Developing Automaticity with Basic Facts

 

Parents often ask us about the basic math facts. “Do students need to know their basic math facts? If so, when? Do students learn their facts in school? What should we do at home to help our children learn the facts?” Because the math curriculum encompasses far more mathematics than most of us experienced as elementary school children -- including topics beyond number such as geometry, probability, data, measurement, and algebra -- it’s easy to wonder if learning the facts is still a priority and how children learn their facts. Here are some responses to some common questions about math facts.

 

Do students need to know their basic math facts?

Yes. Knowing math facts and knowing them with automaticity is an important goal for all our students. Efficient computing and estimation rely on being able to produce answers to math facts with ease.

 

Should students be able to do math facts quickly?

Premature emphasis on speed, or drilling for speed when students’ understanding is less developed, causes anxiety and leads students to use less sophisticated strategies more quickly They become faster counters and use counting to get a result. Automaticity develops over time. Student answers to math facts must be automatic. Not knowing math facts with automaticity slows down estimating, calculating, and problem solving.

 

When do students learn the facts?

By the end of third grade, we expect students to know all their addition and subtraction facts to 20 and their multiplication facts to 10 as easily and fluently as they know their names. Some students will develop automaticity sooner, while others need more time.

 

How do students learn the facts?  

While our goal is for students to provide answers to math facts with automaticity, we aim for more than just a quick recall of answers. Students must also develop a strong understanding of what that fact means and how it’s related to other facts. Understanding relationships between facts contributes to automaticity.

Some children seem to learn their math facts with ease while others seem to struggle to recall answers. Children who seem to have an easier time are not simply those who can memorize better. They tend to be those who have a well-developed understanding of number relationships or a strong number sense. These children understand the operation and they see how individual facts are related to others. For example, consider the math fact 3x6. Beyond being able to produce a correct result with automaticity, we want students to have mental models for the fact and to know how it is related to others. Students should recognize that 3x6 is 3+3+3+3+3+3 and 6+6+6, but they should also recognize that 3x6 can be represented as 3 rows of 6, or 6 groups of 3.

Having a network of number relationships like those shown helps students to learn the large number of addition, subtraction, multiplication, and division facts more efficiently and, if necessary, works as a basis of strategies for reconstructing forgotten facts. For example, if a student forgets 3x6, she or he might use a known fact like 3x3. Knowing 3x3 is half 3x6 the student would double 9 to get 18.

 

What Can We Do at Home?

Practicing facts at home is important and will definitely help your child in math class. Teachers ask students to practice specific facts at home. In addition to these assigned opportunities to practice facts at home, many students need more practice time. Focusing on a few “need to learn facts” for short amounts of time can be helpful. Using flash cards or playing math games can help students learn their facts. There are also a variety of websites that have electronic versions of flash cards or have fact practice games which are appealing to some students.