On learning mathematics
The following is in response to the question, "Is the emphasis of tedious manual calculation making math education in the US boring, inaccessible, impossible to teach, and worst of all, irrelevant?"
Banking on an ancient heritage
One difficulty in teaching mathematics is that we are trying to share an ancient heritage with students who may not yet appreciate its value. Unfortunately, the achievements of previous generations must often be studied before they can be appreciated.
Given all there is to impart, we are forced into the 'banking concept' of education that was so elegantly critiqued by Paolo Friere. This style of instruction is generally avoided by those valuing authentic, democratic education, but some degree of 'banking' seems unavoidable in mathematics, based as it is on millennium of slow, incremental development and discovery.
Global challenges
If humanity survives our barbaric era, we are probably in the early stages of a global civilization, in which a transition from provincial cultures causes the destruction of many hard-won and long-cherished values. Much localized 'good' is lost. In reaction, the confused and fearful are drawn to the easy assurances of various forms of fundamentalism.
Meanwhile in 'the developed world' (more accurately referred to as 'the most colonized world'), the confused replace the search for meaningful change with the worship of novelty. The glitter of trivial 24/7 entertainment distracts the defeated and comforts the numb. Each is left to find their way in an ocean of moral relativism. Each seeks private truths and consolations.
Loss of authority
Everywhere, older forms of authority are challenged. Heroes, gurus, priests, judges, parents, police, politicians, and educators are distrusted, discredited, and disrespected. As religions become suspect, each person invents a private spirituality.
Global emptiness
Many celebrate the destruction of ancient myths as a modern emancipation from superstition, but we should not forget Nietzsche's warning about humanity's need for myths. As the myths die, new stories are provided for us by the celebrities and talking-clowns of mass media, who dutifully parrot messages dictated by their corporate masters. Such messages can often be reduced to the following:
You are not happy.
"You will be happy if you buy x.
Mathematics in an age of decline
When the foundations of a culture are seriously questioned, even mathematics, the universal language of logic, science, religion, art, music, etc., can become suspect. Well-warn, circular, reductio ad absurdum arguments can take on the veneer of elegance and originality.
Unfortunately, even the State works against a meaningful mathematics education (as opposed to 'training') by imposing official curricula and narrowly-defined content standards that deaden the educational process. In this atmosphere, what is the place of 'tedious calculation' as posed in the question above?
Rescuing mathematics from tedium
I think mathematics is only tedious when meaningful values and goals are missing from the learning process. In this age of near-universal relativism, finding meaning has become the task of each individual student. Teachers can no longer provide an official truth, but they can lend a sympathetic ear and a helping hand if the State does not breath too closely down their necks.
Lost opportunities
Given the constant distractions of our globalized consumer society, many students may not take the time to discover the awesome beauty of mathematics. However, I wonder how many students even in earlier times really saw this beauty. More formal roles of authority may have been able to command silent obedience and dutiful memorization, but did real education occur?
The speed with which a seemingly advanced society can descend into barbarism, as Germany did following the Treaty of Versailles and the US did following the second 9/11 attack, leads me to wonder if the authoritarian force-feeding of culture ever really worked.
(Note: Corporate opinion makers would like us to forget that the first 9/11 attack was conducted by the USA against Chile in 1973.)
As local cultures resist, adapt and inevitably merge with an aggressively expansionist corporate system, powerful social disruptions occur. Some are positive, such as the Arab Spring, in which the Middle World is finally shaking off cruel despots imposed by the victors of World War I.
Others changes are dangerous, such as the growing popularity of fundamentalist dogma. This trend demonstrates the degree of barbarism found everywhere today, from the polished marble halls of the US Congress to the rough marble caves of Afghanistan.
The unity of mathematics
No one can own (or 'privatize') mathematics. Mathematics shows us universal principles upon which we all depend. It is one of humanity's few universal languages and one of our crowning achievements. All cultures contributed to its development. All share in its continuing development and its gifts. Therefore, quality mathematics education can help barbarians hordes sense their connection to a larger, more meaningful world.
Mathematics allows us to consider Plato's ancient cosmology and the latest ideas in Quantum Physics at the same time, and in the same language. As a friend of mine who follows the ancient Platonist tradition often says, "We are one."
