Learning Multiplication: Rote Memorization or Meaningful Learning

Three school children doing math equations on the blackboard

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Knowing multiplication facts is an important foundation for being able to solve all types of higher-level math problems, but learning them isn’t always easy. For decades, teachers have relied on rote learning or memorization to teach the multiplication tables.

Does Rote Learning Work?

While this rote learning strategy works for some students, in the past decade or so research indicates that this is not the most effective way to teach multiplication.

Students learn multiplication better when they are able to find ways to make connections, create meaning or otherwise understand the rules governing multiplication.

One research study referred to these different ways of learning math as practically-based explanations and mathematically-based explanations (Levenson, 2009). Practically-based explanations are the ways students find to relate mathematical concepts to their real-life experience. A number of these explanations are practical strategies that can also be formally taught.

Practical Multiplication Strategies

  1. Visual Representation: Many children when first learning multiplication will use manipulatives or drawings to represent each group. For example, 3 x 2 would be represented as three groups of two cubes each. Your child can then visually understand that you are asking him to see the number that is created by three twos.
  2. Doubles: Learning to multiply by two is easy when your child is reminded of his “doubles” addition facts. Multiplying any number by two is the same things as adding it to itself.
  3. Zero: Sometimes your child may have a hard time understanding why a number multiplied by zero is always zero. Reminding him that what is being asked is to show “zero groups of [whatever number]” can help him see that no groups equals nothing.
  4. Fives: Most children know how to skip count by five. What they are actually doing is multiplying by five. Using a placeholder (fingers work well) to keep track of how many times he’s counted, your child can automatically multiply by five.
  5. Tens: Since multiplying by ten is essentially moving the digit over a place, all your child needs to do is add 0 to the end of the number. 5 x 10 = 50; adding 0 to the end moves the five from the ones place to the tens place.
  6. Elevens: When multiplying by a single digit, all your child needs to do is put that number in the tens and ones place. (11 x 3 = 33)

Once your child has learned these practical multiplication strategies, he has ways to find the answers to nearly half of the multiplication tables. There are some other strategies or tricks which, while a bit more complicated, he can use to work out the rest of the tables.

More Complicated Multiplication Tricks

  1. Fours: Four times anything can be thought of as “doubling the doubles.” For example, 2 x 3 is the same as doubling three or 6. Using that as a base strategy, 4 x 3 is simply a matter of doubling the double or 3 + 3 = 6 (the double) and 6 + 6 = 12 (the double-doubled).
  2. Fives (even number): If counting by fives fails, when your child is multiplying an even number all he needs to do is take half of that number and add 0 after it. For example 5 x 6 = 30, which is the same as half of 6 with a zero on the end.
  3. Fives (odd number): Have your child subtract 1 from the number he’s multiplying by, halve it and put 5 after it. For example, 5 x 7 = 35, which is the same as 7-1, halved with a 5 after it.
  4. Nines (finger method): Have your child put his hands out in front of him. The fingers on the left hand are numbers 1 through 5; the right hand is 6 through 10. For the problem 9 x 2, he would bend down his second finger. The number of fingers to the left of the bent down finger is the number in the tens place and the number of fingers to the right of the bent finger is the ones place. Thus, 9 x 2 = one finger on the left and eight on the right or 18.
  5. Nines (adds to 9 method): Have your child subtract 1 from the number he is multiplying by. So, for 9 x 4, he would get 3, which he puts in the tens place. Now he sets up an addition problem to find out what adds to that to make nine, putting that in the ones place. 3 + 6 = 9 , so 9 x 4 = 36.
1 Source
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  1. Levenson E. Fifth-grade Students’ Use and Preferences for Mathematically and Practically Based Explanations. Educational Studies in Mathematics. 2009;73(2):121-142. doi:10.1007/s10649-009-9208-y

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