So you're saying that people who are good at maths are good at mental arithmetic? If that is true, then it doesn't follow that teaching people mental arithmetic will make them good at maths. In fact since mental arithmetic is hard and time consuming to learn, and a decreasingly useful skill, teaching mental arithmetic might turn people off maths!
In accordance with your statement about grouchy old people: I was amazed to find out that they allow calculators on the SAT. Now get off my lawn.