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 the focus of math teaching. At around this time arithmetic teaching became standardized. And this way of teaching still influences how most people think arithmetic should be taught. It involves a focus on procedural learning.
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 arithmetic and use that arithmetic knowledge to go beyond it. 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 experienced it in elementary school.
Effective arithmetic instruction
requires a focus on both the learning of concepts and procedures.
Having instant recall of math facts is a good thing. But it’s also important to understand what multiplication means and how there might be different ways to multiply. For this, number sense is the key.1. Practice Math Facts
1. Practice Math Facts Flashcards for Mastering Number Combinations… 3+4, 7X8…
2. Teach and practice counting strategies when kids don’t know number combinations such as counting up, counting back…
3. Have students chart progress on how well they did on number combination solutions.
4. Practice writing combinations and answers on paper to go beyond oral reading of facts.
Powell SR, Fuchs LS, Fuchs D. Number Combinations Remediation for Students with Mathematics Difficulty. Perspect Lang Lit. 2011 Spring;37(2):11-16. PMID: 23139846; PMCID: PMC3490633.
Doubles Plus 1
Adding two numbers that are close to each other (3+4), you can recall the doubles fact (3+3 +1) to get the answer.
Make sure kids get immediate feedback!
This can come from their teacher, a manipulative that shows answers or a computer program that quickly gives results.
Help kids see their personal growth by filling in a Math Fact tracker!
With number sense, the point of arithmetic changes from memorizing procedures to getting them to use numbers well by thinking with numbers. Number sense includes math facts but goes way beyond them. With number sense, we don’t immediately grab a pencil or a calculator. Instead, we move things around a bit to make the calculation easy enough to do with tools, such as manipulative or drawings or 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!