Question: If you didn’t know the procedure for addition or multiplication, and lacked numeracy skills, could you catch the errors in the calculations shown here?
This is what happens when you teach computations instead of reasoning. Anyone who looks at 14 x 5 and gets 25 does not have basic numeracy and estimation skills developed, and quite possibly has never used real objects to do multiplication before. The error is not primarily in the calculations that they are doing but in the system that leads them to trust their calculations more than their common sense and intuition about the problem they are working on. This kind of error happens independently of the tool used. If you don’t believe me that students can make similar computational mistakes using a calculator, ask math teachers how often they see 4/8 = 2 and other similar mistakes.
A mathematics curriculum based on the ability to do computations and not solve problems is flawed in my mind. We should focus on mathematics as a tool, rather than mathematics as a goal.