I was a private tutor of math for XII Grade students of science for 18 years.
The use of calculators is a very serious problem that is spreading like a wild epidemic all over the world. It is more so in developed countries and based on my teaching experience, I feel it makes the math ability of the student blunt.
Schools and educational fraternity all over the world should have a debate to tackle this menace. My suggestion is that it should be disallowed till the students reach the level of higher mathematics - that of the college level.
I recall my own experience when I was in Grade II when our teacher asked us to answer 56 x 75 orally in flat 5 seconds and we were all perplexed. He, then, explained that he had made all of us memorize multiplication tables from 1 to 40, and also tables of quarter, half, three-quarter, one and a quarter, one and a half and two and a half. He asked a student what is three-quarter of 56. The student quickly replied, "42". He explained that 75 is three-quarter of 100. So 56 x 75 = 4200. We all started answering such questions orally and on returning home started asking our parents the same question who were impressed with what we were learning.
Though I am much better than the younger generation in oral math, I too am slowing falling prey to the use of calculators and softwares like Wolfram Alpha which is eroding my mathematical ability.
I returned to add an anology.
In ancient times, when electronics was not so well developed and there were no tape recorders, a singer's voice was more important. Even today, a singer has to have a good voice even though the effect of his singing is enhanced by musical instruments. But imagine a class of singing when a student is asked to sing a particular song and he just switches on a tape recorder not using his voice at all. Can we call him a singer? Anyone can sing like that. Similarly, anyone can use a calculator. Training laymen to use calculators is fine and will be helpful to them in their daily life, but for a student who has to learn fundamentals of math, it has a negative effect. Afterall, even to develop newer softwares that can solve problems of math, programers will have to be strong in fundamental math.
Thinking further on this question, I have observed that math has been a nightmare for a large percentage of school students. A very small percentage of students have an apptitude and liking for math. In view of this and with the advent of advanced calculators capable of solving math problems, I am foreseeing the new scenerio to develop in future in math teaching in schools. The subject of math will be broken up into two subjects, one called "funadamental math" and the other called "calculator based math" and students will be given option to choose between the two. Those who have good aptitude in and liking for math will select "fundamental math" in which use of calculators will be banned upto college level and those for whom math is not a subject liking but only necessity will take "calculator-based math" as a subject. This seems to me the most practical way to resolve the problem that is cropping up now.