Any student of the word is shown the infinite variety of forms our language can take on their journey. We are encouraged not to prove how good we are at reading by getting exponentially faster at it. We are taught to find meaning in the labor spent turning paper and ink into an active link to an imaginary world within the mind of another. We are shown that some of us have particular inclinations to delve into anywhere on a spectrum between ultra concise legal writing and writing that defy all rules like the works of E. E. Cummings. We are taught to enjoy writing as an explorative medium.
I believe that the Maths are just another medium with which to explore worlds both imagined and measurable. A cod example might be that if I have two sheep and my sister falls ill, her five sheep will fall under my care and I will have seven sheep to tend. No need to count, math provides me with knowledge preceding the moment. With more metrics, I might be able to determine how long I my duties will take and whether or not I have the resources to care for these fuzzy beasts.
But this is the See Jane Run of mathematical literacy. From this modest foothold, one may explore the forces near and inside black holes, places mankind may never go, and fashion narratives of beauty and connectivity as Feinmann and other mathematical poets have done. On a simpler scale, we have children imagining worlds where gravity is half of what it is and imagining themselves dunking balls and flying around like Jedi. The realms to be explored this way are endless.
Mathematics, like all language, is a means to expressing a world in clarity so that it can be experienced. Yet too often I see students of the number who merely sound out each number and use the rote tools to figure out how to say it in the acceptable format. It is like younglings reading aloud ay-ar-arbitr-area-y con-conk-conscious-ness and yet being unable to truly understand their own phonations due to the need to move forward with the doing of reading. In a literature classroom, I would likely give that student an easier book to read, but standardized curricula is slowly taking even that out of our control, leaving many students to flounder and never truly READ for themselves until it is too late. With mathematics, the situation is much more dire. I find that the average Maths teacher has not ever been exposed to the true ability to use their phonations to explore the worlds of poetry and pure beauty that exist therein. With no teacher who remembers, the skill is lost to all but those who pursue the Maths at a collegiate level.
Mathematics MUST be taught with this linguistic imagination at the forefront. We do not DO math in the same way that we do not DO reading. We read to experience the other or express the inexpressible. I math not only to see the world as the beautiful and astounding perfection that it is, but also to imagine and clearly express futures that do not exist yet. My dear reader, this is a tragedy on the scale of the loss of an entire cultural language.
Of all topics, a solution here eludes me, but I do have a few suggestions. First, do not give students isolated, purely numeric problems. That is like having kids speed read aloud random words and say it is improving their recognition. Put students in environments where solutions to problems of ethics and art are brought closure through the application of numbers. Teach students to live in an ever changing democratic union where the voice of the people is heard by 2/3rds majority on a mathematical level. Simply adjusting the daily necessary votes to pass a decision is enough exposure to teach the concept of a ratio. Cleverly throw in some girls only votes and let the discussions of fairness and partisanship arise. These students may or may not have the linguistic ability to express these dilemmas, but they will grow in the mind like a cancer, driving the ability to express themselves. Teach geometry in the pleasurable company of the arts. Show students pieces that rock the occult center and then show how to bring that inexplainable beauty to their works of art through simple tools and a true fluency of the world in numbers.
In the words of Dylan Thomas, do not go quietly into that good night, instead rage, RAGE against the dying of the light. Find the light in the darkness, my dear reader. It exists because you do.