Tower Multiplication is a descriptive name for the conventional multiplica-tion algorithm. The word “tower” alludes to the stack of numbers that ends up above the problem. With a large multiplier, they “tower” over the problem.
The most error-prone step in Tower Multiplication is the adding part, like 45+6 in the example below (after figuring 9x7=63, putting down the 3 and “carrying” the 6), is not an addition fact. So what are elementary school students to do? They do what you may have done: count 46-47-48-49-50-51 and keep track of the counts on their fingers, by nodding their heads, or tapping their pencils, because the concentration that is required to add in one’s head is easily broken, leading to mistakes. Better is to write the addition problem off to the side as a separate problem (and then erase it to fake it). Better yet is to scrap Tower Multiplication and learn and instead where the addition is kept separate from the multiplication, written down, and, using for adding long columns of numbers, added all at once.