Generally, there is a best way to solve a math problem. Math is a lot of rules. It is always important to get the answer exactly right. It is bad to count on your fingers. Math is confusing and difficult to remember.
Good mathematicians solve problems quickly.
It doesn't matter how students solve problems as long as they get the right answer. Math requires a good memory. Math is done by working intensely until the problem is solved. Hands-on manipulatives are rarely necessary after the third grade.