Number fluency is a critical key to student success in math. Let’s break it down, so we know what we are trying to help students develop.
Earlier this year, I spoke about this topic on Instagram. You can see the replay below.
Number fluency begins with number sense. Number sense starts early. It is a person’s understanding of numbers. It is the ability to imagine 5 objects when you see the number 5. It is also the ability to actually see 5 objects and know there are 5 without counting them one by one. It is an understanding of the value of numbers. Number sense is developed by counting and becoming familiar with numbers at an early age.
Number sense should increase as students get older. By middle school, students should have the number sense to compare numbers and know how numbers will be affected by operations. Number sense does not involve following procedures and steps. Number sense is the understanding and reasoning students need to make sense of math.
As students learn more and more math, that number sense develops into number fluency. Being fluent in math means a student can mentally use operations, apply procedures appropriately, problem solve, manipulate numbers, estimate, and think creatively with numbers.
Although procedures are often noted as an indicator of number fluency, simply following procedures is not what is important. The understanding of concepts and reasoning behind those procedures should be emphasized to truly build number fluency.
Helping students learn strategies as they build number fluency will help students retain math facts. Without number sense and fluency, math facts are difficult to learn. Memorization without meaning does not result in long term memory of math facts.
Math facts are not a succinct list. Math facts could go on forever, and depending on whom you ask, you may be told different math facts are the most important. In elementary school, we expect students to add, subtract, and multiply some numbers mentally. Those are math facts. In middle school, we expect them to know factors, multiples, integer operations, and division. If we made a list of all the “math facts” a student should know, the list would be overwhelming.
Many middle and high school students do not know their math facts, which makes learning upper level math extremely difficult and frustrating. As much as many teachers would like to have a growth mindset, it seems hopeless for these students. Strategies to help these students often involve memorization and redundant drills (often with poor results).
Let’s try a better approach. First of all, we cannot write these middle and high schoolers off as just “not math people.” People who lack number fluency (in my experience), simply have not been given the time and strategies to develop it. Not knowing math facts is a symptom of this problem.
When secondary students develop number sense and number fluency, math begins to make sense and become enjoyable.
One way to develop fluency is to teach students mental math strategies. When students get creative and flexible with numbers, their understanding and comfort with numbers increases. Just 5-10 minutes a day can make a big impact.
Try these mental math lessons with your students for free!
Or, find the whole year of powerpoints with visuals here: