I think that the skill needed to avoid Fake Reductions is similar to the skill needed to program a computer (although at a much higher level). Students who are learning to program often call their variables certain names, which lets humans understand what they are for, and assume that the computer will understand as well. To get past this, they must learn that the program needs to have all the algorithm put inside. An English explanation of an algorithm piggybacks on your internal understanding of it. When reading the English, you can use that understanding, but the computer doesn’t have any access to it.
In a nutshell, they need to go past labels and understand what structure the label is referring to.
I think that the skill needed to avoid Fake Reductions is similar to the skill needed to program a computer (although at a much higher level). Students who are learning to program often call their variables certain names, which lets humans understand what they are for, and assume that the computer will understand as well. To get past this, they must learn that the program needs to have all the algorithm put inside. An English explanation of an algorithm piggybacks on your internal understanding of it. When reading the English, you can use that understanding, but the computer doesn’t have any access to it.
In a nutshell, they need to go past labels and understand what structure the label is referring to.