There is a huge amount of research out there (Ando & Ikeda, 1971; Ashlock, 1971; Bezuk & Cegelka, 1995; Carnine & Stein, 1981; Garnett, 1992, Garnett & Fleischner, 1983) that in order to master math facts to the automaticity level students must proceed through three stages: 1) procedural knowledge of figuring out facts; 2) strategies for remembering facts based on relationships; 3) automaticity in math facts—declarative knowledge.
Common Core does a good job with the first level where students need to be able to figure out correctly the answer: counting, count by, arrays, drawing objects or pictures, decomposing and composing numbers, using ten frames etc.
Strategies for Remembering facts
This is often the step that teachers, or publishers either do poorly on or skip altogether. Samples of strategies in addition could be doubles, doubles + 1, in-between doubles etc. Samples of strategies in multiplication might be the nine pattern (subtract 1 from the number being multiplied for the first number, subtract that number from 9 for the second number), the five pattern (cut the number being multiplied by 5 in half, if it is an even number put a zero behind it, if an odd number change the ½ to a 5 e.g. 3 ½ = 35). There are strategies and or mnemonics available for every fact that needs to be taught. All of the math fact lessons in Effective Math Lessons teach those strategies and mnemonics. Click on the words to see these lessons: Addition, Subtraction, Multiplication, Division
Automaticity in math facts
Students who are automatic with math facts answer in less than one second, or write between 40 to 60 answers per minute. Ashlock (1971) showed that children must have “immediate recall” of the basic facts so they can use them “with facility” in computation. Not knowing the facts in this way will greatly hinder their ability in later years when students are taking math classes in junior high, high school or college. When automaticity is developed, one of its most important traits is speed of processing. Think how important that would be for many of today’s careers. Automaticity comes from frequent practice through timed tests, flash cards, or today, iphone, ipad, or computer math fact games.
In retrospect, ask yourself as a teacher if you are making sure your students go through each of these steps in order to master the basic facts. Effective Math Lessons can help you greatly in this area, especially with step 2) Strategies for Remembering Facts.