Teaching multiplication is a case in point, this is because it involves merging new information and ability with the knowledge the children have previously acquired (in particular, addition skills).

We will look at two studies that observed developmental changes in the understanding of mathematics then teaching multiplication. These are the changes in the children's comprehension of mathematics between single-digit addition and simple multiplication.

The first study dealt with teaching multiplication to third-graders, fifth-graders, and adults. The subjects performed simple addition or multiplication in mixed- and blocked-operations formats. There were substantial interfering effects from related knowledge found at all age levels, believe it or not. However, these problems were much more apparent in the younger children tested.

From this we can conclude that in the early stages of teaching multiplication, one consequence of learning something new is trying to separate the newer skill from an earlier, related skill, less recently studied. In teaching multiplication we considered error tendencies that supported the problem we addressed"the problem of integrating operations. This is definitely a prominent issue even in the early stages.

The common errors were generally found in patterns consistent across all age groups. For instance: all groups were much more likely in learning multiplication to answer an addition problem with the correct multiplication answer than the reverse. This means that when learning multiplication the knowledge the students had absorbed about addition fell away somehow, and if not, in the very least the skills were muddled enough for them to give the wrong response.

The second study in teaching multiplication was a longitudinal study that confirmed this theory. There was evidence of impaired performance in addition skills over time within individual children in the second, third, and fourth grades who were tested with simple addition and multiplication problems for several months.

The reaction times for the addition problems showed that second-graders in higher level math classes and third-graders in the usual math classes tended to slow down when they came across addition problems. The fourth-graders, though, mostly increased their speed of addition. Over the year(s), in either late third or early fourth grade, their understanding had improved. Thus teaching multiplication will disrupt mathematical skills previously learned, but in most cases, in the course of time, by teaching multiplication and other mathematical skills with repetition, both new skills and old skills can be integrated.