Math is cumulative

Many subjects and skills are not as obviously cumulative as math. It is possible to be able to cook bread without having the slightest idea of how to do a stir fry and vice versa, yet they both come in the category of cooking. However it is impossible to do long division without doing doing short division (for estimating), multiplication by a one digit number, comparing two numbers to see which is larger, and subtraction. Yet long division is usually taught by fifth grade.

One reason to like teaching is that every time a teacher starts with a new class, he is starting fresh. Any mistakes will from a previous class are gone, because these are different students. The students don’t have that luxury. If they haven’t learned something, it will still be with them. A common complaint among math teachers is “My students are taking _______ and they still don’t know _______.”

There is no way a teacher can teach long division without the students knowing subtraction. The students will learn some of the motions, but their answers will be consistently wrong. This gets worse and worse as math progresses. Although there are some skills that are independent of others, there are many subjects in mathematics that require a wide variety of knowledge.

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