We solve the dynamics of on-line Hebbian learning in large perceptrons exactly, for the regime where the size of the training set scales linearly with the number of inputs. We consider both noiseless and noisy teachers. Our calculation cannot be extended to non-Hebbian rules, but the solution provides a convenient and welcome benchmark with which to test more general and advanced theories for solving the dynamics of learning with restricted training sets.

Accessible summaryWe looked at how much teachers knew about helping children with a learning disability who had behaviour that was challenging in school. We found that:• Some teachers knew very little about challenging behaviour and all the different ways to help children with this. • Some teachers had beliefs about challenging behaviour that can be unhelpful. We need to find ways to help teachers find out more about challenging behaviour and to think about it in different ways. One way to do this could be to give them training about it. SummaryThe present study examined Scottish teaching staff knowledge about the definition and management of challenging behaviour displayed by children with an intellectual disability. Knowledge levels were relatively low, and participants were most likely to define challenging behaviour by function or topography. Teaching staff were largely unaware of positive programming strategies, suggesting that they may not be properly equipped to manage challenging behaviour effectively in the longer term. The teaching staff were found to hold attributions which research suggests are associated with reduced helping behaviour and increased anger. This indicates a continuing need to identify effective ways of promoting more accurate knowledge and positive attributions in teaching staff.

The present study examines the impact of a short training session on the knowledge of teaching staff in Scotland about children with an intellectual disability. Despite the majority of participants reporting that they had a child with an intellectual disability in their classroom, the initial level of knowledge concerning intellectual disability was low. This was partly considered to be due to terminology differences that exist between the health and education sectors and a lack of training specific to the needs of children with an intellectual disability. Training was shown to significantly improve the basic knowledge needed to understand intellectual disability immediately after training and at a 1 month follow-up, suggesting that the knowledge gains would be sustained in the longer term.

Children with a learning disability in Scotland, many of whom are likely to have behavior that challenges (Harris et al., 1996), are increasingly being educated in mainstream classrooms. The present study investigates the attitudes of teaching staff in Scotland towards the inclusion in mainstream education of children with a learning disability who display challenging behaviour.

The reasonable chastisement of children remains legal despite intensive lobbying by various groups to rule out smacking and despite the physical abuse of children being problematic. All professionals working with children have a duty to safeguard and promote children's welfare. This includes knowledge about child protection legislation and child discipline practices. This study assessed the knowledge of 55 health care professionals working in children's services in one NHS trust in relation to child protection legislation and child discipline practices. The study aimed to establish if workers from more specialist child services (e.g. tiers three and four) demonstrated greater knowledge in these two areas than workers from less specialist services (e.g. tiers one and two) and if experience was positively correlated with knowledge. The results suggest that workers in more specialist children's services demonstrated greater knowledge about child protection legislation. There was no difference found between the two groups of health workers in relation to knowledge about child discipline practices. The number of years' experience was not signifi cantly related to knowledge in either area considered. The results are discussed. Inconsistencies and gaps shown in knowledge across both groups of participants are outlined and the clinical implications are highlighted.