Automaticity is the third stage of learning. (Buckle up. We need to review a bit of Ed. Theory here. Ed who? No, Education Theory. Don’t worry, it won’t be painful and it is really quite smart and interesting.)

Here’s an illustrated video explanation instead.  This Marine Corps band demonstrates automaticity.

First we learn facts to the level of accuracy — we can do them correctly if we take our time and concentrate.

Second we learn facts to the level of fluency.  Next, if we continue practicing, we can develop fluency. Then we can go quickly without making mistakes.

Third we can learn facts to the level of automaticity.  Finally, after fluency, if we keep practicing we can develop automaticity. Automaticity is when we can go quickly without errors and without much conscious attention. We can perform other tasks at the same time and still perform quickly and accurately. Automaticity with math facts means we can answer any math fact instantly and without having to stop and think about it. In fact, one good description of automaticity is that it is “obligatory” — you can’t help but do it. Students who are automatic in decoding can’t help but read a word if you hold it up in front of them. Similarly students who are automatic with their math facts can’t help but think of the answer to a math fact when they say the problem to themselves. (See, that didn’t hurt much huh?)

Automaticity with math facts is important because the whole point of learning math facts is to use them in the service of higher and more complex math problems. We want students to be thinking about the complex process, the problem-solving or the multi-step algorithm they are learning — not having to stop and ponder the answer to simple math facts. (Taking off their shoes and socks to count toes is a good indication that perhaps automaticity is not present!) So not only do we want them accurate and fast (fluent) but we also want them to be thinking about other things at the same time (automaticity). One characteristic of students who lack automaticity in math facts is that their math work is full of simple, easy-to-fix errors. We used to call these “careless errors.” But these errors stem from not knowing math facts to automaticity — the student can either focus on getting the facts correct or on getting the procedures correct — but cannot focus on both at the same time. So helping students learn math facts to automaticity will improve their ability to learn and retain higher order math skills— because they won’t be distracted by trying to remember math facts.