Would you want to use a computer language that only gives the answer (of a numeric integral or the number of registered users) after you give a suitable estimate?
The problem is that this is a tool that an author designed for another people to use. There is an essay from pg that says that the good languages are designed by the authors for themselves, but I can't find the link. The same idea applies to the other tools.
I'm teaching elementary calculus and linear algebra in the university, and I think that it is very important that the students get a general idea of what they are doing. (For example: The integral from 0 to 1 of e^-x is less than 1, because the area is inside a 1x1 square. If a linear equation system includes x+y+z=1000 and each variable is positive, then x=2117 is not a good answer) But an annoying tool is not the answer to this problem.
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.
The problem is that this is a tool that an author designed for another people to use. There is an essay from pg that says that the good languages are designed by the authors for themselves, but I can't find the link. The same idea applies to the other tools.
I'm teaching elementary calculus and linear algebra in the university, and I think that it is very important that the students get a general idea of what they are doing. (For example: The integral from 0 to 1 of e^-x is less than 1, because the area is inside a 1x1 square. If a linear equation system includes x+y+z=1000 and each variable is positive, then x=2117 is not a good answer) But an annoying tool is not the answer to this problem.