What makes a person want to learn?
What makes a person want to teach?
What does it take to convince a 14-year old that knowing how to add/subtract/multiple/divide fractions is valuable? Is knowing how to manipulate fractions valuable?
I spent some time reading a book about algebra recently, and noticed the author put special, but still less than I would have, emphasis on some major moments in the history of math. The first being the invention/recognition of the number “0”. Another being the move from numbers being practical to being abstract; that is, from counting 5 apples or 5 sheep to understanding that “5” can be a useful concept without the practical application. Did you catch that? Numbers began with practical application. Afterwards, the giants of math discovered numbers and math in abstraction. Because of these giants, we’ll be colonizing other planets in our lifetime.
In reviewing this chronology, I think I picked up on something. The problem a high school teacher faces is not convincing several-grade-levels-behind teenagers of the practical application of fractions, but convincing them of the importance of abstract thought. You might be thinking that reminding students that if Matt pays $3.75 and John $1.25, unless Matt is feeling nice, John should only get 2 slices of the Hot’n’Ready seems the better route at this juncture. Don’t be foolish, it is not. Really, who cares how many slices of pizza a couple of high teenagers eat? The bigger problem is that there are four years left until these two knuckleheads will never again be members of a captive audience. There are four years until they will officially become adults in the legal sense of the word, regardless of their not having achieved manhood in the abstract sense of the word.
How to proceed then? How about heeding Thoreau?
“No wonder that Alexander carried the Iliad with him on his expeditions in a precious casket. A written word is the choicest of relics. It is something at once more intimate with us and more universal than any other work of art. It is the work of art nearest to life itself. It may be translated into every language, and not only be read but actually breathed from all human lips; — not be represented on canvas or in marble only, but be carved out of the breath of life itself. The symbol of an ancient man’s thought becomes a modern man’s speech. Two thousand summers have imparted to the monuments of Grecian literature, as to her marbles, only a maturer golden and autumnal tint, for they have carried their own serene and celestial atmosphere into all lands to protect them against the corrosion of time. Books are the treasured wealth of the world and the fit inheritance of generations and nations. Books, the oldest and the best, stand naturally and rightfully on the shelves of every cottage. They have no cause of their own to plead, but while they enlighten and sustain the reader his common sense will not refuse them. Their authors are a natural and irresistible aristocracy in every society, and, more than kings or emperors, exert an influence on mankind. When the illiterate and perhaps scornful trader has earned by enterprise and industry his coveted leisure and independence, and is admitted to the circles of wealth and fashion, he turns inevitably at last to those still higher but yet inaccessible circles of intellect and genius, and is sensible only of the imperfection of his culture and the vanity and insufficiency of all his riches, and further proves his good sense by the pains which be takes to secure for his children that intellectual culture whose want he so keenly feels; and thus it is that he becomes the founder of a family.”