I think with high school math teachers in particular they have an aversion to shortcuts, and maybe rightly so.
All Shortcuts Are Not Necessarily Bad.
Take learning multiplication tables or doing multiplying, dividing, adding and subtraction long hand. Surely there is that pocket calculator that could have that answer for you in about two seconds.
I think with all tools or methods we aquire there might be an optimum one to pick as a short cut to save us energy, time or a very good reason, money. To keep forcing people to do things the old way just to learn it sometimes does sound plain stupid.
But maybe rather than saying the old way needs to be learned to feel good just again think---
All shortcuts are not necessarily bad. I contend that TWO or more ways of doing something, perhaps the old way and also the best new shortcut way may come in handy some day.
You might need to make change as a cashier the old way when the electronic register dies on you one day. I have ordered take out food and seen clerks absolutely paralyzed when the cash register went caput.
I was in Navy ROTC and we learned semaphore signaling between ships at sea to preserve radio silence using flags or Morse Code with light flashes. The Navajo Indians had a code used that the Japanese Army could not decrypt during World War II.
Can you imagine the old days in real estate someone saying these telephone size books of listing were EASIER to access homes today by turning pages than looking it up online? Even if a web site for home search WENT DOWN, there are so many more you could look at. If your office LAN internet connection went down go down the street and connect with the WiFi at the coffee shop.
The point is don't gravitate only to methods you are familiar with and not look if now a NEW AND BETTER shortcut is right there for you. But just MAYBE keep the old one as a back up. Look at CURSIVE WRITING, many are teaching keyboard typing or printing techniques only in third grade now. Maybe cursive writing will be for hand writing pretty Christmas cards or something. Hard to tell on that one.
Even if a Physics or Math teacher says NO PROGRAMMABLE calculators for the exam and all you get is a crib sheet for writing down all your equations, know that you have that advanced calculator at home for the REAL world but you still know Newton's laws of motion in your head. You do know them right? The third one has to do with equal and opposite actions and reactions. Probably why when you dive out of that row boat solo in the lake you go one way, and the boat goes the other way. ha ha
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