
A tough habit to break
From a very young age students are taught to add by using their fingers to count. This can be a very difficult habit to break and can be an impediment to developing good number sense later on.
Even when I ask students to sit on their hands to stop using their fingers to count, you can still see their little fingers moving under their legs! How do you get students to stop using their fingers and to start using their head?
Using objects and picture arrays are a great way to start. After that, using the simple number grids that follow will make it easy for students to learn their basic math facts, without using their fingers.
Learn These Six Relationships. The following number grid shows the addition facts for all numbers 1-10. By mastering the following six rules, a student has all of the tools necessary to calculate all but 8 addition math facts from 0-20.
- Any number +1
- Any number +10
- equations for the sum of 10 (i.e., 6+4, 7+3, etc.)
- doubles (2+2, 3+3, etc.)
- sums of 10 “plus or minus” 1
- doubles “plus or minus” 1
In the number grid below contains all addition math facts for the numbers 1-10. The ”+ 1″ and “+10″ are highlighted in tan:

Figure 1: +1, +10, doubles and sums that equal 10
Getting a student to understand that adding “1″ to any number will result in the next number in sequential order is an easy enough concept, as is adding “10″ to any number.
Thereafter, have students learn the equations for the sum of ten (the blue squares in figure 1), and then learning all doubles (the red squares in figure 1).
Playing games like MANGO’s Double Down, Cue and Azuki Addition are great, fun ways to learn these simple rules. With repeated play children should be able to memorize these math facts in the same manner they can identify a color or simple sight words.
Once they have those facts down, have students work on “sums of 10 + or – 1″ (the light blue squares in figure 2 below), and then “doubles + or – 1″ (the light red squares in figure 2 below):

Figure 2: multiples of 10 "plus or minus" 1; doubles "plus or minus" 1
For students struggling to memorize their math facts, these six shortcuts allow them to better understand and extrapolate the relationships that underlie these simple rules to come up with the correct answer, without resorting to their fingers.
Memorize these 8 math facts. Once these simple rules are learned a student only needs to memorize the following 8 math facts to know all of their addition facts from 0 to 20:
2 + 4 2 + 5 2 + 6
8 + 3 8 + 4 8 + 5 8 + 6
7 + 5
Teach Addition and Subtraction at the Same Time. Rather than teaching addition, then subtraction, I suggest teaching both at the same time. Learning addition and subtraction together helps show the relationships among the numbers involved, making it that much easier to memorize and learn. If a student knows that 6 + 6 = 12, then learning 12 – 6 = 6 at the same time creates a relationship among those numbers as well as the relationship between addition and subtraction that may not be grasped by learning them separately, and certainly not by finger-counting.
Do you have other good ideas for breaking the finger-counting habit? Let us know!