Why teachers and textbooks should stop making real concepts abstract.
Hating mathematics is worn as a badge of honor by many people. The fields of math are so universally seen as difficult, useless, and hard that people often bond over their inability to understand them. How many times have you heard someone say something along the lines of "I sucked at algebra so bad" in an almost gleeful tone? How many teachers have heard students ask the question "When will I ever use this in real life?" or something similar?
Being a programmer I'm used to taking specific problems and trying to abstract them into a more general concept. Programmers live in the abstract, however, it was 100% a learned skill. I would also put forth that we learn it because it's useful. Making a program too specific can be very constraining to future use. Math and science are not the same thing AT ALL.
Today, as I read over a chapter in a Trigonometry book I was struck by how variables were given the most meaningless of names. A line EF and an angle G. The variables x and y are notorious in algebra. Then I went over a linear algebra lesson I am preparing and it struck me as beyond odd that none of the real world uses for the materials being presented by my textbook were mentioned during the lesson at all. The real life uses for these methods had been stripped from them entirely.
Take for example, the simplest concept in all of linear algebra, the matrix. A matrix in real life applications might be an array of pixels in an image, the coordinate system of a map, or the rendering of a path a robot takes when moving. Yet, here is was being presented as this weird set of arbitrary numbers surrounded by brackets. Is it any wonder a student who doesn't know the usefulness of this tool doesn't see the myriad of purposes it could be put to?
Today, more than ever, it seems like everything in our world is fighting for our attention. In this attention seeking world, textbooks and dull lessons feel like the least of things we should be paying attention to. For college students, their entire education is based on the notion that they're being prepared for a future discipline. These people are looking at every lesson and trying to figure out what's useful and what may be filler information.
When I was in college, I saw everything I was learning through a lens of utility. How could I apply this? What was this useful for? Do I need to know this? These were questions I asked myself regularly. So in taking concepts and making them wholly unrelated to the real world you're giving students unconscious or conscious cues to disregard what you're saying as benign filler.
You're also making problem solving more difficult. Students ask their teachers when something will be used in real life because they can't see how what they're learning is applicable to anything. How then, I ask you, will students do when the encounter real life situations in which they could have used a skill? I'll tell you. They'll completely miss out on the opportunity.
Sure, if you give them a long time and nudge them in the right direction they might figure it out. However, when I was doing tests I most often looked for cues in the wording of a question to know what I was supposed to apply to that question. In real life there usually aren't such blatant cues or any at all. If you don't tell students how something is useful then they won't know when to use it.