Do you remember how you first learned how to count? Like most, it was likely using your fingers, and maybe your toes too.
Counting using your fingers as manipulatives (which are physical objects used to teach math concepts), is an excellent approach when a child is young, to help master addition and subtraction, especially when working with small numbers.
Today many children still heavily rely on counting on their fingers as they move up through school. This is a serious issue because it stifles their mathematical development by keeping them in the ridged headspace of one-by-one counting. As their math learning advances, this computation technique becomes ineffective, inaccurate, tiresome, and also embarrassing at higher grade levels.
How do children get past counting on fingers and toes?
By developing numerical fluency, which is a student’s ability to recall basic number facts, both mentally and effortlessly through developing frameworks for learning. With numerical fluency, students gain a broader understanding of the relationships between numbers and how numbers work. Achieving numerical fluency is also a crucial step on the journey towards developing solid number sense, which is a logical and intuitive understanding of how numbers work.
When a student gets past counting on their fingers and toes, their confidence with counting (and numbers in general) soars, growing exponentially, and they develop the ability to handle larger numbers effortlessly.
Let’s take a look at some examples of numerical fluency in action together.
Example 1: 9 + 8
A student who counts one-by-one will try to solve this by figuring out “9 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ 1.” By comparison, a student with numerical fluency solves this example mentally by working with a much friendlier number, which in this case is 10:
9 + 1 = 10
10 + 7 = 17
Example 2: 6 + 8
Instead of thinking, “6 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1,” a numerically fluent student sees that 8 is two more than 6, and can default to the strategy of doubling 6 and adding 2:
6 + 6 = 12
12 + 2 = 14
Example 3: 13 – 7
In this math problem, the number 10, comes in handy, like it did in the first example. How far apart are 13 and 7? Well, 7 is 3 away from 10 and 13 is 3 away from 10. By adding the differences together (3 + 3) you get the correct answer, 6. This is far more efficient than thinking, “13 – 1 – 1 – 1 – 1 – 1 – 1 – 1”.
Over time, as their numerical fluency builds, students will quickly discover that the number 10 is their best friend. They will also say goodbye to basic addition and subtraction practice and find it easier to tackle more complex operations like multiplication and division.
Building numerical fluency does not happen overnight (no matter how hard you try or wish it would). It requires consistent and steady practice working with these frameworks over time. This hard work comes with ongoing rewards as all throughout the learning journey, students will continuously reap the benefits of becoming stronger, more nimble mathematical thinkers and problem solvers…and they will retain this long after they close their school math books.
Mathnasium of Newmarket specializes in helping students learn and develop numerical fluency and number sense. We offer personalized math tutoring and math learning programs custom designed to help children in grade 1 to 12 develop numerical fluency.
Contact our Newmarket math learning centre today to learn more and to schedule your free trial math tutoring session.
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