Math Teaching Strategies #2: Ensure math facts are mastered before starting computation

Rocket Math can make learning math facts easy.  But even more important it can make teaching computation easy too!  One of the first teachers to field test Rocket Math was able to teach addition facts to her first grade class, and then loop with them into second grade, where she helped them master subtraction facts as well.  She told me that because her second graders were fluent with their subtraction facts, they were ALL able to master regrouping (or borrowing) in subtraction in three days.  What had previously been a three week long painful unit was over in less than a week.  All of them had it down, because all they had to think about was the rule for when to regroup.  None of them were distracted by trying to figure out subtraction facts.

Math teaching strategy: Get single-digit math facts memorized before trying to teach computation.

When math facts aren’t memorized, computation will hard to learn, hard to do, and full of errors.

When math facts aren’t memorized, computation will be hard to learn.   I used to think computation was intrinsically hard for children to learn.  Because it was certainly hard for all of my students with learning disabilities.  But none of them had memorized the basic math facts to the point where they could answer them instantly.  They always had to count on their fingers for math.

When I learned more about the process of learning, I found out that weak tool skills, such as not knowing math facts,  interferes with learning the algorithms of math.  When the teacher is explaining the process, the student who hasn’t memorized math facts is forced to stop listening to the instruction to figure out the fact.  When the student tunes back into instruction they’ve missed some essential steps.  Every step of computation involves recalling a math fact, and if every time the learner has to turn his/her attention to deriving the math fact they are constantly distracted.  That interferes with the learning process.

When math facts aren’t memorized, computation will be hard to do.   Having to stop in the middle of the process of a multi-digit computation problem to “figure out” a fact slows students down and distracts them from the process.  It is easy to lose your place, or forget a step when you are distracted by the difficulty of deriving a math fact or counting on your fingers.  It is hard to keep track of what you’re doing when you are constantly being distracted by those pesky math facts.  And of course, having to figure out facts slows everything down.

I once stood behind a student in a math class who was doing multiplication computation and when he hesitated I simply gave him the answer to the math fact (as if he actually knew them).  He loved it and he was done with the small set of problems in less than half the time of anyone else in his class.  Children hate going slow and slogging through computation. Conversely, when they know their facts to the level of automaticity (where the answers pop unbidden into their minds) they can go fast and they love it.  That’s why “Because going fast is more fun!” is the Rocket Math tag line.

When math facts aren’t memorized, computation will be full of errors.  When I learned more about basic learning, I found out that the frequent student errors in computation were not simply “careless errors.”  I thought they were because when I pointed out simple things like, “Look you carried the 3 in 63 instead of the 6.” my students would always go “Oh, yeah.” and immediately correct the error.  If I asked them they knew that they were supposed to carry the number in the tens column, but they didn’t.

I thought it was carelessness until I learned that such errors were the result of being distracted.  Not by the pretty girl next to you, but by having to figure out what 7 times 9 was in the first place.  After going through the long thinking process of figuring out it was 63 they were so distracted that they carried the wrong digit.  Not carelessness but distraction.  Once students instantly know math facts without having to think about it, they can pay full attention to the process.  They make far fewer errors.

In short, don’t be cruel.  If you have any autonomy available to you, first help your students memorize math facts and then teach them how to do computation in that operation.  In other words, teach subtraction facts before subtraction computation.  If you help them get to the point where math fact answers in the operation come to them without effort, you’ll be amazed at how much easier it is to teach computation, for them to do it and at the accuracy with which they work.

Why do multiplication facts have priority after 3rd grade?

Because older students CANNOT succeed in math without multiplication facts.

Am I sure? Yes, I’m sure. “But,” you say, “my students are still counting addition and subtraction on their fingers.”

I know. And I am still sure—fourth grade and up—multiplication. Why? Once children are in fourth grade it is critical that teachers make sure they memorize multiplication facts—primarily because you can’t be sure of how much help they will get later to learn the math facts. Sadly, your students may only learn one operation to fluency. If so, multiplication facts have priority over addition and subtraction. Besides complex multiplication and division, the multiplication facts are needed for success in fractions and ratios. Students have to immediately see the relationships between numbers in order to understand topics like equivalent fractions, reducing fractions, combining unlike fractions, as well as ratios. Let’s be honest here…those are the things that state tests LOVE to ask about. Not to mention, these are the pre-algebra skills students need to be successful in algebra and the rest of math.

If you have the students for long enough (at least one year) you may find that they finish and have mastered both multiplication and division facts. Then you can go back and have them learn addition and subtraction facts as well.

Don’t get me wrong — I know that addition and subtraction facts are VERY IMPORTANT — it’s just that multiplication is MORE IMPORTANT.

What best honors & motivates achievement?

Recognition for real, tangible accomplishments, that not everyone gets.

What makes for a great award, or great recognition that really motivates?  In the final analysis, recognition, like an olympic gold medal, is not about what you receive–it’s about how hard you worked to get it.  If students worked hard, and accomplished something real and tangible, then the recognition they are given, regardless of its form, will be valuable and meaningful.  A paper certificate given out by an adult that represents weeks or months of effort, an honest accomplishment, will be highly prized.  Those are the certificates that are posted prominently in the bedroom or on the refrigerator at home, because it was hard to get.

Remember that when you want to honor student achievement at the end of the year.  If you give awards to every student, then an award means little or nothing.  If on the other hand, students know they had to work and put forth effort to earn the reward, then it is a real honor.  Rocket Math has many built in landmarks of accomplishment that are great to recognize publicly.  Certainly completing an operation is one of the most commonly celebrated achievements.
Chase

This student’s teacher tweeted this picture of the student and his Rocket Chart, proving his accomplishment.  This is something to be really proud of, because it represents a real, tangible accomplishment.  Another accomplishment is when a student beats his or her individual best in two-minute timings.  Yet another tangible Rocket Math accomplishment is being able to pass two levels in one week or ten levels in a month!

What motivates students to try to achieve is knowing what has to be done and believing they can do it. This is another reason why recognizing real, tangible accomplishments works so well. If the other students can see what their recognized peer did and they understand what has to be done to get there, they are motivated to get some of that glory for themselves. Getting through Level Z of Rocket Math is something students know they can do, if they just keep working at it. It is hard to believe you will become Student of the Month, if you don’t know what the previous recipients did to achieve that honor. But if you know that working hard and practicing your math facts every day can get you there–then you can believe it is possible.