I think a lot of topics are much less sequential the further you go. As an adult I spend most of my time repeating the fundamentals of my field, and learning a topic deeply as needed. For children it probably makes sense to cram the multiplication tables.
Basically all undergrad stuff is fundamentals and "optimized cramming" (we call it bulimic learning, because you stuff knowledge into you just in time to throw it back up in the test) means tons of people "achieve" degrees without being even dimly aware of the existence of the fundamentals afterwards. If you have a bachelor's degree in e.g. computer science, the idea of encoding data shouldn't be an unknown unknown to you.
I would think that the opportunities to immediately "use" multiplication, instead of just practice it for tests, or some future numerate citizenship, would be omnipresent.
If you don't use something after you learned it, you miss out on:
1. Learning how it is actually applied
2. Discovering how the knowledge is useful for you personally, in ways you may not expect if you don't actually experience using it
3. Deeper understanding and mastery of the knowledge
4. Much much much better retention
It is worth creating some immediate use for new knowledge, even the smallest possible useful or creative project, for better retention alone.
> learning a topic deeply as needed
That is the ultimate use-driven learning model.
As for non-sequential, I agree. The more we manage our own learning, the more it is a directed graph (i.e. prerequisites translate to many follow up paths), and eventually just graphs (many ways to order topics, and alternate combinations of prerequisites for each topic, in any complex area).
To be clear, in the context of this article, the alternative to drilling multiplication until you've memorized it is to space out the learning over a period of time. It's probably good to study for the test, because next week we're learning PEMDAS, so you better be solid on your multiplication.
"these days"?
The goal is to memorize single digit products and use the multi-column algorithms when you need to do more digits. To which days are you referring where kids would be called upon to memorize multidigit multiplications?
In the 1980s I had a trapper keeper with a 12x12 table printed on it but even my seven year old ass knew back then that everything >10 was wasteful to memorize. :P
20 years ago my kid still had to learn up to 12x20. The 12s are pretty handy for a bunch of reasons, and especially if you live in the USA. Using base 10 for the metric system was a mistake.
