I believe that understanding should come before memorization. Students should develop a foundation of skills and strategies associated with multiplication before memorizing facts. I remember being in third grade and memorizing my facts because that was the expectation. I cannot tell you when I truly understood that multiplication represented repeated groups.
I work with students to understand multiplication by first relating it to skip counting (1s, 2s, 5s, and 10s) and then repeated addition. These are helpful strategies for solving multiplication. We then move to understanding concrete representations of multiplication as repeated groups by using hands-on materials. After using these concrete representations, we move to more abstract models by drawing pictures and using symbols. Soon, we begin to develop an understanding of multiplication. We move to looking at how multiplication and division are related.
So, what can you do at home to help foster an understanding of multiplication? Involve your child in helping out around the house. For example, if you are setting the table for dinner, ask your child if there are 8 people attending dinner and each person will have 2 pieces of silverware, how many pieces of silverware will be on the table? Or, use money to help. I have 6 dimes. How much money do I have? I like to tie real life problems back to the equation it represents. Six dimes would be represented by 6 x 10 = 60 cents. Tying in these real life scenarios helps students see the real-life usefulness of multiplication and helps them develop a deeper understanding.
Rote memorization can start once students are able to explain what a multiplication equation represents. For example, 2 x 5 means 2 groups of 5 or 5 + 5 or 2 + 2 + 2 + 2 +2 or 5 groups of 2. Below are some great resources for building fact fluency.
Please let me know if you use one of these resources at home and find them useful. Also, let me know if you want even more information.