AbstractThis exploratory study aimed to compare the effectiveness of a computer programme and direct teaching in promoting simple number estimation skills for a group of eight children (ages from 9 to 12 years) in a special school for children with moderate learning difficulties. A modified single case study design using random group allocation was used with performance gains being monitored with teaching related and generalization tasks. Average gains made by both groups on both kinds of tasks were maintained over a 4 week period. The results are discussed in terms of the differential gains for the two groups for the teaching‐related and generalization tasks and individual variations in response to the teaching approaches. Despite methodological difficulties the study indicates that both teaching approaches are associated with direct and transfer gains in simple number estimation which are durable over a 4 week period.