There has been a running debate on our campus about the importance of memorizing multiplication tables.
Pro:
- The state test doesn’t allow calculators, so students need to multiply without a calculator.
- It’s the math equivalent to English/Language Arts teachers’ alphabet: the building blocks necessary to accomplish bigger things.
- Automaticity increases performance on multi-step problems. If students have to stop to make “groups of” or count on their fingers, they lose track of their progress in a problem.
- Knowing the multiplication table improves pattern recognition.
- Knowing the multiplication table improves number sense.
Con:
- Wrote memorization = bad. Memorizing this list of facts is a low-level skill, when we should be emphasizing higher order thinking.
- Since many of our students still struggle (and likely will continue to struggle) with multiplication facts, we should find an alternative (such as writing down or being given a multiplication chart).
A blog entry from Jon McLoone looks at the question beyond this: If our students are living in a technology-rich world, how much of the “times table” is really useful?
As a child, I was expected to learn my times tables up to the 10s. Knowing your facts up to the 9s allowed you to accurately use the multiplication algorithm most of us are familiar with. And the 10s, well, that’s virtually trivial. I remember it was tough (and I still struggle with the 8s). However, those loooong days struggling with my mother over those tables have led me to a theory: very few people who know their times tables learned them at school. Most of us learned them at home, often drilling with a parent or sibling. The changing dynamic of the family is as important to this trend as changes in technology.
McLoone says he learned his multiplication facts up to the 12s. He always assumed it was because of Britain’s pre-decimal coinage where 12 pennies made up 1 shilling. This leads directly to Jon’s three reasons for knowing multiplication facts:
- To quickly solve small, everyday multiplication (and division) problems that we encounter. It would be nice to be able to skip the calculator when I need to know the total cost for 6 Happy Meals that are [approximately] $2 each.
- To use multiplication algorithms. When calculating multi-digit products without a calculator — either mentally or with paper — the common algorithms require us to multiply single digits by single digits. So we need to know our facts up to the 9s.
- Estimating products. When I need a rough answer to a large multiplication problem, I can decompose it into smaller problems.
McLoone uses a computer model to analyze this last reason, and concludes that the accuracy of our estimations don’t improve much once we get past memorizing the 7s.