Somewhere in middle school they give up on the “if you have two apples and buy two more apples you have four apples” or “if you have 3 pizzas cut into 8 slices each and your family eats 13 slices how many pizzas do you have left?” and they start trying to teach 11 year olds by making them memorize proofs and phrases like the transitive property of equality.
To a lot of high schools and colleges, the aesthetic of academia is much more important than students actually learning anything useful, so they teach math class with a chalkboard full of squiggles rather than any kind of practical approach.
From Algebra class on up, it’s taught as a rules following exercise. “Okay, now we do this, and then who knows what we do next?” And it is amazing how many of them are set up as trick questions, how often out of the infinite span of numbers there’s often one right answer and one wrong answer. “How many of you got five? Well you’re wrong, it’s negative 3.”
Meanwhile, I was learning how to fly. In flight school, you learn how to navigate by dead reckoning. I want to fly this course on the map, which is x distance and x degrees from true north as measured from the chart. Given a weather brief and the performance characteristics of the plane from the pilot’s operating handbook, calculate:
true airspeed given indicated airspeed, altitude and temperature
wind correction angle, given true course, true airspeed, wind direction and wind speed
ground speed, given true course, true airspeed, wind direction and wind speed
true heading given true course and wind correction angle
magnetic heading given true heading and local magnetic variation
time aloft given distance to travel and ground speed
fuel consumed given time aloft and fuel consumption
The tool you’re taught to use to calculate all of this looks like this:
It’s basically a circular slide rule, that has a vector plotter on the back. The trigonometry is done by accurately drawing and measuring the triangle, the ratio problems (anything “per hour”) is done by rubbing a couple of logarithms together, and you’re on your own for the addition and subtraction. Ever used a slide rule? They don’t keep track of the decimal point for you. So you have to do these built-in sanity checks, like “Wait, no, the plane doesn’t even hold 70 gallons of gas, there’s no way I’ll burn that much in ten minutes.”
I learned how to do that before I took physics class, and surprised my physics teacher that I knew how to do “boat crossing a river” problems with a weird piece of cardboard. Later on, when I was teaching flight school, I taught that procedure to “It’s been 30 years since math class” boomers and “Trigonometry is next semester” teenagers. They all picked up on it without much problem, because “the wind is blowing you to the right” is a real thing they’ve felt in their own asses by now.
Somewhere in middle school they give up on the “if you have two apples and buy two more apples you have four apples” or “if you have 3 pizzas cut into 8 slices each and your family eats 13 slices how many pizzas do you have left?” and they start trying to teach 11 year olds by making them memorize proofs and phrases like the transitive property of equality.
To a lot of high schools and colleges, the aesthetic of academia is much more important than students actually learning anything useful, so they teach math class with a chalkboard full of squiggles rather than any kind of practical approach.
From Algebra class on up, it’s taught as a rules following exercise. “Okay, now we do this, and then who knows what we do next?” And it is amazing how many of them are set up as trick questions, how often out of the infinite span of numbers there’s often one right answer and one wrong answer. “How many of you got five? Well you’re wrong, it’s negative 3.”
Meanwhile, I was learning how to fly. In flight school, you learn how to navigate by dead reckoning. I want to fly this course on the map, which is x distance and x degrees from true north as measured from the chart. Given a weather brief and the performance characteristics of the plane from the pilot’s operating handbook, calculate: true airspeed given indicated airspeed, altitude and temperature wind correction angle, given true course, true airspeed, wind direction and wind speed ground speed, given true course, true airspeed, wind direction and wind speed true heading given true course and wind correction angle magnetic heading given true heading and local magnetic variation time aloft given distance to travel and ground speed fuel consumed given time aloft and fuel consumption
The tool you’re taught to use to calculate all of this looks like this:
It’s basically a circular slide rule, that has a vector plotter on the back. The trigonometry is done by accurately drawing and measuring the triangle, the ratio problems (anything “per hour”) is done by rubbing a couple of logarithms together, and you’re on your own for the addition and subtraction. Ever used a slide rule? They don’t keep track of the decimal point for you. So you have to do these built-in sanity checks, like “Wait, no, the plane doesn’t even hold 70 gallons of gas, there’s no way I’ll burn that much in ten minutes.”
I learned how to do that before I took physics class, and surprised my physics teacher that I knew how to do “boat crossing a river” problems with a weird piece of cardboard. Later on, when I was teaching flight school, I taught that procedure to “It’s been 30 years since math class” boomers and “Trigonometry is next semester” teenagers. They all picked up on it without much problem, because “the wind is blowing you to the right” is a real thing they’ve felt in their own asses by now.