## E—What operation do I begin with? and When are students ready to begin memorization?

Here is our basic recommendation:

Yes, even for those poor kids who are still adding and subtracting on their fingers in the upper grades! Why? See below in “Why do multiplication facts have priority in 4th grade and up?”

Please don’t start children on subtraction facts until you are certain that addition facts have been mastered. Use the placement tests to see whether or not they are fluent with addition, or where to begin in addition. “What’s fluent?” you ask. See the section entitled “What is fluent performance on math facts?” Sorry you asked? Then after they are fluent with addition, and you know they are fluent, you can begin with subtraction.

Why? The two operations of addition and subtraction are very similar—being just the reverse of each other. Because of their similarity, a person trying to memorize some subtraction facts before the addition facts have been firmly committed to memory, will experience proactive and retroactive inhibition. Those are fancy psychological terms for confusion—but a special kind of confusion. “There are special kinds of confusion?” you ask. Why, yes there are. This special kind of confusion occurs whenever a person begins to try to learn something that is too similar to something the person is still in the process of learning. The new information conflicts with the recently not-quite learned information and vice versa and…VIOLA… confusion!

Please don’t start children with division facts (this may sound familiar!) until you are certain that multiplication facts have been mastered. Yep… confusion! Use the placement tests to see whether or not they are fluent with multiplication, or where they should begin memorizing multiplication facts. Then, after they are fluent with multiplication, and you know they are fluent, you can begin with division. The reasons are the same as for addition and subtraction above.

### When are students ready to begin fact memorization in an operation?

When they “understand the concept” of the operation. “And how does one know that?” you might be asking. Well, we’re going to tell you. Drum roll, please.

Children “understand” an operation when they are able to compute or figure out any fact in the operation. They can use their fingers to figure out the addition and subtraction facts. Or they can use successive addition to figure out the multiplication facts. Or they can use manipulative and get the right answer. Or they can draw lines, or horses, or dots, or cookies (we’ve seen it all) and get the answer. Somehow, some way, given any fact in the operation, and unlimited time, the child can figure out the answer. Then the child is ready to begin memorizing.

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