First graders don't dabble too much in algorithms. I suppose the double digit addition algorithm might be taught in some first grade classrooms towards the end of the year, but I've never been one to teach it that way. In the past few years though, I've found that the quote above is true. I don't have to teach to specific problem solving strategies or even algorithms for that matter. When given the chance, kids can and do solve problems in ways that make sense to them. They surprise me with the solutions they come up with, but most importantly, they understand what they're doing and can teach each other as well. If math is supposed to make sense, then allowing each individual to solve challenging problems in a way that makes sense to them, well, kind of makes sense.
(By no means am I an expert, but I hear there's a place for algorithms in the upper elementary grades but only after the kids have first been allowed to explore and invent their own strategies. Once they have done so, the algorithms are more likely to make sense.)