The Case for Memorization in Math

Some math facts need to become automatic. By the time they take Algebra, students should know:

• Multiplication tables

• Perfect squares through 20 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400)

• Perfect cubes through 10 (1, 8, 27, 64, 125, 216, 343, 512, 789, 1000

• Prime numbers through 19 (2, 3, 5, 7, 11, 13, 17, 19)

• Powers of two (2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048)

These facts appear often enough that memorizing them saves time and reduces the number of steps students have to manage. And for college testing, every second matters. This strategy can make a lot of difference!

When a student has to stop in the middle of a problem and reach for a calculator, the interruption can break the thought process. They may know what they are doing, but after entering the calculation, they have to return to the problem and remember why they needed that number. For students who already find multistep problems difficult, that pause can be enough to lose their place completely.

Knowing common number facts by heart helps students stay focused on the larger process. A student who immediately recognizes that 144 is 12 squared can continue factoring or simplifying without interruption. A student who knows that 16 is a power of two can recognize a pattern more quickly. Knowing the prime numbers through 19 also makes factoring and reducing fractions much more efficient.

Calculators are useful and necessary for many problems. Students still need enough number fluency to decide whether a calculator answer makes sense and to recognize familiar values when they appear.

Memorization gives students a stronger foundation for problem solving. Each fact they can recall automatically removes one small task from the process. That leaves more attention available for deciding what to do next and understanding how the steps fit together.