Arithmetic is the gateway to algebra, Weekend Edition Math Guy Keith Devlin says.
The Way We Used To Multiply
The old way to multiply required a student to add the products of 36 x 4 and 36 x 2. The trick is to add that 0 at the end of the second product.
Your fifth-grader asks you for help with the day's math homework. The assignment: Create a "stem-and-leaf" plot of the birthdays of each student in the class and use it to determine if one month has more birthdays than the rest, and if so, which month? Do you:
a) Stare blankly
b) Google "stem-and-leaf plot"
c) Say, "Why do you need to know that?"
d) Shrug and say, "I must have been sick the day they taught that in math class."
If you're a parent of a certain age, your kids' homework can be confounding. Blame it on changes in the way children are taught math nowadays — which can make you feel like you're not very good with numbers.
Well, our math guy, Keith Devlin, who is very good at math, tells Weekend Edition Saturday host Scott Simon that there's a reason elementary schools are teaching arithmetic in a new way.
How Kids Learn To Multiply Now
These days, students add four products to get the answer.
"That's largely to reflect the different needs of society," he says. "No one ever in their real life anymore needs to — and in most cases never does — do the calculations themselves."
Computers do arithmetic for us, Devlin says, but making computers do the things we want them to do requires algebraic thinking. For instance, take a computer spreadsheet. The computer does all the calculations for you automatically. But you have to write the macros that tell it what calculations to do — and that is algebraic thinking.
"You cannot become good at algebra without a mastery of arithmetic," Devlin says, "but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers.
That doesn't mean that kids can skip learning their multiplications tables. "But the way it's taught now is you get to the multiplication tables by understanding the number system and understanding what numbers mean," Devlin says.
If it sounds too complex for adults, let alone 7-year-olds, you're not the only one scratching your head. A friend of Devlin's once said, "There's nothing elementary about elementary mathematics education."
"And boy, is that correct," Devlin says. "Teachers have a very difficult task, and the task they have now is even more difficult, because in previous generations they could assume that in many cases the parents could help."