This may surprise you, but I never use the results of a computation without first estimating what the answer should be, estimating the errors in that estimation, and having some alternative ways of deciding how accurate the calculation is. Of course, I do work in safety critical application.
But I also deal with students, and constantly, constantly struggle against their willingness to accept just any old number simply because it came from a calculator, a program, a newspaper, or wikipedia. Recently a colleague recounted how a student had been doing some work and had come up with a result. When asked "How accurate is this?" the student clearly just didn't understand the question, let alone have a clue how to answer it.
There is no single solution, there is no single way to make the lazy work harder, there is no single tool that will solve all the problems that exist in education as a whole.
But having a collection of tools, a collection of techniques, and a collection of approaches has to be a good thing.
But I also deal with students, and constantly, constantly struggle against their willingness to accept just any old number simply because it came from a calculator, a program, a newspaper, or wikipedia. Recently a colleague recounted how a student had been doing some work and had come up with a result. When asked "How accurate is this?" the student clearly just didn't understand the question, let alone have a clue how to answer it.
There is no single solution, there is no single way to make the lazy work harder, there is no single tool that will solve all the problems that exist in education as a whole.
But having a collection of tools, a collection of techniques, and a collection of approaches has to be a good thing.