conflicts on corporate boards sometimes find a positive effect and sometimes a negative effect on the performance of boards. These mixed findings are considered a result of the triggering of harmful personal conflicts through disagreements about process and content within boards. In order to gain more insight into the complex ways in which conflicts influence the effectiveness of supervisory boards in education, a multidimensional operationalisation of conflict has been designed, in which three different types of conflict -- task, process and relationship conflict -- are distinguished. Chairs of the executive boards of schools in the Netherlands (N = 300) were questioned via a survey on various conflict dimensions and their supervisory board's task performance. The results of hierarchical regression analyses underscore the need for a multidimensional approach to conflicts on supervisory boards in education. Task conflict has a positive effect and relationship conflict a negative effect, while process conflict seems to have no significant effect on supervisory board effectiveness. Furthermore, task conflicts have a mitigating, rather than a triggering, effect on relationship conflicts. Supervisory boards in education should therefore not avoid substantive discussions on the differences of opinion among their members to be more effective.