It is known that computer games are motivating for children, but there is limited direct evidence of their effects on classroom learning. The studies that are available tend to be limited in terms of output data reported, or small in scale, or both. The aim of this randomised controlled trial was to upscale a recent study by Miller and Robertson investigating the effects of a commercial off-the-shelf computer game on children's mental computation skills and self-perceptions. A pre-post design was employed, with 634 primary (elementary) school children (10-11 years old) from 32 schools across Scotland. Schools were randomly assigned to experimental or control conditions. In the experimental schools, children used a games console for 20 minutes each day, running a "brain training" game. The controls continued with their normal routine. The treatment period was 9 weeks. Significant pre-post gains in accuracy and speed of calculations were found in both experimental and control groups over the treatment period. Gains in the experimental group were 50% greater than those of the controls in accuracy, and twice those of the controls in speed. There were no significant changes in two measures of self-concept for either group. There was a small but statistically significant improvement in attitude towards school among the experimental group but not the controls. When scores were analysed by ability, different patterns were apparent. The design of the study allows a degree of confidence when generalising from these results. Some implications of the findings are discussed.