Christy Hovanetz, Ph.D., is a Senior Policy Fellow for ExcelinEd focusing on school accountability and math policies.
In reading, if a student struggles to sound out every word in a sentence, by the time she gets to the end, it will be difficult to comprehend the meaning of the whole piece.
Likewise, if a student must stop and struggle to determine 2 x 7 equals 14…and then muddle through 8 x 4 equals 32…he wasted a lot of working memory computing basic math facts when solving a multistep problem.
Math fact fluency is the ability to recall answers quickly and accurately to basic math facts, such as single-digit addition, subtraction, multiplication and division problems.
Fluency is developed through structured learning, consistent practice and evaluation, enabling a student to commit these facts to long-term memory. Fluency is the skill that reduces cognitive load, allowing students to solve more difficult math problems quicker and more accurately while also building confidence in their math ability. Studies show that math fact fluency serves as the foundation for learning and using advanced math skills.
State standards for math require students to fluently multiply and divide within 100. This means that by the end of Grade 3, students should know from memory all products of two one-digit numbers.
Ah, yes…the famed “times tables” of 121 facts. Most of us remember the task of multiplying any two numbers, 0 through 10, and committing the products to memory.
Let’s break down how you may have done that:
Some of the times tables are just plain easy, such as the 0, 1 and 10. Any number multiplied by 0 equals 0; any number multiplied by 1 equals that number; any number multiplied by 10 just requires adding a 0 to the number to get the product.
For 2 and 5, the times tables are almost as easy. Doubling any number is multiplying by 2, and knowing how to count by 5s helps with those answers.
That leaves the 3, 4, 6, 7, 8 and 9 times tables, which amounts to only 36 facts to commit to memory, right? Not quite! Multiplication is commutative, which means that changing the order of the factors does not change the product, so, for example, 3 x 4 yields the same answer as 4 x 3. Therefore, the number of multiplication facts students need to learn and memorize is reduced to just 21.
Compare that to the 10,000 words the average third grader knows. Learning and committing to memory these 21 multiplication facts is realistic and achievable for most every student.
You can become fluent in the recommendations of the National Mathematics Advisory Panel by reading ExcelinEd’s math policy fundamental principles and comprehensive K-8 math model policy. They’ll enable you to quickly and accurately recall effective strategies for improving student math achievement outcomes—and free up your time to work on more difficult problems!
Read more: What Is Math ‘Fact Fluency,’ and How Does It Develop? (edweek.org).
