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Century Tower, University of Florida

Excerpt:

An emperor will defend his empire with far more fierceness than a mercenary; i.e. one will invest far more energy in developing intellectual property that one creates than furthering the interests of some random theory.

November 13, 2006 at 2:14am

Our educators have taken from mathematics what keeps it alive - its connection to this world. Current teaching methods emphasize problem solving in existing axiomatic systems. This is the one and only method used for teaching mathematics at UF (by the majority of faculty anyways). That our educators employ only one weapon from their arsenal implies that our system is impoverished and needs help!

What can be done in this situation? How can mathematics be taught more effectively? The first step is to define the role of our educators.  They must compel, reason and encourage students to action. An educator must be an adept psychologist, someone with the ability to reach into the mind of the student to motivate him/her. This is the most important task of an educator. Current technology makes access to knowledge a trivial problem, and so the role of educators must change – evolve. Their hands must point to a possibility where the dwarves of today morph into Titans of tomorrow; an affirmation of becoming. Genius is not inherited; it is the confluence of opportunity and natural ability. What is usually neglected is the all important role motivation plays in this game. What have our educators done to motivate students?

What is required is a re-valuation of what mathematics is and how it is taught. One must place the magnifying glass on the thought process that leads to a solution vs. the solution itself. The solutions to such problems as building a functional equivalent of the human mind or for that matter models that simulate gene expression will give rise to the mathematics of tomorrow. It is this creative problem solving (vs. problem solving in existing axiomatic systems) that must be emphasized. Why? Because the former approach exploits individual differences the most while the latter forces conformity and therefore reduces the number of successful individuals. This is a key point. Students who attempt to create knowledge will automatically look towards existing axiomatic systems for tools – and therefore learn what is required. You can either force everyone to use pistols in a war or give some the freedom to build tanks and atomic weapons.

We must make education an exercise in self-overcoming and reinvention not a futile exercise in familiarizing oneself with everything under the Sun. In concrete terms, let students define their problems and work towards solving them.

An emperor will defend his empire with far more fierceness than a mercenary; i.e. one will invest far more energy in developing intellectual property that one creates than furthering the interests of some random theory.

In a nutshell, find YOUR problem, and attack it in an all out do or die effort.

Finally, I would like to point out the impersonal nature of our educational system. What have we done to change this? Do our students discuss mathematics with each other? Do they communicate with each other? Do they socialize? Do our educators communicate effectively with students? Simply putting theorems on blackboards is an exercise in futility. There is no connection between you and me. Unless an organization invests in its human resources, the humans will not invest in it!

I have pointed out flaws in our current methods of instruction. I have endeavored to propose an alternative method for teaching. It is my sincere hope that the ideas presented above will not just arouse discussion but lead to some change – change among those given the responsibility for safeguarding and advancing our culture. After all a culture is recognized and remembered because of its outstanding individuals. Any effort that encourages the development of exceptional abilities must be preferred over monotonous regimens that excel at producing the average.