One of the major problems in the mathematics curriculum in the US lately, is the fact that students get introduced to calculators too early and are often overexposed to them.
In Russia, and other countries that were part of the former USSR, students are only introduced to calculators in their late elementary education. Also, even after that, students are expected to use the paper-pencil algorithms for arithmetic operations and for square-roots. And when they take tests and quizzes, unless the test is on concepts that truly require calculators, most teachers and schools use a no-calculators rule. Thus they can't get by if they didn't master the addition and multiplication tables. This includes Middle school and High school. This promotes learning as students don't become overly dependent on calculators for their mathematical needs.
Because of over exposure to calculators, I had many students before my recent move to WyzAnt who would instantly grab calculators on problems such as 2+2 or 0*3. Some students may blank on these problems because they're afraid to fail. However, the number of students like this is too great to explain away using the "anxiety" argument.
One good practice that some teachers and school exercises is to do "mad minute" exercises on a regular basis. But this may not be enough.
As tutors, we are responsible to teach students the math in the classes they are attending. If a student is this far behind in math, however, we essentially face teaching him/her mathematics from scratch. So I think that we really need to rethink the rules of calculator use in our classrooms.
The bottom line is that when it comes to math skills, calculator abuse is rotting the minds of our youth.