Did you know there's a controversy about how children should learn basic math facts? Some say kids should learn addition and multiplication tables through repetitive drill. Others feel they will absorb this information by osmosis as they solve problems. And still others think the answer lies somewhere betwixt these two.
Here's the part everyone agrees on: all kids need to (eventually) learn basic addition and multiplication facts.
Math wars rage between progressives who favor "discovery learning" and "arithmetical fundamentalists" (don't you love that!) who see a good bit of value in repetition and, yes, drill."Fluency without Fear," argues for a deemphasis on memorization and drill:
While research shows that knowledge of math facts is important, Boaler said the best way for students to know math facts is by using them regularly and developing understanding of numerical relations. Memorization, speed and test pressure can be damaging, she added. (Learn Math Without Fear)Others disagree with this idea.
One critic of the [Canadian] government’s adoption of “discovery-based learning,” Ken Porteous, a retired engineering professor, put it bluntly: “There is nothing to discover. The tried and true methods of addition, subtraction, multiplication and division work just fine as they have for centuries. There is no benefit and in fact a huge downside to students being asked to discover other methods of performing these operations and picking the one which they like. This just leads to confusion which ultimately translates into frustration, a strong dislike for mathematics and a desire to drop out of any form of mathematics course at the earliest opportunity.” (Math Wars)
Which philosophy do I subscribe to? Both, actually. Of course I want my children to "develop understanding of numerical relations," and thus my young children spent a good bit of time in math play. Messing around with Cuisinaire rods, for example, helps develop a sense that 5+3=8 without hardly thinking about it. They just knew that a yellow rod and a light green one are the same length as a brown rod. And playing math games with preschoolers and primary aged children also goes a long way towards painless acquisition of math facts.
BUT - drill with triangle flashcards, wrap-ups, and Calculadder sheets, and even computer games was also an essential part of each one of my children's early math education.
Because no matter which approach you (or your child's school) takes, the reality is that by about fourth grade, children who don't have their facts mastered start falling behind. Counting on fingers may be just fine for first graders, but by the time kids are doing long-division, that won't cut it. And no, calculators aren't the answer. Kids need enough proficiency with arithmetic to determine if their calculators answers are even in the ballpark. (And did you know that calculators are banned from certain sections of college admission tests and even from a number of college math courses including many calc classes?)
Some kids absorb math facts very readily and need little drill. For others, learning the addition and multiplication tables is painful! I've had children who feel into both categories. Recently I've had questions from a couple of moms about what to do when a child struggles more than his peers.
So, as time allows, I'm planning to write about teaching math facts using teams (math families), tools, and tricks.
In the meanwhile, you might want to take a look at this article on the Living Math website.