Within many contemporary social, workplace and sporting contexts, mistakes are often perceived to negative, resulting in underperformance and something to be avoided. Within education, in contrast, prominent educational researcher John Hattie (2012) suggests "mistakes are the essence of learning" (p. 26). For Hattie, the role of mistakes within the learning process needs to be seen as positive. Creating opportunities for students to learn from mistakes through effective feedback is key to raising achievement. Yet in traditional outdoor education, where risky activities are often a central feature, the role of mistakes in the teaching and learning process has seldom been examined. This paper, therefore, explores how secondary outdoor education teachers perceive the notion that mistakes are the essence of learning, and how they view the role that mistakes have in the learning processes in their outdoor education programs. Employing a qualitative approach, the findings of this study emphasise teachers' beliefs that mistakes are indeed important in the learning process. The inclusion of mistakes and feedback in outdoor education programs is, however, less than clear. Many teachers spoke of constraints such as short duration programs, not knowing students, and risky activities which made it unlikely for mistakes to be welcomed. In contrast one teacher with a yearlong program sought opportunities for students to make mistakes and learn from these through feedback.

We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths, a system with interactions is always less stable than a system without interactions. Contrarily to the uncorrelated case, interactions that are antagonistic, i.e., characterised by negative correlations, can stabilise linear dynamical systems. In particular, when the strength of the interactions is not too strong, systems with antagonistic interactions are more stable than systems without interactions. These results are obtained with an exact theory for the spectral properties of fully connected random matrices with diagonal disorder.

We analyse the stability of large, linear dynamical systems of degrees of freedoms with inhomogeneous growth rates that interact through a fully connected random matrix. We show that in the absence of correlations between the coupling strengths a system with interactions is always less stable than a system without interactions. On the other hand, interactions that are antagonistic, i.e., characterised by negative correlations, can stabilise linear dynamical systems. In particular, we show that systems that have a finite fraction of the degrees of freedom that are unstable in isolation can be stabilised when introducing antagonistic interactions that are neither too weak nor too strong. On contrary, antagonistic interactions that are too strong destabilise further random, linear systems and thus do not help in stabilising the system. These results are obtained with an exact theory for the spectral properties of fully connected random matrices with diagonal disorder.