Section 25.4 Closing Ideas
Addition is the very first arithmetic operation that children learn. The idea of putting collections of objects together into a single collection fits perfectly with the idea of counting. But as the collections of objects become larger, we are forced to find different ways to organize that information, and that's where many of the concepts we have for numbers come from. It's all about organizing information in a useful way.
Once we have the framework in place, we can then move on to see how the organization is helpful. As we discussed earlier, adding in columns used to be an important organizational framework when all of these calculations were done by hand. And it is that framework that leads us to ideas like "carrying the one." In today's world, that specific way of organizing information is less useful. This doesn't mean that it's wrong or that it can't still be used. But we are seeing that there is more value in helping students develop flexible ways of thinking rather than focusing on computational algorithms.
Being able to think about numbers in different bases is important if you are interested in learning more about how computers work, especially if you want to get into programming. Being able to work in the framework of the number line helps with any job that uses geometric ideas, including many forms of design. And those are the reasons why we're taking the time to explore these concepts here. Even though we've been discussing addition, we're really just building a framework to help you work with numbers in whatever context you will see them in the future.
As we continue to explore mathematical thinking, it will be helpful to take time to reflect on the new ways of looking at math that you're seeing. A lot of students struggle with their confidence when it comes to math, and that's usually the result of being told that there is only one way of doing things that doesn't really connect with them. That is an unfortunate legacy of the current math education system. But it's never too late to start something new. Hopefully, the approaches that you see in the coming sections will provide you with an opportunity to overturn past negative experiences and help you to see both the logic and the beauty of mathematics.