Every so often in my math path I encounter an area which is full of formulas or processes which I have to memorize. Much of the "math and physics teaching" I read doesn't approve of just memorizing formulas, and discourages such rote learning, but there are some places where I find that it is necessary. Otherwise I have to "re-invent" the entire thing every time I work with it, which gets tedious. Examples of this are the quadratic formula on how to solve quadratic equations, and the trigonometric identities which I was working with last week. Now that I have enough trigonometry to resume my work in learning basic mechanics in physics, the same holds true for those formulas about vectors, and vertical, horizontal, and curved trajectories of projectiles in ideal space.

When I'm faced with these formulas, as well as the mathematical processes which were used to derive them, I can get stuck in the grinding gears. I try in vain to visualize the different lengths on the graph or in a triangle which are then combined and recombined to make trigonometric relationships. Drawing diagrams only helps in the short run; after the basic sines and cosines, verticals and horizontals, things get too complex for me to visualize. And yet I have to know these things and become familiar with them in order to proceed.

What I have done throughout my work is to create a "calligraphed" page which shows the formula and its derivation, and some uses it is put to. Despite doing signs professionally, I am not really a calligrapher, and my lettering styles are limited. For these pages I mostly use what might be called "architect's capitals" or "graphic design block letters," familiar to those who work with architectural drawings. I include whatever I think will help me to remember how the formula works, and what the components are. I may use different colors, but usually I don't add any extra drawing or art, which would distract from the austere purpose of the written page.

What I have found is that the act of writing it down formally, helps me fix it in my mind. I can remember it not only by referring back to the page I have drawn, but by remembering the page in my mind's eye. I also find that the handwork of carefully making up the page adds strength to the memorizing process. That's why doing it on the computer wouldn't be as effective. I have done pages on polynomials, on conic sections, on formulas for describing acceleration, and on trigonometry. Here is an image of my latest page showing the formula for the trajectory of a projectile fired at an angle. The arrangement is mine, but the sequence of information comes from one of my trigonometry books. I keep all the pages I have done in looseleaf notebooks, where I can return to review what I need. Looking at the pages brings back not only the mathematics, but the memory of when I did the work, along with the mood, circumstances, and events of the time when I was writing it.

Posted at 3:17 am | link