Oh please. I am so tired of uninformed people posting stuff like this! We have all seen kids who create "another way" to solve a problem that is not as efficient as another way. Again the point of solving problems by decomposition is partly to become efficient at computing, but another reason to do it is to build a robust understanding of numbers. The only problem I have with this example is the judgement of the US Standard Algorithm as "old fashioned", as it communicates a negative attitude toward a pretty slick way of calculating. And, saying "new way" (these terms were probably introduced by a well-meaning teacher, but misguided) also seems mislabeled, since the goal is not to do something new, but something smart. Impressively (and probably not understood by the everyday person), the representation describes a strategy related to the number line, which can become more and more efficient over time.
One more thing: I have seen teachers (again, well-intentioned, but misguided) interpret "use a numberline", or "decompose numbers", or "use addition to solve subtraction", as an entry point for showing kids a specific way to solve problems rather than letting kids analyze the numbers and make computing decisions and then discuss those decisions as a mathematical activity.
One more thing: I have seen teachers (again, well-intentioned, but misguided) interpret "use a numberline", or "decompose numbers", or "use addition to solve subtraction", as an entry point for showing kids a specific way to solve problems rather than letting kids analyze the numbers and make computing decisions and then discuss those decisions as a mathematical activity.
