Mathing Matters: Fighting the Fingers

Breaking the Finger Counting Habit

When learning addition and subtraction, many students resort to finger counting to answer problems. Two things are wrong with this scenario:

• they are counting on their fingers, and
• they very often get the wrong answer.

Here's what's going on:

When kids solve problems by finger counting, they aren't "holding" the numbers in their minds; they don't really have a mental grasp of the numbers. They write down the number they get from counting on their fingers but have no sense of whether their answer is right, wrong, reasonable, and/or unreasonable. They haven't been taught the "tricks" for learning and conceptualizing addition and subtraction facts and resort to finger counting as the only strategy available to them. 

What to do:

Finger counting is a habit. The best way to break a habit is to replace it with something else. We want to replace finger counting-based addition and subtraction with techniques and a solid understanding of number facts that will last a lifetime. 

Here is a structured process for learning addition and subtraction facts (as well as some examples) for you to use as you help your child solve addition and subtraction problems. Training your child to approach problems with these frameworks in place will give them context for solving addition and subtraction problems mentally, helping them kick the finger counting habit for good!

Addition:

Doubles

 5 + 5 = _______       9 + 9 = ________

Doubles plus one & Doubles minus one

5 + 6 = 5 + 5 + 1 = _________

8 + 7 = 8 + 8 – 1 = __________

Counting on (start at x and "count up" by y)

7 + 2 = __________ (start at 7 and "count up" by 2)

8 + 3 = __________

Breaking down numbers

6 + _______ = 9                     _________ + 7 = 11

How far apart are two numbers?

How far apart are 6 and 10? __________

How far is it from x up to y? 

How far is it from 9 up to 12?

Most importantly Combinations that make 10

8 + 2 = ________                     6 + 4 = _________

10 plus a number

10 + 7 = 17                     10 + 9 = 19

10 plus what number

10 + _______ = 16 (10 plus what number equals 16?)

10 + _______ = 19 (10 plus what number equals 19?)

Subtraction:

Subtraction has two aspects:

• the notion of "how much is left," and
• the idea of "how far apart are the two numbers" – how far is it from the smaller number up to the bigger number.

Use the notion of "how much is left" when the numbers are fairly far apart, and countdown. For example:

Think of 12 – 3 as "counting down" from 12 by 3.

Think of 11 – 1 as "counting down" from 11 by 1.

On the other hand, use the notion of "how far apart are the two numbers" when the numbers are fairly close to each other, and count up. For example:

Think of 12 – 9 as "how far is it from 9 up to 12."

You can break this down: 

How far is it from 9 up to 10? 1 

How far is it from 10 up to 12? 2

...and put the answers together: 1 + 2 = 3

Again:

Think of 15 – 8 as "how far is it from 8 up to 15."

You can break this down:

How far is it from 8 up to 10? 2

How far is it from 10 up to 15? 5

...and put the answers together: 2 + 5 = 7

While it may seem time consuming at first to approach problems in these ways, taking the time to understand these structures will make it much easier in the long run for your child to solve addition and subtraction problems mentally. Also, it's been said that it takes 21 days to break a habit. Even after teaching kids a better way to approach these problems, without extended practice and reinforcement, they may slip back into their old habits. Please keep this in mind as you work with your child to break the finger counting habit.

Rish Bhandari is the owner of Mathnasium – The Math Learning Center, located in Fairfax Corner. Year round, the center helps kids get caught up, keep up and get ahead while they develop confidence and a love for math. For more information call 703-625-MATH (6284) or consult the web site at www.mathnasium.com/fairfax.