Formal discipline theory led to views that learning Latin and geometry were important, even if few students would use these skills in their lives, because by their formal character they acted as the ideal dumbbells for mental strength training.

Training on one task didn’t help much with training on dissimilar tasks. Identical elements theory suggested that in order for training in one skill to apply to another, the two problems must share common elements.

Provided a person has the ability to see the correspondence, the problems “three times three” and “3 x 3” are the same, even if they look different. In short, an idea, as a more abstract, general notion, can influence your thinking on a wider range of problems than a procedure you memorize.