Section 29.4 Closing Ideas
We have reached the end of the exploration of addition and subtraction. We have covered a variety of ways of thinking about those mathematical operations. Remember that the point is not that you need to use all of these ideas all of the time, but rather that having that diverse toolbox of ideas and approaches will give you more flexibility to solve problem you come across in the future.
Many students think of math as a set of rules that you need to follow, rather than a diverse set of concepts that are related to each other. That conceptual diversity in many ways reflects the diversity of students. Different students come to mathematics with different experiences and intuitions. Perhaps one student finds the movement diagrams easier to understand while another student thinks that blocks are easiest. It doesn't really matter that much. The goal is for students to come to their own experience of understanding of mathematical thinking and the diversity of approaches in the last several sections helps to reflect the diversity of perspectives that exist within mathematical reasoning.
We'll close this section with a very important note. If you find one way of looking at something to be difficult to understand, that's usually a signal to probe more deeply into it. It's not a signal that you should simply do something else. It is far better to take an intellectual posture that seeks to understand rather than seeks to not understand. Having a broader understanding of ideas only stands to benefit you. Maybe you will eventually understand it, or maybe not. But if you don't try, you definitely won't.