The basis for TouchMath is that each digit has "TouchPoints" on it. Usually, the TouchPoints are marked with circles or dots. The number one has a single point in the center of the digit. The number two has a point at the left end of the curve and another at the right end of the tail. Each number has a specific pattern of TouchPoints.
Students learn to count by touching every point on each number and reciting the value aloud. Counting to three sounds like "One. One,Two. One, Two, Three." as the student touches each point on all three digits.
Once the students have mastered counting, they are ready to begin using the system for addition and subtraction. Addition is done by counting forward on the TouchPoints and subtraction by counting backward. Multiplication and division can also be taught using TouchMath. Word problems are frequently illustrated by changing the points to images from the word problem. As an example, a word problem about apples would use apples on the TouchPoints instead of the standard circles and dots.
The benefit of the TouchPoints over students counting on their fingers is the pattern associated with each digit. The points on a three don't have anything in common with those on a four. When one counts on his fingers there is no way to create a unique pattern for each digit.