My previous post about solving problems in multiple ways has been interpreted in multiple ways. In previous eras, students were taught the standard algorithm first. The standard algorithms for multi-digit addition and subtraction were explained via diagrams and other means to show what was really happening when we “carry” and “borrow” (now called “regrouping”). I.e., it was not taught without understanding.
After mastery of the standard algorithm, students were shown alternative methods such as “making tens” and other short-cuts, which spotlighted the conceptual underpinning behind the standard algorithm. Often, students discovered these methods themselves. Anchoring mastery with the standard algorithm first created a distinction and students could see what was the main dish versus the side dish.
Current procedure under textbook interpretations of Common Core, is to delay teaching the standard algorithm, and to teach the alternative methods first under the belief that the standard algorithms eclipse understanding. In so…
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