The main goal of the research was to study how children develop new competencies through social interaction in different contexts. The pre-post test experimental design was used. In the pre-test students were assessed by the PISA 2003 test of mathematics, and based on the results three equal groups for treatment phase were formed. In the treatment phase students from the three groups were solving 5 additional PISA items from the zone of proximal development (ZPD) under three different conditions: group IV - collaboration with an equally competent peer in the out-of-school setting with opportunity to consult others and to use available cultural tools (N=22), group IO - collaboration with an adult who deliver gradual levels of help (N=22), and group KG - individual item solving (N=25). The quantitative analysis showed that all three groups progressed, and group IV (children who collaborated with an equally competent peer in out-of-school setting) progressed more than other two groups. The qualitative analysis suggested that children who progressed most reported on the interview that they had the most symmetric collaboration and managed to rich consensus in spite of difficulties accompanied with the process of joint thinking ('discourse equality'). It shows also that children who were involved in collaboration where partner dominated interaction ('discourse inequality') did not progress or even regressed. Results also show that wider social context made an effect on interaction between partners.