The following article is one I use on my class website. I think we underestimate the power of numbers and the ability of young elementary age students. Many parents do not understand what a number really is and how numbers can work together. I have had parents question my reasoning in spending so much time on number sense, fact families and basic fact skills. I share this article and discuss the reasoning behind why I do what I do. It is always an 'ah-ha' moment for them to realize how complicated our number system can be and how valuable having a deep understanding of numbers is at an early age. 'Playing' with numbers is an awesome way to learn many great and important things.

DON'T FORGET THE FACTS

Getting back to basics can pave the way for higher level learning.

Drilling children on basic math facts and administering timed tests seem to have gotten a bad rap. Increasingly, teachers are encouraged to move to a math curriculum rich with problem solving, manipulatives, and active learning. Yet, focusing on mastering math facts has an important place in children's math education.

Children are able to reason more quickly and flexibly when armed with the basic facts. Imagine having to relearn letter sounds and combinations each time you start to spell a word. Children experience something similar if they do not have basic addition, subtraction, multiplication, and division facts memorized as they progress to algebra and other higher-level math concepts. Stopping to multiply by counting or adding slows them down. Important math processes like estimation and mental computation are based on recall of math facts which can empower learners and give them confidence to be problem solvers.

To determine when students are ready to memorize math facts, you must closely monitor their understanding of the meaning behind addition and subtraction equations. Most children under the age of seven are still developing this understanding. Some second grade children are still developing the concept of equality, and the notion that addition and subtraction equations are logical inverses of each other. Once one knows that 6+4=10, then 10-4=6 is a logical reversal of the problem. Piaget called these "operations." Before children are operational in their thinking, it is important not to rush them into memorizing series of facts, which might force them to rely on rote memory instead of their emerging logical skills.

Giving children meaningful experiences using math facts in the earliest years of schooling lays a firm foundation for later mastery. Arranging, counting, and manipulating objects, as well as games and other engaging activities that use addition and subtraction, give children the chance to solve problems over and over. They then begin to grasp the consistency of the facts. For example, every time 6-year-old Samantha rolls double 4s on dice, she counts the dots and gets a sum of 8. Soon she figures out that she does not need to count the dots each time. Once she knows that 4 + 4 = 8, she can easily confront the problem 4 + 5. "That's one more than 4 plus 4," she reasons, "so it must be 9." She is building a solid knowledge base developed through repeated experiences and logical reasoning.

In third and fourth grade, as children progress into multiplication and division, they continue to build on what they already know. At first they may calculate the answers to multiplication problems, such as 3 x 6, by using repeated addition. As they develop an understanding and recognize that the two multipliers can be reversed leaving the answer the same, they gain the power to calculate the answer in a more efficient way.

At the point when children are advancing to multiplication and division, they need to have basic addition and subtraction facts under their belt for automatic recall. They need to know that 9 + 9 is always 18. They should easily be able to demonstrate the basic addition and subtraction facts using counters, fingers, or other examples, but should not need to check the answers using manipulatives.

By Sandra Waite-Stupiansky, Ph.D. & Nicolas G. Stupiansky, Ph.D.

Instructor-Primary; Sep98, Vol. 108 Issue 2, p82