This unit introduces you to the idea of “number sense” as an important outcome of arithmetic instruction in elementary school. Number sense helps students develop knowledge of both math facts and math ideas—long before they arrive in their first algebra class. It’s far more crucial now than in the past that they develop understandings about the connection between numbers and ideas.

In 1900 hardly anyone went to high school. That’s right—just about 11% of 14-17 year olds. The typical school experience for most people was a little bit of grade school, where math facts were beaten into everyone’s head. At around this time the teaching of arithmetic became standardized. And this way of teaching still influences how most people think arithmetic should be taught. It involves memorization of math facts, lots and lots of practice, and training in how to follow step-by-step instructions to get right answers.

In 2000, however, 95% of 14-17 year olds—that is, almost everyone in this age range—attended high school. These students—including those with disabilities—have the chance to learn more than arithmetic. They can learn algebra, geometry, trigonometry, and calculus (for instance).

The world today is very different from the world of 1900 in many other ways. In short we hope for more from students and we expect it in mathematics learning. This means that the way arithmetic is taught should be different from the way most of us actually experienced it in elementary school.  Memorizing math facts is less important than it once seemed to be.

Having instant recall of math facts is a good thing. But it’s not essential that everyone memorize the fact that 6 times 9 equals 54. Really. Number sense is the key.

With number sense, the point of arithmetic changes from beating the facts into students’ heads to getting them to use numbers well by thinking with numbers. Number sense includes facts but goes way beyond them. With number sense, we don’t grab a pencil or a calculator. Instead, we move things around a bit to make the calculation easy enough to do in our heads! In this way, thinking also applies to arithmetic—which so many people think of as the “drill-n-kill” memorization of math facts. In fact, simple math facts also contain powerful ideas!