Using only one hand?

I have noticed this year that very curiously many young students are doing maths with one hand on the side of their seat while the other hand is solving a maths problem with a pencil. I have always used both hands while problem solving maths - one hand holds the paper flat, or the index finger is used to keep track on a list of numbers or to point to the number I am taking out of the written problem passage to form a picture of the problem or to locate a number in a diagram. Both arms/hands are engaged in the maths solving process. It makes me wonder about the engagement of both sides of the brain when only one side of the body is 'active' during maths work. Does this make a difference cognitively? (I am no authority on this, just curious!)

Another unusual habit I have noticed is that students write one number down and then drop their pencil on the desk, even though the problem isn't finished. I am not sure whether the "high use of devices" has caused this habit where they write one thing and then have to switch to keyboard entry or touch screen input. It is quite inefficient and not a good habit to develop for getting through exams where time is so often an issue.

Now I am going to contradict myself as my final observation is that students are holding their calculators like a cellphone and using both hands (thumbs to be exact). I find this highly inefficient as students drop their pencil/pen and pick up their calculator and then put down their calculator and pick up their pencil to continue writing. However, if the calculator stays on the desk and numbers are tapped in with one finger, the pencil can remain in the hand. In my opinion there is also less chance of entering the digits the wrong way round. Cognitively both sides of the brain are engaged but it is only for data entry and not for thinking logically or mathematically about a maths problem.

The question for me as a tutor is whether to make corrections for these things or whether they don't deserved comment! Will it encourage inefficiency in assessments but ultimately in the workplace?