A time as well as a place
To make accurate mental calculations, children need a good understanding of quantity value. The review shows that a significant proportion of 10 and 11-year-olds have difficulties in understanding the relationship between adjacent columns of multi-digit numbers.
A number of studies indicate that place-value concepts are being introduced at the same time as two-digit numbers. This means that six and seven-year-olds are having to grapple with the irregularities in the naming of "teen numbers (11 and 12 don't have "teen" in them, while 13 does not have the word three nor 15 five) at the same time as having to come to grips with the sophisticated concept of 100s, 10s and units.
When children do mental arithmetic, they use partitioning rather than place value, which they ignore. Partitioning involves splitting the two-digit number into quantities represented by their names. So, 24 + 25 is worked out by adding the 2s, then adding the 4 and 5, and putting them together to make 49. This, and other calculations such as doubling and halving, rely on the children understanding quantity value rather than place value.
Teaching place value in the UK by Ian Thompson, Department of Education, University of Newcastle, St Thomas Street, Newcastle upon Tyne NE1 7RU