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Teaching Multiplication
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 One
major stumbling block you will find as a teacher is that when acquiring
a new skill in the same subject (particularly mathematics) can be
integrating this new skill with what the children have already learned.
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).
We will look at two studies that observed developmental changes
in the understanding of mathematics then teaching multiplication.
These are the changes in the childrens 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 subjects.
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 of teaching multiplication.
The common errors were generally found to be 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 teaching multiplication the knowledge the students had absorbed
about addition were somewhat stripped away if not, in the very least
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.
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