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Statement of Educational Philosophy


Albert Einstein once wrote that imagination is more important than knowledge. I would add that it takes a threshold amount of knowledge for this to be true. In fact, imagination cannot access ideas until the intuition assimilates the knowledge behind the idea. An idea is not understood until it is intuitive. The mind registers an idea, ponders it, examines its veracity, explores the ramifications of it, and ultimately allows the idea to become intuitively clear. Then, and only then, can the imagination take hold and render an idea substantive.


The duty of an educator is initially to expose our students to ideas, and to expand the knowledge base of our students. Facts are the bricks in the edifice of knowledge. Ultimately, the student will find facts individually. Our job, as teachers, is to show our students how to make the mortar that will bind bricks together to make the structures the student will need to be an intellectually autonomous person. The flaw in this metaphor is that, while mortar dries and is ultimately rigid, the structure of knowledge must always be fixed and improved upon. Thus, we must also show our students an intellectual mutability.


Some think that the most dangerous person in society is the person who has never had, nor been exposed to a single idea. This is not true. The most dangerous person in society is the person in the midst of having their first idea. The ghastly totalitarian movements of the Twentieth Century were epitomized by millions of people being exposed to their first idea all at the same time. In the United States, we try to expose our children to so many ideas that they are comfortable with a myriad of different ideas by the time they reach adulthood. As educators, we are responsible for dispensing this exposure to our students, and if we fail in our task, we endanger the foundation of a free society.


But it is not enough to ensure that our students are comfortable with many rich, complex ideas. We must show the role that imagination plays in developing new ideas. Thinking up new ideas is an act of pure creativity, and progress comes about as a result of this creativity. A ripple in a canal becomes an equation in the mind of a physicist, and the equation becomes a physical law, which is observed to govern the way that blips of light travel down a fiber optic cable, which allows our society have cellular phones and the internet. Never forget that it begins with a curious mind and a hungry imagination, following a ripple along a canal. Einstein is right: Imagination is more important than knowledge.


About mathematics education in particular: The high school curriculum is set up to ensure that there are enough people who know calculus by the time they enter university to suit the needs of science and engineering. As mathematics educators, our duties are more personal. Mathematics has been an area of active research since 500 BCE, and we must introduce this tapestry of history, knowledge, and philosophy in a way that welcomes the newcomer, while instilling a propensity for the rigorous mental processes inherent in mathematical activity. We must balance a respect for pure mathematics with an appreciation for the plethora of applications the mathematical techniques we show have. Without mathematics, there is a huge realm of scientific ideas that is closed off to the inquisitive mind. As mathematics educators, we can encourage our students to enter that realm, fearlessly, boldly, calmly, and deliberately, even if as a guest and not as a permanent resident.