This is all you need to do:
$((COUNTER++))
Here's an excerpt from Learning the bash Shell, 3rd Edition, pp. 147, 148:
bash arithmetic expressions are equivalent to their counterparts in the Java and C languages.[9] Precedence and associativity are the same as in C. Table 6-2 shows the arithmetic operators that are supported. Although some of these are (or contain) special characters, there is no need to backslash-escape them, because they are within the $((...)) syntax.
..........................
The ++ and - operators are useful when you want to increment or decrement a value by one.[11] They work the same as in Java and C, e.g., value++ increments value by 1. This is called post-increment; there is also a pre-increment: ++value. The difference becomes evident with an example:
$ i=0
$ echo $i
0
$ echo $((i++))
0
$ echo $i
1
$ echo $((++i))
2
$ echo $i
2
See http://www.safaribooksonline.com/a/learning-the-bash/7572399/