Math is not about memorization.

I’ve always had a bit paradoxical relationship with math. On one hand, i often find math both interesting and fascinating in the way it can do seemingly impossible things. To find numbers using a small subset of what you know, and solving problems that puzzle the brain has always been interesting to me. However, in most math classes, i, like most, have been bored out of my mind.

There seems to be the running paradigm of most math classes to keep what you teach secret. Basically, tell the student to do their problems in this order, using this formula, but don’t tell what they are actually doing. Take for example negative numbers. I remember with clarity i was confused when these introduced these in high school, especially combinations of different positive and negative numbers.

We were given a set of rules to remember: Like numbers become positive(. ++ = +, — = +), different ones become negative (+- = -, -+ = -). The double minus especially threw me a curve ball? Why is does it become negative? Why does this happen? My teachers were very reluctant to answer, telling me to memorize the rules if i was having trouble. I had to beg them to teach me why this actually is. It’s this over focus on memorization and practicing that really kills math for me.

It was with sadness then i started math class about trigonometry yesterday and found that a lot of material the teacher went through, although centers around proofs, did not properly explain what we are doing. What is Sine? How does it relate to a triangle? What are we actually doing when we are doing this problem??? Sometimes i think that the teachers forget that students has never done these problems before. When i tried to search for help later on, i found only more rules and formulas to my dismay. Sin V = A/B,SOHCAHTOA, the circle diagram.

WHAT IS SINE? WHAT DOES IT MEAN.

Finally, by sitting down and trying to solve it, i found the answer i was looking for. I will post it here for others convenience.

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Sides and angles in a right triangle have a connection and a certain symmetry, since only certain angles can allow for a triangle of a certain size, and a certain size triangle is always has certain angles. (a 2, by 4, by 3 triangle always has certain set of angles, regardless of configuration). Due to this connection, a triangles angles can be calculated using its sides, and with the angles and one side, you can form the missing sides.
Sine works as a conversion factor between these triangles.

The sine is equal to the opposing side of a triangle divided by the hypotenuse ( e.g: Sin V = O/H). Doing this results in a sort of conversion factor, which can be used to get the side or an angle of a triangle. If you need the angle, you can use the function know as sine Prim, which returns an angle of the triangle. If you need the sides and know of one of the sides and the angle, you can use a bit of algebraic magic to get to it (F.E side O is 5, side H is x, angle V = 35. Note that sin V = O/H. Since we need the hyponenuse, lets just rearange the equation using basic algebra: SIN V * H = O, H = O/SIN V. The simply input the values: H = 5 / sin 35)

Note the underlined part. Most teachers would skip this part, especially the one that explains what sine actually is.

I truly belie we now have a faulty thinking in our math education, reducing it down to rote memorization and boring exercises, while never pondering on the why’s and why nots of math. Never is math treated as a bit of fun, and never is a lecture ever just explaining concepts and doing example numbers.

For anyone who sees some reason in what i am saying, give “Lockharts Lament” a read, it summaries my positions on math education neatly.

Peace out

-J