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News from Mathnasium of Stapleton

Safe Hands: Finger Counting Dos and Don’ts

Jun 20, 2019

Fingers are useful for so many things in life… especially math! Despite that there has been lots of negative editorial about the use of fingers for kids learning how to do math, we’re here to tell you that it is perfectly acceptable for young kids first learning to count, add and subtract to use their fingers as tools. Using visual representations for teaching math is something that’s been recognized as useful – especially for kids who are visual learners. Schools have adopted many different ways to visually teach kids over the years. Fingers are then just built in visual tools to help kids learn. 

Math is a subject that can give kids trouble and start a long path of lack of self-confidence. Allowing students to use fingers when they are first learning the basics encourages them to pick up the concept of counting, while some cultures even use it for very advanced math concepts. Let’s explore some of the tangible ways that fingers can help with math and how to appropriately use them.

  1. A visual tool that attached and is always available.
  2. Increased numerical retention and memorization. 
  3. Increased numerical understanding, including counting, subtraction and addition. 
  4. Understanding conceptually of numbers in smaller units, like 2+5=7
Counting + Addition + Subtraction Up to 10

This the most obvious way to count using fingers and most used in US culture. Most of us have 10 fingers, 5 on each hand. Count all of the fingers on one hand and then all the fingers on the other hand and you have 10.

Counting + Addition + Subtraction Up to 30

As mentioned above, most of us have 10 fingers. Each of those fingers has 2 places where the finger bends at joints, leaving 3 “sections” of finger. Counting up to 30 can then be done using each section of a finger. For example, if you look at your pinky finger and bend it, notice where it bends twice, almost into a 3 sided square, if you bend it far enough. Those 3 sides of the square are the sections you can count on each finger.

Counting + Addition + Subtraction Up to 99

Counting beyond 30 using fingers is known as the Chisenbop method. If you put your hands on a table down with your thumbs toward each other, like you were about to type, the fingers on your right hand represent increments of 1 and your right thumb represents 5. The finger on your left hand represent increments of 10 and your thumb represents 50. Memorizing this can help you count to 99 using addition.

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

There is an old Chinese method for using fingers that allows counting up to 100,000 on one hand and up to 10,000,000,000 on both hands. This method is pretty sophisticated and is different than using each finger or section of finger to represent one unit. It requires special training and most educators in the states aren’t referring to this method when they’re talking about finger counting. They’re more referring to counting with each finger representing a unit of 1.

Should there be a limit to 1 Unit Finger Counting? 

Finger counting the way we think of it – 1 unit as a time – is a great tool for thinking in single digit counting with sums and quantities under 10. It can be good for beginning addition and subtraction as a way to visually help kids see things appear and disappear. However, it would be really hard and timely to do more difficult calculations such as 3,769x13 using just units of 1.

Moving Past 1 Unit Finger Counting

One-by-one calculating is very prone to errors and takes a long time, which why thinking outside of one-by-one should be encouraged. It’s much more efficient to calculate large sums by using numerical relationships and patterns, which is why people who can do math mentally don’t do so by 1 unit counting. If a child is still using finger counting past 2nd grade, it’s time to work on more efficient ways of thinking about math. To find out where they are, ask a student to solve 100 – 17 and watch them solve it. 

If the student counts backwards from 100, they are still calculating using a one-by-one method. Whether they are using their fingers or not, they likely haven’t developed much number sense and numerical fluency yet and they need help if they are beyond 2ndgrade. This is where we come in at Mathnasium of Stapleton! Building number sense and numerical fluency is our specialty and honestly, it’s important to get them help for their future relationship with math. 

If the student counts 100 – 15 in their head and then uses their fingers to count 2 backwards from 15, they are at least starting to think by the 5s or 10s – in larger increments. Using their fingers for just a piece of it tells you that they likely have the skillset to be able to count without their fingers, they’re just using them for support. This is a perfect point to introduce more efficient methods to them. Because they have done most of the work mentally, they will likely find it helpful to have other ways of mentally doing math with their fingers. 

If the student thinks of it as 100 – 10 is 90 and then 3 more after 90 is 93 and puts up 3 fingers, they are thinking about math in much larger pieces, which is good. Encouraging them to try and not use the 3 fingers is good in this instance, because if they are thinking about numbers in this way, their number sense and ability to do mental math is where it should be. 

In the end, the concept of finger counting can be really useful and beneficial for grades K-2. It certainly should be encouraged over calculators. When young students are given calculators to solve their math problems too soon, they skip the basics of math and don’t always have a grasp of why they’re typing in numbers to make other number appear. Using visual tools such as fingers can help young students get a grasp on basic math concepts and those concepts will help them build on and achieve higher levels of success in math later on.