| Summary: | This is the first of two articles on the use of a written
multiplication algorithm and the mathematics that
underpins it. In this first article, we present a brief
overview of research by mathematics educators and
will then provide a small selection of some of the many
student work samples we have collected during our
research into multiplicative thinking. We contend that
many primary-aged children are taught algorithms for
multiplication and division without an appropriate
understanding of the mathematical structure and
concepts that underpin those algorithms. This is not
about demeaning the use of standard algorithms. They
have stood the test of time and can be elegant ways of
getting a solution. However, imagine the power we give
to students if we underpin the strength of algorithms
with understanding! In the second article, we elaborate
on what we believe are the key mathematical underpinnings of algorithms.
Algorithms are very useful methods for calculation when numbers are too large to mentally calculate quickly or accurately. For multiplication, this is generally when there is a need to multiply numbers of two digits or more by another number of a similar magnitude. For example, when attempting to multiply a single-digit number by a double-digit number, students should be considering other strategies, such as applying the distributive property, and exercising their understanding of place value (e.g., 17 x 6 is 10 x 6 which is 60 and 7 x 6 which is 42 so 17 x 6 is 60 + 42 = 102), which allows them to complete these calculations mentally. However, where algorithms are deemed as necessary it would be preferable if the user of the algorithm had an understanding of not only what they were doing, but also, why they are doing it.
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