An algorithm (according to wikipedia) is a step-by-step procedure for doing calculations. Most of us have spent hours practicing them in procedures like adding decimals, doing multi-digit multiplication or long division. The problem with algorithms is the fact that the step-by-step procedure is nothing more than a set of rules, and a person does not have to understand the mathematics behind the procedure to follow the instructions. I wrote about this idea last month in the post titled “Place Value not Face Value”. Until students really understand the concepts, it is not a good idea to practice what does not make sense to them.
I won’t rewrite all my views here, but I do want to add a link to a video that drives home this point. You may have seen this Ma and Pa Kettle math clip before, but it is worth watching again.
We need students to be really thinking about mathematics and what the numbers really mean.