1 Through 10, With Fingers You Can!

Fingers are useful for so many things as a human, but there has been great debate over many years whether they should be used to teach and learn math. Some of us may have grown up with parents and teachers who encouraged the use of fingers for learning math, while others were scolded for it, but we’re here to tell you that for young kids first learning to count, add and subtract, fingers a great tool. Most neuroscientists and educators these days believe that children who use their fingers as math tools during their early years of learning math will have more success with math later on vs. those who don’t ever use their fingers. Let's then explore more about finger counting.

Benefits

1. A visual tool that is literally attached to us all and therefore always available.
2. Increased numerical understand, including counting, subtraction and addition.
3. Increased numerical retention and memorization.
4. Understanding conceptually of numbers and quantities in smaller units, like 3+3=6

Counting, Addition and Subtraction Up to 10

This is probably the most obvious way to count using fingers, but most of us have 10 fingers – 5 on each hand. Counting up to 10 is then the simplest form of math using fingers. 

Counting, Addition and Subtraction Up to 30

Counting up to 30 can be done using each section of a finger that bends at the joint.  For instance, if you look at your index finger, there are 3 sections on it divided by creases. Using these 3 sections on each finger, one can count to 30.

Counting, Addition and Subtraction Up to 99

This is a method known as Chisenbop Counting. If you put your hands on the table and palms down with your thumbs toward each other, like you would if you were about to play a piano, the fingers on your right hand represent 1 and your thumb represents 5. The fingers on your left hand represent 10s. and your thumb represents 50. With that memorization, you can get to 99.

Counting, Addition and Subtraction Up to 10,000,000,000 

There is an old Chinese method that allows counting up to 100,000 on one hand and up to 10,000,000,000 on both hands. This method is very different than using each finger to represent one unit and require special training. Typically educators don’t teach this or the Chisenbop method when they are referring to finger counting. They’re more referring to finger counting with each finger representing 1. 

Is there a Limit to 1 Unit Finger Counting?

Finger counting is a great tool for thinking in single units with quantities under 10. It can be used for counting and addition and subtraction, but it would be very hard and timely to do more difficult calculations with it such as 2,457x19 using just units of 1. Perhaps it would be different if we had 2,000 fingers! 

Like with most tools, there is a time and place where finger counting is useful and appropriate. When kids are still learning how to count and the very basic fundamentals of addition and subtraction, fingers are great. Once a child has mastered these basic skills, new tools can and should be introduced to help them upgrade to new levels of comprehension. Unless they are going to try and learn Chisenbop or another more complex tool for finger counting, they will need a bit more than finger counting for later math mastery and comprehension. 

Moving Past 1 Unit Finger Counting

The movement to not use finger counting is founded in the belief that it doesn’t create a space for people to think outside of one-by-one calculations. One-by-one calculating is very prone to errors and takes a long time. It’s much more efficient to calculate by using numerical relationships and logic which is why people who are very strong at mental math then usually don’t operate by doing 1 unit counting. If a kid is still using finger counting in 3^rdgrade and beyond, it’s time to introduce them to more efficient ways of thinking about math. Ask the student to solve 100 – 21 and watch them try and solve it:

1. If the student counts backwards from 100, they likely haven’t developed good number sense and numerical fluency, which means they’re still calculating using a one-by-one method. Whether they are still using their fingers or not to do this, they need help. This would be a good time to intervene by coming into Mathnasium of Parker. Building number sense and numerical fluency is super important for their relationship with math through secondary school and beyond. 
2. If the student counts 100 – 20 and then uses their fingers to count 1 backward from 20, they are at least starting to think by the 10s or 20s – in larger increments. Still, they are still using their fingers for a piece of it. They then do most of the work mentally, but they give up and do the hardest part with a crutch. Kids who can do this should be introduced to more efficiency. Because they have done most of the work mentally, they will likely pick up on other ways of being more mental math confident, if introduced and if they practice. 
3. If the student thinks of if as 100 – 25 is 75 and then 4 more after 75 is 79 and puts up 4 fingers, they are thinking about math in much larger pieces and using subtraction and addition. You may want to encourage them to try and not use the 4 fingers, because if they can think that large picture, they don’t need them. The fingers at that point are not holding them back mentally. 

In the end, the concept of basic finger counting can and should be implemented, especially in grades K-2. When young students are given calculators to solve their math problems too soon, they don’t learn the basics of math. Using visual tools such as fingers can help young students get a grasp on math which will then help them achieve higher levels of success later on.