Background: In the context of the British Government's policy directed on improving standards in schools, this paper presents research on the effects of a programme intended to promote the cognitive development of children in the first 2 years of primary school (Y1 & 2, aged 5-7 years). The programme is based on earlier work dealing with classroom-based interventions with older children at both primary and secondary levels of schooling. Aim: The hypothesis tested is that it is possible to increase the cognitive ability of children by assisting teachers towards that aim in the context of mathematics. A corollary hypothesis is that such an increase would result in an increase in long-term school achievement. Sample: The participants were 8 teachers in one local education authority (LEA) and 10 teachers in another. Data were analysed on 275 children present at Year 1 pre-test in 2002 and at long-term Key Stage 2 post-test in 2008. Method: Two intervention methods were employed: a Y1 set of interactive activities designed around Piagetian concrete operational schemata, and mathematics lessons in both Y1 and Y2 designed from a theory-base derived from both Piaget and Vygotsky. Results: At post-test in 2004, the mean effect sizes for cognitive development of the children--assessed by the Piagetian test "Spatial Relations"--were 0.71 "SD" in one LEA and 0.60 "SD" in the other. Five classes achieved a median increase of 1.3 "SD". The mean gains over pre-test in 2002 for all children in Key Stage 1 English in 2004 were 0.51 "SD", and at Key Stage 2 English in 2008--the long-term effect - were 0.36 SD, an improvement of 14 percentile points. Conclusions: The main hypothesis was supported by the data on cognitive development. The corollary hypothesis is supported by the gains in English. The implications of this study are that relative intelligence can be increased and is not fixed, and that children can be led into collaborating with each other to the benefit of their own thinking, and that there does exist a theory-based methodology for the improvement of teaching.