The government is considering giving food supplements to pupils in England in an effort to improve behaviour and performance, according to reports.
Fish oil is said to improve behaviour and performance
Ministers are awaiting results of a review by the Food Standards Agency into the effects of diet on behaviour.
A school in Surrey is beginning a separate trial into the effects of food supplements, diet and exercise.
Research suggests that Omega 3 and 6 oils boost learning abilities - but some studies have cast doubt on this.
The Department for Education and Skills (DfES) will base any advice on the outcome of the Food Standards Agency review.
A DfES spokesman said: "The government is committed to ensuring that children are provided with the healthy food and nutrients they require during the school day, not just to aid their physical health, but to ensure they can study hard and behave well.
"The Food Standards Agency is currently conducting a systematic review of research looking at the effect of nutrition and diet on performance and behaviour of children in schools.
"This includes investigating studies that have used Omega 3 and 6 fish oil supplements in schools. While this work is not yet concluded, we will of course examine its results with interest."
A revamp of school meals is intended to stipulate regular inclusion of oily fish in the school menu.
A spokeswoman for the FSA said: "Oily fish should be part of a healthy balanced diet. Evidence on the benefits of fish consumption is currently limited to cardiovascular diseases.
"No clear conclusions can be drawn for other health benefits, including the association of all aspects of diet and performance in children."
Several local education authorities have organised trials of fish oil supplements.
More than 120 pupils aged between six and 12 took part in trials organised by Durham County Council.
Half used a combination of omega 3 fish oil and omega 6 evening primrose oil and half an olive oil placebo.
It suggested that after three months the group taking the natural fatty acids had significantly improved behaviour.
Schoolchildren across Teesside are also taking fish oil supplements after an initial pilot suggested positive results.
Cricket Green school in Merton, Surrey, is launching a trial organised by the not-for-profit Food For the Brain campaign.
'Culture of food'
Pupils at Cricket Green, a special school, have undergone a "nutritional makeover" involving workshops for parents and teachers as well as pupils.
In preparation for the nine-month trial the parents and teachers have been taught to cook while the school has instigated a strict rule of no sugary drinks, no crisps and no confectionery.
The children also have access to water at all times and take part in daily structured exercise.
A second school, a standard state primary, will join the trial in September and the campaign aims to work with 100 schools.
Campaign founder, nutritionist Patrick Holford, said: "The purpose of this trial is not just to prove what works but also to prove what works in terms of changing the whole culture of food in the community."
He added: "Kids used to have cod liver oil which is a supplement. A fact is a quarter of a million children are medicated with drugs like Ritalin - the evidence is that this number could be halved by giving food for the brain."