Quality, not quantity
From a student’s perspective, what I observe in the math class is related to the overall perception of school, and the lack of interest in it.
Anyone who does not pursue a career in mathematics is challenged to find how the content taught in class has practical application. So, then, the continuance of the series with geometry, trigonometry and so on is not just for the subject matter, but for the thought process induced by it.
It can be defined as a certain problem solving method, used not only for mathematics but for a wide variety of tasks, thus heightening the academic expertise of the student. You can call it whatever you like, but its effects are all that need be understood; it develops a creative, conceptual knack in which a derivative and its simple functions are expanded to understand something complex. It’s a beautiful mix of logical and empirical reasoning, and has prevalence in all subjects, from physics to U.S. history.
But there is a disparity between the purpose of this process and its reality. Math is taught in a manner which makes the former almost inconceivable to a given student (in no way am I criticizing those who teach it, but rather those constraints forced on them by higher institution). I am reminded of the one who asks, “What’s the point of this?”
Moreover, it creates a negative perspective — that math is there to find fault, to puzzle, to separate the competent from the incompetent. The hate directed at an object of the brain’s capacity no doubt shows the effects of how it is presented.
The structure in many math classes is fragmentary and the pace is light-speed; there’s no time to ponder or make discoveries of the discoveries — it’s rote memorization. That’s why, come exam time, everyone will have forgotten the meaning of the period in a sine curve. They’ll need study guides to muster one last recollection of procedure before it dissipates during summer recess. They don’t own the material.
Exploration is essential for true understanding and, consequently, more enjoyment. Newton, Gauss, and Faraday were not in a race for knowledge; they were in deep, “patient thought” as Newton said. Now, obviously it’s logistically impossible for the education system to allot said time. But the true beauty should lie somewhere in between the race and exploration.
Memorization is tedious work, not hard work, and its rewards are conditional, whereas a system that refrains from delivering the solution in mere minutes is one that emphasizes hard work.
Through hard work comes self achievement and a sense of accomplishment. It is the through the opportunity to think, struggle and express ideas that students are compelled to succeed.
We distance ourselves from knowledge and seek entertainment because its mediums allow for the all-important self expression. The act of laughing at a “vine” or being enveloped in a drama is an assertion of taste and interest. The act of posting pictures or videos is an assertion of personality, and conviction. Vanity is the life of it, really; it makes us feel special, an intoxicating effect which harbors continuous interest. What if math class did something similar? Yes, there is only one correct answer (usually) for each problem, but the ways to get there are many. If a typical math session would allow for freedoms and the latitude for each student to self express through discovery and manipulation of mathematical procedures, there would be true efficacy. Students, not the instructor, will have solved the problem with perseverance, in their own style. And this satisfaction will breed intellectual activity. A virtuous cycle.
Let’s also consider the economic implications of this cycle, if it were successfully implemented. Such an approach would encourage agency and the obligation to ask questions.
It is representative of practical intelligence coinciding with the analytical pursuits of the classroom. Now if the math class supported this — doing something more by teaching less —it may produce students with more practical intelligence.
The effects would be significant. The product of transforming something detested into something invigorating and enjoyable is inspiration. I have experienced something like this in middle school. Seventh grade was abysmal, but it was eighth grade when I came to grips, and much of my new attitude originated from the creativity and conversation encouraged among my peers in the algebra period; it carried over into the rest of my schedule.
Practical intelligence, essentially the art of navigating the social sphere, is fundamental to success; it might someday take precedence over analytical pursuits, and then generations of analytically and practically sound graduates would naturally have better careers.