So, I’m looking at http://www.oercommons.org/courses/analyzing-word-problems-involving-multiplication/view and realizing that this is exactly the kind of lesson where automaticity can make or break the experience for the student.
If we’ve really, thoroughly explored parts and wholes in addition and subtraction, and students are basically automatic at recognizing when that’s happening and how to tell the difference between the two, then making the leap to apply that idea to multiplication will … still be a challenge, but be far more likely to make sense, and students might just have a chance of being able to figure out a mixture of adding & subtracting & multiplying.
It also reminded me of what it’s like when a student is starting to get that automaticity. It’s so much like music. Once you know the mechanics, often it’s not until *then* that you can start getting musical with it. Now, you have music in mind from the start (unlike too much so-called math), but you spend time getting the mechanics down.