The Mathematics Generation Gap
12th September 2011
An economic concept that requires a deep understanding of how to use and manipulate fractions is elasticity: the percentage change in X/percentage change in Y. I wonder: how many students struggle with elasticity formulas because they struggle to manipulate and understand fractions?
Another aspect of the mental arithmetic gap that is easily overlooked is its widening over time. Calculators became affordable in the mid- to late-1970s. Students in the 1980s were taught by teachers who had learned mathematics without calculators, and could do basic mental arithmetic. Students today might be taught by a teacher who is himself unable to work out 37+16 without help. The consequences are neatly described in an “Alex” cartoon I have on my fridge about a proposal to ban the use of calculators in school. “Faced with home work which requires him to work out simple sums in his head today’s lazy seven-year-old will instinctively turn to the quick and easy method of arriving at the answer… i.e. asking his dad, who, embarrassingly also wouldn’t have a clue without a calculator.”
I don’t imagine things are any better in the U.S.
Recent research is suggesting that deep understanding of mathematical concepts is related to basic number sense. A person who can look at two sets of dots and quickly determine which set is larger will also generally be better at abstract, conceptual, mathematical reasoning. I have had a student in my office who could not work out 3×5=? without a calculator. I wonder: what else was she missing out on?
Indeed.
September 13th, 2011 at 06:37
Isaac Asimov once wrote an essay discussing the multitude of weights and measures once in common circulation in the US and the various conversions between them, which took up a significant chunk of arithmatic texts of the time. His conclusion was that cultural progress can not only be measured by the new stuff we learn, but also by the old stuff we can afford to forget. (Not saying that fractions aren’t important, but I remember that they were my nemesis in school and I avoid dealing with them whenever possible.)
September 13th, 2011 at 07:58
He also wrote a story about a future in which everyone calculated using personal slide-rule-based computers (hey, it was A While Ago) in which some technician through trial and error rediscovered mental arithmetic. As I recall it turned out badly, as the Powers That Be decided to use people rather than computers in their missile guidance systems because they were cheaper.