I was thinking about how increases in the division of labor result in a more efficient economy, and how labor-saving devices make certain kinds of labor either easier or obsolete.
Therefore, I am beginning to think that math class is inefficient, since writing out the equations and showing your work when using a computer program is so much faster. I agree that if someone is going to go into a science for their career, then being able to solve mathematical equations by hand MAY be useful.
However, I cannot see any point in continuing to write out one's math when one could use a computer program to do the same work, but more quickly. I haven't found any such programs, though I imagine that one could make a lot of money. Let's call this program AutoMath.
AutoMath's gui would provide a list of equations, a custom equation field, the ouput, and an option to output each step from equation to answer. Also, AutoMath should be able to read and output equations written in LaTeX. Obviously, this would not help those instances where you have a word problem, but that could be another program entirely.
AutoMath is a labor-saving device, of sorts, that makes any mathematical work faster, which would be a desktop version of what is already used in financial, military, avionic, and aerospace industries. For instance, the Moon-lander used in 1969 had a computer that solved equations constantly through out the historic landing on the moon. Also, financial institutions use extremely sophisticated mathematical models to attempt to either predict prices or to attempt to buy and sell products and services at the best possible time.
Industries already use the concept behind AutoMath, though AutoMath is meant to be used by math students and scientists. Programmers may or may not find it useful, since a few lines of Ruby could do the same thing.
One last thing: I see this absence of a kind of AutoMath, especially for students, is an atavism that may hopefully vanish within the next generation, as the baby-boomers leave the work-force.