• # What is Math Fluency, and Why is it Important?

Let's first understand what fluency in mathematics IS NOT.  Math fluency is NOT speed and accuracy!  To this day, many people erronously cling to this definition, despite the fact that it is glaringly superficial and misdirected.  If these tenants were the only marks of a great mathematician, then a student who excelled in rote memorization, but had no idea why he was performing a certain calculation to solve a problem, could be classified as a pretty decent mathematician.

Don't get me wrong -- speed and accuracy are important in math.  (Otherwise, long division becomes a day-long task as students struggle to remember 6 x 7.)  However, the added piece to this definition can't be missed: math fluency is the ability to quickly and accurately complete calculations using a deep understanding of number sense.  If a student is mathematically fluent, it means that he can:

• Utilize flexibility in his thinking about a problem;
• Understand AND explain the methods he uses to solve; and

#### Bottom line: Math fluency is all about how a student THINKS about the problem.  Conceptual understanding comes first; speed and accuracy follow -- not the other way around.

For example, a student in fourth grade may give the correct answer to 7 + 9 in less than a second.  But, if questioned about what that student did to find the sum, would he say, "I know that I could take one away from the 7 and give to the 9 to make it 10.  Therefore, 10 + 6 equals 16."?  If so, that student DEFINITELY demonstrates math fluency.  He is able to think FLEXIBLY about the problem, EXPLAIN his thinking, and still give the answer ACCURATELY and QUICKLY.  This student understands place value, the rules of addition, the associative property, AND was able to synthesize all of that material in a matter of seconds.

This is precisely why the national math standards have taken a turn in the last few decades towards a deeper conceptual understanding, rather than just procedural knowledge -- and rightfully so!  Teachers are presenting math concepts differently to allow students to tackle problems in more ways than one; because even though the beauty of math is in the discrete nature of a right or wrong answer, the paths to get there may be very different!

So, with all that said, HOW do you teach your child to be fluent in math?  As with anything, it takes repeated exposure and continued practice.  A few tips:

• Don't over-emphasize memorizing facts, but also give your child an opportunity to look at basic computation through a new lense.
• Ask him if he can think of a different way to solve.