I am going to explain more clearly why I think the teaching about can/could, and about modality generally, is currently inadequate. This is long, apologies, but there was confusion up thread - some of it mine. NB how these verbs are used is apparently still subject to debate at academic levels. In summary there used to be a lot more detail readily available and I will say why I think this matters in the next post.
How it is taught now:
Can/could appears to be taught at a very basic level across the board in, primarily, in its sense “to be able to”, and examples given are very basic such as “he can ride a bike” and “she could play the music easily”; it is taught that can is a defective verb and only really exists in the present tense, that could is used as the past tense and is itself a separate very basic one tense verb. They are referred to as “modal” with “modal” being the only explanation ie scant information about what modal means. It is stated in absolute terms that “could” is (not “can be”) the polite form of can. Most contemporary dictionary entries only say “modal” without more detail about meanings and without explanation of meaning of “modal”. There is confusion and incorrect information online.
In contrast, how it was taught in the 1980s:
The entry for can and could in my dictionary from the 1980s is as follows:
can transitive verb, verbal auxiliary. Meanings:
1(a) know how to (“he can read”);
1(b) be physically or mentally able to (“I can't think why”);
1(c) may perhaps, used chiefly in questions (“what can they want”);
1(d) be logically inferred or supposed to used chiefly in negatives (“he can hardly have meant that”);
(compare with must);
1(e) be permitted by conscience or feeling to (“can hardly blame him”);
1(f) be inherently able or designed to (“everything that money can buy”);
1(g) logically able to (“x can also be written y”);
1(h) be enabled by law, agreement, or custom to;
2 - have permission to, used interchangeably with may;
3 – will, used in questions with the force of a request (“can you hold on please”)
4 - will have to (“if you don't like it you can lump it”)
"Could": past of "can"; conditional of "can" (“he would if he could”); as alternative to "can" suggesting less force or certainty (“you could be right”); as an alternative to might; expressing purpose in the past (“I wrote it it down so that I could remember it”); as an alternative to ought or should (“you could at least apologise”); feel impelled to.
The entries for will and other modal verbs were equally detailed back in the 1980s.
In relation to modality the following came from grammar books and academic sources from the 1980s or around that time and NB this is still considered good authority today:
Auxiliary verbs are split into primary and secondary, the secondary being modal. To determine whether a verb is an auxiliary, or a “full” verb, the NICE test is used – negation, inversion, code and emphasis. Full verbs can also be picked up by an auxiliary for example “he might/he ought to/he can't/he needn't” where the meaning is the full verb. Re secondary modals there are different classes – "be" and "have" are in a different class to "do/will/shall/may" and "need/ought/dare/must" and when "dare" and "need" are complemented by "to" scholars regard them as full verbs. The form used to express present and past of the modal auxiliaries can also be used to express future time often with hypothetical or tentative meaning.
Modal verbs have a unique function and are essential linguistic devices, the insertion of which into an otherwise non-modal environment generally introduces a different understanding of the whole statement. Modality is the term used to relate to meanings that are usually associated with mood and the usual meanings covered by modals are ability, volition, permission, possibility, necessity, obligation, probability, futurity and intentions such as prediction, hypothesis, (quasi)subjunctive. This can be further categorised into intrinsic, where there is some kind of intrinsic human control over events, and extrinsic, where there is human judgement of what is or is not likely to happen.
Modality can be used to express the speaker's attitude to the truthfulness of a proposition, or about what is possible and what is necessary with respect to some authority or moral values, or to evaluate the occurrence of events or the existence of state of affairs as necessary, important, advisable, possible, desirable within a circumstantial frame of reference stated or not stated, or references to abilities or volition.
For each modal meaning there are one or more modal verbs available ie there is overlap. Can and may for permission, or could and might expressing possibility for example. Where there is overlap modals used can be interpreted with nuances depending on context and speaker so that obligations, inference and possibility are able to be expressed and understood, eg strong or weak obligation, or confident or tentative inference.
So there seems to be a big difference in how it is taught, but there have been no substantive changes in relation to grammar, just in relation to how it is represented and taught