- Number Sense: an awareness that number and quantity have relationships
- Teachers can't "teach" number sense; it must be developed. Number sense develops gradually as a result of exploring numbers and repeated practice with numbers. In order for a child to truly understand a concept, they must experience that concept in a variety of ways. Number sense is learned informally and formally.
- In other words, number sense typically comes as a by-product of learning rather than through direct instruction. Research has shown that mathematical classroom routines and hands-on games build a strong foundation of number sense.
The National Council for Teaching Mathematics defines number sense as "moving from the initial development of basic counting techniques to more sophisticated understanding of the size of numbers, number relationships, patterns, operations, and place value."
Gersten and Chard define number sense as "a child's fluidity and flexibility in using and manipulating numbers, an almost intuitive sense of what numbers mean, and an ability to perform mental mathematics and look at the world and make what, in essence, boils down to quantitative comparisons without difficulty."
Number sense reliably predicts mathematics achievement. In fact, performance and development of number sense in Kindergarten more accurately predicts first grade math performance than any other factor tested. Students with strong number sense possess the following:
1. A sense of what numbers mean.
2. An ability to look at the world in quantities.
3. An ability to compare quantities.
4. An ability to be flexible, automatic, and fluent with numbers.
5. Ability to perform mental math.
6. Ability to be flexible with problems.
7. Ability to be automatic with math information.
8. An ability to determine reasonableness of an answer.
9. An ability to decide on a strategy depending on the numbers given.
Students with a strong number sense will look at mathematics as a form of reaching understandings...rather than just looking at math as a set of rules to follow. -Shumway
They learn:
-to use #'s in meaningful ways (they are not focused solely on getting the correct answer).
-to tell when an answer is reasonable or not
-to see relationships among #'s
1. A sense of what numbers mean.
2. An ability to look at the world in quantities.
3. An ability to compare quantities.
4. An ability to be flexible, automatic, and fluent with numbers.
5. Ability to perform mental math.
6. Ability to be flexible with problems.
7. Ability to be automatic with math information.
8. An ability to determine reasonableness of an answer.
9. An ability to decide on a strategy depending on the numbers given.
Students with a strong number sense will look at mathematics as a form of reaching understandings...rather than just looking at math as a set of rules to follow. -Shumway
They learn:
-to use #'s in meaningful ways (they are not focused solely on getting the correct answer).
-to tell when an answer is reasonable or not
-to see relationships among #'s
In a number sense rich classroom you will hear the teacher asking students to answer questions like these;
What do you notice?
What do you think? Why?
What might come next?
What do you predict will happen?
How did you figure it out?
Does anyone have a different answer?
Does anyone have a different way to solve this problem?
Can you convince us?
To develop number sense
- understand number symbols, vocabulary, and meaning
- subitize
- compose and decompose numbers (represent numbers differently)
- learn the importance of 5 and 10
- realize that rote counting is not a race, look for patterns (especially over 20, "twenty"one, "twenty" two)
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