id: 06664520
dt: j
an: 2016f.00906
au: Lewis, Robert
ti: Dividing fractions: a pedagogical technique.
so: Aust. Math. Teach. 72, No. 1, 18-19 (2016).
py: 2016
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: F40
ut: fractions; multiplication; mathematical concepts; concept formation
ci:
li:
ab: Summary: When dividing one fraction by a second fraction, invert, that is,
flip the second fraction, then multiply it by the first fraction. To
multiply fractions, simply multiply across the denominators, and
multiply across the numerators to get the resultant fraction. So by
inverting the division of fractions it is turned into an easy
multiplication of fractions problem. The author received a phone call
from a primary school teacher who was teaching this method to her Year
6 class. She had been asked a question, one that she had never before
been asked. An inquisitive 12 year old was not happy to just accept the
methodology taught; he wanted to know why “flip” the second
fraction over. The author teaches a bridging mathematics course at
university and hardly ever has had anyone ask “why” ‒ why invert
a fraction and then multiply? ‒ so it is not surprising that this
young teacher has not encountered the question before. Knowing why
certain mathematical actions are performed rather than just rote
learning will lead to deep understanding. In practice, the authors
finds that explaining “why” cements that deep understanding. The
author went over two reasons with the colleague and the answers may be
of interest. The two reasons are presented in this article. The first
explanation would be suitable for younger students learning fractions.
(ERIC)
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