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.
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).