Number Skills in Junior Classrooms

What number concepts and skills do children have when they start school? How has their understanding changed after a year? How aware are teachers of what the children know? What number concepts and skills are taught in the first year? These questions are important. If we underestimate what children can do their achievement will be less than it might have been.
The results of this study were very cheering - teachers can, after only about 12 days teaching a child, make very accurate judgements about mathematical knowledge and skill. However, there are also some clear warning results about certain ways of using teaching programmes which do not bring about maximum progress.