Why Study Math?
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The opening of all my mathematics courses begins with an explanation of both my philosophy and my definition of mathematics in order to answer the singular question plaguing my students’ minds: “Why am I learning this, anyway?” This is my answer: The studying of mathematics takes its form as a non-linear narrative passed down from one person to another through the generations of humanity. No one person knows the whole story, but each person has a piece of it. Some people discover new parts of the story. Mathematicians are the keepers of these stories and the associated questions and examples which both accompany and engender them. Mathematics is that which makes sense; mathematics is that which can be understood. A mathematician, therefore, is a maker of sense. If you are actively engaged in making sense, and, if at any point, what I am saying does not make sense to you, then I am not doing my job. There is an active role the student must play in the making of sense of mathematics and, therefore, it is my job to impart the desire for them to play such a role. Mathematics can be delineated into two categories: the culture and the content. The culture includes the symbols, definitions, practices, demonstrations, and examples that we teach to one another. The content, however, is harder to pin down. All known civilizations have developed symbols to represent mathematical objects. The content of mathematics is whatever it is that these symbols represent. The metaphysical nature of the content of mathematics has been debated for millennia. However, the overwhelming circumstances of different people proving the same theorems, completely independent of eachother, convince me of the objective nature of mathematical experience. This evidence supports my hypothesis that mathematical objects are, in the very least, archetypes of the collective unconsciousness of humanity. It is my belief that you cannot “teach” someone mathematics. Instead, every individual must personally investigate and bring forth the mathematical avatars lying unmanifested in their minds by way of carefully chosen examples and counterexamples. The contents of mathematics are what inform and teach its pupils, not the mathematicians themselves who can only impart the culture. In my view, it is undeniable that the investigations into the contents of mathematics have been the most productive and fruitful activities undertaken by human kind. The undeniable proof of this has pervaded our lives so much so that we often cannot see it. I can’t help but do everything I can to help permeate the respect, awe, and gratitude which we all owe to the contents of mathematics and to the culture created by the mathematicians who discover it.
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