What is number sense? “Number sense is the ability to use and understand numbers” (http://www.mathsisfun.com/definitions/number-sense.html). In the article by Russell Gersten and David J. Chard, “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities” , (2001) the authors compare number sense to phonemic awareness. In order to understand how to read, a child needs to understand how sounds work together to make words. In math, students have to understand the attributes of numbers in order to become proficient problem solvers.
Here are some of the characteristics of number sense:
Fluidity-It is important for students to learn that numbers are flexible. 10 can be broken up to 8+2 or 14-4. This concept is used in Singapore Math to demonstrate how numbers can be broken apart in order to solve more complicated problems.
Meaning-Just as words have meaning so do numbers. Students, especially during early elementary school, need to be able to express numeric meaning through representation. This can be shown through manipulatives (dried beans, cubes, candy, etc.). The student should be able to show the meaning of 10 by counting out 10 cubes or drawing 10 circles.
Mental Math-Students who develop fluidity in math can begin to picture and manipulate numbers in their head. By conserving energy on math facts, the brain is able to spend more time on problem solving.
Strategies-The beauty of math is there is more than one way to solve a problem. As a student becomes more proficient in understanding the properties of numbers, they can spend more time on figuring ways to solve a problem. For example, a multiplication problem can be represented with pictures, through repeated addition, broken down into a smaller multiplication problem and added together, using a known to find an unknown, etc. What is important is for the student to see that math is pliable and there is not just one way to find an answer.
Recognizing Patterns-Math patterns occur everywhere in nature, such as the pattern on the outside of a pineapple or the nautilus shell. Finding patterns in math increases a students ability to solve problems more quickly and accurately. One example of a pattern in multiplication is the products of 9. The digits in the product, when added together, equal 9. For instance, 9×9=81. 8+1=9.
Recognizing Errors-A person with good number sense is able to recognize errors in problems. They understand that if the answer for a subtraction problem is greater than the number they started with then there is something wrong. The student is able to understand that 8 is greater than 6.
These skills can be incorporated in everyday activities. Whether it is cooking, shopping or playing a game, these concepts can be part of an informal home program that will make math learning fun. In my next post, I will go into some specific ideas that you can use.
If you would like to read the article cited in this blog, this link will take you there: