John Van de Walle is one of my favorite authors of books on how to teach mathematics. Here is the front cover of one of his books.
Here are the Big Ideas from Chapter 6 "Strategies for Whole-Number Computation"
And some more information from a couple of pages later.
Here are examples of how a student might use an "invented strategy."
These are examples of how a second grader might do subtraction. Notice toward the bottom, the "Counting Up" strategies. Adults don't tend to think about counting up strategies, and they can be helpful. It might be easier for you to mentally compute the answer by counting up, rather than by subtracting. The goal is deep number understanding and flexibility with problem solving.
Second grade is a time for grappling with math ideas. As they make sense of math, they may not always get the right answer. Accuracy is important, don't get me wrong, and when we gain confidence with concepts there are times we make mistakes. Again, my goal is to have kids think and understand. They should be able to tell when they finish a problem whether the answer makes sense.
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