School spies on kids through student laptops

[Kevin]

Depends. I had a graduate adviser that told me to "Estimate the answer using your physical intuition, then actually calculate it. Use the result to improve your physical intuition." The ability to do rough calculations in my head made it possible to follow his advice, which in turn often lead to good ideas or helped me to avoid bad ones. I doubt this would have happened had I used calculators throughout my school years.

I agree with this as well, teach the thinking, teach the estimation and sanity checks. But I do think one of the failings of our education system is too many synthetic problems for the sake of easier teaching. You need to not only teach the knowledge but how to apply it is as well. I don't think calculators should be allowed for everything in those disciplines, but I do think it's good to do some problems, where real world numbers just get ugly because that is what they do, and then you can allow the software to handle that work for you. The trick on that is the balance. But hopefully if the basic math is taught correctly they have a fair bit of the skill set needed for the critical thinking parts anyway.