## Don’t switch back and forth between all addition facts and all subtraction facts

Teachers often ask me if they can start Rocket Math and do both addition and subtraction at the same time–to help their students catch up quicker. No, don’t do it! It will cause special kinds of confusion (called proactive and retroactive inhibition) as students try to memorize the relationships among the numbers.

Students learning only addition for example, are learning one number family 5*3=8 and 3*5=8. So 5 and 3, no matter which order you put them, they go with 8. That’s pretty easy, no way to get confused. But if students are learning subtraction facts at the same time they have a lot more to remember. On top of learning which numbers go together students have to learn which operation is going on. They also have to remember that 5*3 is sometimes 8, and sometimes 5*3 is 2. And 8*3 is sometimes 11 and sometimes 5 depending on which operation is going on. Switching back and forth from addition to subtraction adds a layer of confusion. It does not make it impossible, it just makes it harder because it is a little more confusing. If you teach only one operation at a time students will find it much easier and they will learn faster and be more successful. That is what we want after all, right?

## Can you teach through Fact Families?

Yes, you can. If students learn facts in families (3+2=5, 2+3=5, 5-2=3, 5-3=2) they learn the three numbers as a family. They know if they know any two of the numbers of that family, then they can recall the third number. This is a good way to learn facts. Many teachers prefer it, so we offer it as an option in Rocket Math. The only research I have seen on this showed that learning operations separately, first all addition, then all subtraction, was a bit more efficient than learning through fact families. But there may be a benefit from learning in fact families that makes the fact that it is slower worthwhile. That’s an open question. Would make a great master’s study–especially since Rocket Math has both fact families and single operations available. We have it in the Worksheet Program and the Online Game, so it would be easy to compare and students could be randomly assigned to the condition.

How does this blog fit with the family sequence that you offer? Is it easier to do like all addition levels and then all subtraction levels? Where does the “family” sequence fit in?

When you learn both operations carefully through families, it is possible to avoid confusion. We’ll be adding fact families to Rocket Math soon. But if you’re not learning the facts in families then doing both addition and subtraction (for example) at the same time will cause confusion. It appears to take a little longer to learn facts in families than it does to learn them separately, which is why I’ve been reluctant to create fact family learning programs until now. I would recommend doing fact families AFTER learning the facts separately, for students who have enough time.

You see I disagree with this notion of confusing them because if you present the understanding that they are inverse operations. In 2nd grade when we do math facts orally we say: 2 + 3 = 5 because 5 – 3 =2. Its the natural relationship between the 2 operations that makes it comprehensible. Otherwise, they learn to think of subtractions as a complete different genre of math when in fact they are interrelated.

Teaching in fact families is a fine way to do this. Rocket Math offers fact families and it is a legitimate way to learn. That teaches the reciprocal relationships all at once in a family, such as 2+3=5, 3+2=5, 5-3=2, 5-2=3. This is not confusing. Because they are learned in a group. Rocket Math teaches four facts in each set, and in the Fact Family Learning Tracks each set is a family.

However, mixing back and forth from addition facts and subtraction facts can lead to confusion. Learning a bunch of addition facts like 5+2=7 and at the same time learning 5-2=3 is likely to be confusing. Learning something new that is similar to something you haven’t yet mastered leads to a special kind of confusion that is known in psychology. It is called proactive and retroactive confusion. Similar to trying to learn the cha-cha when you haven’t yet mastered the rumba. You’re going to get the two sets of dance steps confused.

Actually, once students learn addition math facts to automaticity they can then easily move on to subtraction math facts. They readily notice the reciprocal relationship because they know the facts well.

Also, I would point out that most often teachers are trying to do addition and multiplication at the same time, which really leads to the proactive and retroactive inhibition. If you want to teach addition and subtraction at the same time, you need to help students learn them as fact families. You have to present an inter-related set of facts to learn at a time.