Sure. You can’t only drop literally only my comment on someone who has never seen this subject before. But in my experience, trying to explain the basics of 2-

Sure. You can’t only drop literally only my comment on someone who has never seen this subject before. But in my experience, trying to explain the basics of 2- and 3-dimensional geometric algebra to someone followed by explaining quaternion rotation results in a lot less confusion (and might even save time overall, while resulting in dramatically richer understanding) versus trying to explain quaternions qua quaternions. It’s also very helpful for people who have worked with quaternions before in code but previously treated them as a mysterious black box. If you explain how (multi)vector multiplication (Clifford product) works, then the behavior of quaternions can be clearly explained, and makes straight-forward geometrical sense. If you just dive into talking about quaternions, they seem entirely arbitrary and mystical. In neither case will the typical person be able to figure out what is going on instantly, without thinking about it for themselves. Disclaimer: the above is based on my pretty limited, anecdotal experience. I would be interested to see a study try teaching e.g. undergraduates using two different formalisms, and see which group comes out with better understanding after a semester.