There is a lot of cognitive science research confirming the point you're making. Cognitive scientists draw a major distinction between working memory and long-t

There is a lot of cognitive science research confirming the point you're making. Cognitive scientists draw a major distinction between working memory and long-term memory (there's also a third "sensory memory" that appears in the literature but isn't all that germane to learning math). In cognitive load theory, managing working memory is important to getting things into long-term memory, so if you have to do 6+6+...+6, that's going to eat up your working memory and you're less likely to be able to commit the more important thing you're trying to learn to long-term memory. There's a lot of published research on this. It is appealing to some educators to lean on 6+6+...+6 because it shows conceptual understanding, but counterintuitively students who don't make the jump to memorizing 6x7 or something close like 6*6+6 (cognitive scientists call this "fluency") end up having difficulty learning higher-order concepts because of the working memory bottleneck.