Imagine a class of Martians in a class in their schools in the subject Earthology(the study of earth). The First chapter in their books says “SCREWDRIVERS“. And the teacher begins
“A screwdriver is a tool on earth that has a metal rod embedded in an insulated handle to apply torque… and so forth”.
He then proceeds to ‘educate’ the students about a hundred types of screwdriver heads and the exact differences between them. He proceeds to tell them the material types, strengths and all the stuff but, and this is important, never tells them what the same would be or is used for. The students learn the same, and regurgitate on the answer sheets in their examinations.
Now this imagination is not too far-fetched. In our first high school mathematics class, the first chapter was complex numbers, and it started:
‘i’ pronounced as iota, is defined as the square root of -1 and hence is imaginary. Any number with an imaginary part is called a complex number.
And then the details for operations on complex numbers followed. We never gained an understanding of where a study of something that does not exist matters or is relevant. The same story repeated, we regurgitated on the answer sheets and went on from there. Some people were better at it, and scored better, which has no relation to the amount of fundamental understanding of where these matter.
And this, the lack of context for what is being taught, utter disregard to its physical significance and more importantly- however utopic that may sound- a lack of understanding for the philosophy of a subject or an area of study is what causes grad students appears like a deer in headlights when real world knocks at the door. It has happened to me personally as well. A question that I asked my professor, when I was doing my EE, regarding the physical significance of a fantastic mathematical expression just derived was considered as an affront to the professor and a disruptive influence to the class.
The result: in the course of tens of interviews for hiring fresh engineering graduates, any question is met with exact-to-the-word textbook definitions, but a follow up question of “what–does-that-mean-?” is met with blank stares. The textbooks are designed to be incredibly dry. Why can’t a book on introductory calculus start with Zeno’s paradoxes? Why can’t an introductory course on DSP start with a pre-generated set time domain samples? Why can’t the students be told the meaning of the complicated mathematical expressions that they just learnt to derive? Taking the example of complex numbers, here’s the explanation by the legendary physicist, Nobel Laureate and educator, Richard Feynman (paraphrased):
Complex numbers can be mathematical tool to visualise a quantity in 2 dimensions. As an example, if we say that there are 3.4 people per square kilometre, no one looks for a 0.4 person.
While I can understand and appreciate that there are concepts that are abstract and assigning physical meaning may be difficult, but at least an attempt to contextualise is definitely warranted. So, the failure of our curricula to bridge academics and the context pertaining to the real world is what robs the subject of its meaning and the capability or the motivation to delve deeper into it.