I am old enough to recall the New Math controversy of the 1960s. The
first thing I learned in Algebra I was that " the null set is a subset
of all sets ". I remember that to this day .
Then it did get better for
the curious student : there was the idea of really proving things based
on the " properties of real numbers "- like the associative,
distributive, and commutative properties.
The idea was to teach the students that math at least is rational and logical.
But also, in the late 70s, Professor Morris Kline wrote two books
explaining why the kids don't get math : " Why Johnny Can't Add " and "
Why the Professor Can't Teach."
Professor Kline's main
point was that the math text books had divorced math from real life.
Always link it with practical physics, for example. A parabola on the
blackboard should be seen as more than abstract geometry. It is the path
of rocket launched from earth; an ellipse was the path of a planet in
its journey around the sun. And so on.
Sometimes
good teaching can overcome a poor environment. But how often in high
school interest and Einstein's " holy curiosity " die in the "
underprivileged " young.
I needed to know this stuff ! (Circa 1962)
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Then it did get better for the curious student : there was the idea of really proving things based on the " properties of real numbers "- like the associative, distributive, and commutative properties.
The idea was to teach the students that math at least is rational and logical.
But also, in the late 70s, Professor Morris Kline wrote two books explaining why the kids don't get math : " Why Johnny Can't Add " and " Why the Professor Can't Teach."
Professor Kline's main point was that the math text books had divorced math from real life.
Always link it with practical physics, for example. A parabola on the blackboard should be seen as more than abstract geometry. It is the path of rocket launched from earth; an ellipse was the path of a planet in its journey around the sun. And so on.
Sometimes good teaching can overcome a poor environment. But how often in high school interest and Einstein's " holy curiosity " die in the " underprivileged " young.