There are four methods of division that we teach the students. In the new math the idea is to have them understand what they are doing with division, not just teach them one set way of approaching a task. When a student understands what division is they can then choose any of the four methods that would work for a specific division task. Having 4 ways to approach the question is like picking the best tool to solve a problem, instead of using one tool for every task. The problem directs the method rather then a student simply following a set form without understanding.
A) traditional way of doing long division
The downfalls of the Long division method are:
-it take up too much space on a page
-the students when they bring down a number loose sight of the original number leading to errors
-if the student is not neat and does not keep the numbers lined up well it will lead to errors
-with all those steps using a calculator seems like a way better option but what to do with all those extra numbers.
B) The way taught in France is simple but the students have to be able to subtract and multiply well in their heads. It works well for students great at math who do not want to go through all the steps of writing out the question in long division.
C) Like long division but with less chance of making mistakes due to not keeping the numbers lined up. It resembles long division but is less spread out.
One of the main problems in teaching division is that once students learn one way they do not want to learn another.
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