Waldorf Math: Different kinds of Subtraction

068532-antique-glowing-copper-orb-icon-alphanumeric-minus-sign-simpleIn the Waldorf math classroom, there are (at least) three ways of looking at a subtraction problem. (This is for the teacher to keep in mind; the students may not be fully conscious of this until 3rd grade.) Let’s take the example of 20 – 13:

As a Take Away (or Subtraction) problem. We take away 13 from 20.

As a Difference Problem. We ask ourselves: “How far apart are 13 and 20?” or “How many steps are there going from 13 to 20?” This will be especially clear to the students once they have moved it on the number line.

As the Reverse of Addition. We ask ourselves: “13 plus what is 20?”

The goal is to develop flexibility in the children’s thinking, so that sometimes they look at it as a difference problem, and sometimes, as a take away problem, depending upon which approach is easier for a given problem. The teacher should try to be consistent in the use of the words “take away”, “difference”, “subtract”, etc. By saying “26 minus 14”, we leave it open for the children to solve the problem by either taking away or finding the difference. The students should still be doing subtraction predominantly in the horizontal form (and in mental arithmetic) well into third grade, and beyond.

Carrying and Borrowing. It is best to delay vertical addition and subtraction until third grade. See the Making Math Meaningful Source Book for Teaching Math in Grades One through Five for more information on this topic.

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