When people think about math, they usually think about formulas, problems, and boring class lectures. They associate math with something tangible, objectively correct, and sterile. That is probably because the math which non-majors usually are exposed to is pointed towards two main purposes: 1. To teach children how to do basic arithmetic, and 2. To tangibly test schools and the ability of teachers through standardized tests. Although these two things are appealing, there is a beauty in math as a creative, abstract art, which often times gets forgotten.
In math, we are forced to think of things differently. A large part of math deals with the imaginary world. In calculus II, students are asked to find the area of infinite curves rotated around axis. This sounds crazy! But there are actual, correct answers to this question. But even more on the basic level, we have to use our imagination to find more basic answers to elementary questions. Think about a triangle for a minute. How do we find it's area? Instead of thinking of the formula, or exiting out of this blog to google it, think about how we would get the area from areas of shapes similar to the triangle. Surround the triangle with a rectangle, so that the triangle is completely encaptured. The height of the rectangle is the same as the height of the triangle, and the widths and lengths also equate. Now, draw a line down the height of the triangle, and what do you have? Two boxes split down completely in the middle, making sense of our formula, 1/2bh. We had to think about math in a different way than normal, coming up with a more imaginative way to solve the problem than just regurgitating the formula and plugging away numbers.
In the classroom, we discussed how to apply this different way of teaching math so that the students are engaged and challenged. My professor showed us that the best way to challenge the students is to teach math through the Socratic method, asking guiding questions so that the student ends up learning the desired material more organically instead of having it thrown to them. In this way, learning becomes slightly hidden, and the student will hopefully understand why specific theorems in math make sense. My professor suggested that each class begin with a question that should be challenging but doable, with its discovery as directly related with the larger topic of class. Through engaging with the students, the professor guides the students through their thoughts and helps them learn how to use their imagination to understand the class topic.
Although it is important to be able to know formulas for quick arithmetic, being able to understand them and why they are important is so special, it is sad that math has been quantified and subjected to standardized testing. With so much pressure to teach students about formulas and drills, teachers may easily forget that math is beautiful too. It is like music. When we just see notes on the sheets, we can add them up to count how many beats fall in a measure. But when we play the music, the notes pluck at our heartstrings and we are forever changed.