What is Number Fluency?

  I am always hearing that students need to develop number fluency but what is meant by that?  Number fluency is another way of saying students need to develop number sense. 

Students need to develop number fluency in conjunction with conceptual understanding and computational fluency.  In other words, they need to understand the concept and be about to perform calculations fluidly.

According to one definition, number fluency means a student can compose and decompose numbers in a variety of ways, is able to see patterns in numbers, knows their basic mathematical facts fluently, is able to work fluently and quickly with numbers to solve problems,  and is able to work well with place value and with numbers.

People often wonder why number fluency is important.  Number fluency is the bridge between recognizing numbers and understanding how to solve problems.  A student with number fluency is able to look at the problem rather than focus on basic facts.  They are able to make connections with prior knowledge more easily than someone who has to focus on their calculations.

Too many of my students arrive in high school still skip counting on their fingers rather than knowing their multiplication by heart.  I realize there are calculators out there but if a student has not developed a sense of what the answer should be, they do not know if their answer is even close.  Too many of my students accept the answer from a calculator as the correct value rather than taking time to ask themselves if it is a reasonable answer.

Since almost every student has a mobile device with a calculator, they want to use it rather than trying to remember their multiplication and division facts.  If I allow the use of a calculator, I insist that two students work together and each one run the numbers.  This way if they disagree, they can try to figure out who put the numbers in incorrectly.  This way, I hope it helps them build a sense of the way numbers work.

When it comes to fractions, the first thing they want to do is change the fractions into decimals because they find decimals so much more comfortable to work with.  Unfortunately, there are certain fractions that when changed into decimals become repeating numbers and rounding the value does not help.

Once thing I love to do is to have students analyze problems during warm-up to determine if they are correct or incorrect.  If they are incorrect, students have to determine what the error is and when it occurred during the calculation.  This makes students slow down and think so at least they are developing more of a number sense than what they arrive with in high school.

Let me know what you think.  I'd love to hear.