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Sure. Many, many examples. For instance algebraic understanding of electricity and fluids flow is much more intuitive than the tensor calculus versions. In some cases, you need high powered pre-reqs to even do the proof. Also, in many cases, students don't need a proof. Do enlisted reactor operators need a tensor calculus and quantum mechanics and stat ...


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I would consider how intricate your homework is. For "drill", more of the advantage comes from solo trials. For "projects", collaboration may have an advantage, or at least less of a disadvantage.* I would also consider if there are ways to get some social interaction without full joint responsibility (half a loaf, quarter of a loaf). "Trade papers and ...


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I think a lot of the issue is the algebraic complexity. Having to write a lot, carry a lot of relationships, etc. It's just more work. Note, humans are far from computers in our ability to carry a lot of relations at one time. And many students are not as used to being drilled and working on writing a lot of expressions. We even routinely see "questions"...


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I think there are more like three (or even four) aspects of education here: A. Theoretical understanding (basis, range of applicability, exceptions, etc.) B. Motivation (why care, what's it good for, is it fun, will it make me money, etc.) C. The basic technique (what you do) D. Practice (we are not biological computes--we burn grooves in the brain with ...


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