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There are two ways to approach your question: with or without dualism. I will highlight the dualist approach since it is more salient. Keep in mind that I do not find this approach reasonable, and doubt my summary will do it justice. You might be interested in the concept of philosophical zombie, it is a modal argument against physicalism in the spirit of ...

I think "teaching of high-level strategies will allow students to use learned strategies across different domains" is the very rationale of mathematics. Math gives very good examples of both abstract strategies for solving problems across different domains and also specific, explicit strategies. You don't seem to want the abstract strategies, but if you ...