Wednesday, July 22, 2015
John Cook makes an interesting point
regarding a rule you may have had drummed into your head when you
first learned fractions:
[It] serves some purpose in the early years, but somewhere along the way students need to learn reducing fractions is not only unnecessary, but can be bad for communication. For example, if the fraction 45/365 comes up in the discussion of something that happened 45 days in a year, the fraction 45/365 is clearer than 9/73. The fraction 45/365 is not simpler in a number theoretic sense, but it is psychologically simpler since it's obvious where the denominator came from. In this context, writing 9/73 is not a simplification but an obfuscation.This touches on something I have noticed as a parent of an increasingly inquisitive toddler: The need to focus on one lesson frequently requires setting aside a wider context so the matter at hand can be held in mind. It is perhaps harsh to call reducing fractions pedantic, but there is a serious issue here. Teaching such rules as if they must always be followed or come from a vacuum discourages subsequent questioning and integration with other knowledge. A full explanation is likely impractical at the time, but perhaps teachers should more often say something like, "We will be doing things this way because it makes these lessons easier to learn."
Simplifying fractions sometimes makes things clearer, but not always. It depends on context, and context is something students don't understand at first. So it makes sense to be pedantic at some stage, but then students need to learn that clear communication trumps pedantic conventions. [emphasis in original]
Today: Changed "of the time" to "at the time" in last sentence.