Division

I learned division a long long long time ago. So long ago, that I do not recall the exact manner or manners in which I was taught to divide. Whenever I need to divide something now, and do not have the use of a calculator I divide the same way as the example on the right. Seeing as I will be in a classroom in the near future. I will be the one teaching students to divide. In class, Professor Antozs demonstrated a different approach to long division, one that I was unfamiliar with. Instead of doing it the way we see here on the right, it involved taking out large groups of 1000's, 100's, 10's and singles. The division is an entirely new idea. I had difficulty at first rapping my head around it. I will illustrate an example.



As we can see in the example on the left, we are taking out large sums of numbers. Once we have taken out all of the numbers, we add them up to give us our final answer. Observing this at first, I was confused due to the increased number of steps, as well as the fact that there are now two columns. Once I looked at this process a little longer, and tried a few more examples, it became clear that this process works. It works very well!

Looking back, example number 2 does look more complex. However, when looking at step by step, it tends to be easier to follow. What I mean by this is you can see the steps and where the numbers are all coming from. In example 1, the numbers get pushed down without any real reasoning behind why?  Though we arrive at the proper answer, visually the second example leads us in each sequence without any crazy `just because` steps.

In conclusion, both systems work. They both serve well in coming up with the correct answers. The second example tends to be easier to understand. Yet if the children in your classroom can grasp example 1, there is no harm in learning that way too! As a result, I believe that opening up different learning avenues with regards to division is essential in the development of learning. I learned a new technique today. Had I been shown this process as a child there is a possibility that I may have done better in mathematics. All children differ in the way they learn. The 2nd example gives us as teachers some variety when trying to educate our students.