This is in contrast to doing operations on either the "types" or the "effects" that are happening during code. So, you have to show people what are the equivalent of + and * in types and effects to show them how these can be thought of algebraically.

I still think this would be easier if a type system was made that let you use + and * in defining something. It would give an obvious path to seeing how things relate to algebra. Would almost certainly make some things harder, of course. Maybe it would be a good worksheet asking questions about stuff?

The big underline, though, is getting people to realize what algebra there is is not on the values that your code represents. It is treating something else as the value for the algebra.

While I like the above blog post, I don't think that it will be very useful to people trying to understand algebraic effects. I see a lot of explainers like this one that shy away from some of the more gnarly-looking maths terms in an effort to appear more approachable, but as a result they can end up giving imprecise or vague definitions. When coupled with some subtle mistakes I think it can leave beginners more confused than helped (for instance, this author seems to conflate a few different notions of "composition", and they seem to think that the presence of equations makes an effect algebraic, which isn't really what the term "algebraic" is referring to in a technical sense).

The paper I linked above is not easy, and it would probably take at least a few hours to understand, but that's because it takes about that long to understand the material.