The positive effects of bilingualism on cognitive abilities are receiving increased attention from researchers. These effects include greater ability to unconsciously focus one's attention, faster processing of conflicting evidence, and better cognitive health in later life. Schools who educate their students bilingually are giving them advantages that are only now beginning to be scientifically documented.
Bilinguals must constantly choose which language to speak to whom and must then suppress the language they are not using at the moment. As a result, bilinguals have to quickly and unconsciously focus their attention. Processing two languages simultaneously enhances the ability to quickly process conflicting evidence, as shown in the Stroop test . This test involves identifying the colour of a word, e.g. "red", when the word is printed in a different colour, e.g. green. Bilinguals are able to use their attention network to perform the test faster, more efficiently and using less brain power. Attention tasks such as this one are the basis for higher cognitive processes later on in life. 
Adults who are bilinguals are often better at multitasking and have increased grey matter, which improves their cognitive reserve. Interestingly, research suggests that bilinguals have a delayed onset of dementia in old age. They also seem to recover better from strokes. This may be due to the greater number of synaptic connections formed as languages are processed in parallel. 
Since the 1960s, numerous schools around the world have established immersion education programmes, in which some school subjects are taught through a non-native language. In Berlin, the SESB (Staatliche Europa-Schule Berlin) offers immersion teaching through nine languages . Schiller Gymnasium is the secondary school in the SESB which offers a Bilingual Abitur in English and German.
A large-scale study carried out by the University of Kiel  has recently documented the effectiveness of the SESB programme. Pupils of all nine SESB languages were tested in classes 4, 6 and 9. They were compared with pupils from standard Berlin schools as well as with pupils in Great Britain using the international PISA tests. SESB pupils were matched to pupils from similar backgrounds to counteract the effects of socioeconomic status and parent literacy. The pupils were tested for numerous abilities including Math competence in German, German literacy, English literacy, and Science competence in German and in the partner tongue (English for Schiller Gymnasium).
The results speak clearly. SESB children had enhanced literacy in both German and English and were as good as monolinguals in Maths and Science. Bilingual pupils at Schiller performed better than average compared to the PISA tests on Science in 2012 carried out in Great Britain. The results correspond with similar results as described in the BBC Discovery podcasts on Bilingualism .
Other studies carried out in the SESB have shown that multilingual pupils demonstrate enhanced intercultural competence and are more willing to study in another country .
1. https://en.wikipedia.org/wiki/Stroop effect
2. Benefits of bilingualism Part 2 http://www.bbc.co.uk/programmes/p03tknz9
5. Benefits of bilingualism Part I http://www.bbc.co.uk/programmes/p03stqfh