One problem is that nobody adds (can add?) in their head anymore - because we have calculators on our phones. In my first science-qualified job in 1983, I was in charge of massive 1st Year Genetics classes which generated large amounts of individual data. These had to be aggregated to get a class total. One of my graduate teaching assistants used to stand in front of the blackboard where the results were tallied, adopt a fixed expression, make a faint whirring sound and after a couple of minutes announce the answer. Where are you now when we need you, Rob?
So in class last week, I wrote up the formula asked the class to calculate the molecular weight and write it down in top right hand corner of their manuals in ink and put a box round it. 5/15 got it right, which was about as good as I did. And nobody was allowed to pretend that they knew how to do it really, and would have got the right answer if they’d had time to check it. So I think that was a valuable lesson. But how do you know what the right answer is, if there is no neighbour to copy from or teacher doesn’t tell you? One method is to add the numbers up in two different ways:
By groups (the natural way). (NH4)2. = 36 + Fe = 56 + (SO4)2 = 192 + 6H20 = 108
By atoms (20xH=20; 2xN=28, 14xO=224, 2xS=64, 1xFe=56)
If they tally, you just might have the right answer. Being confident enough to stand over your calculations/results/data is an essential part of the training to become a scientist.