I know it's been a while since this post was replied to, but does anyone mind if I do so? (This is more of a 'drive-by' reply, since I'm bored, and am waiting for my lunch to cook.)
Note: I am not a current teacher of language, but have been studying the basic functionality and identity of language, by myself, (especially in relation to its greater context, (communication/semiosis/semiotics), and further application as (modern) English), for the past 7 1/2 years, after noticing a basic problem, that was then confirmed by a teacher at a local university. (My findings/realisations have further been confirmed by a now-retired professor from Cambridge University (Neil Mercer.))
I cannot provide the entire context for my reply, here, for that would be far to great for such a reply, but this will hopefully start people thinking in a manner that is more consistent with how language truly functions.
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The basic problem with this perception and definition of grammar, is that it is far too general, and not consistent with the context in which language itself exists, (for what it is, separately and in addition to its subjective application), in order to help us understand exactly how and why any language functions and therefore exists, to begin with.
(There is another post in addition to this one that talks about the functions of language, that I will reply to aswell, that may be useful, too.)
One of the problems we currently have with language, is recognising its relationship with its greater context, especially communicating/communication itself, directly, and also semiosis/semiotics, indirectly.
Unfortunately, what this definition of grammar does, is deny the difference between semantics and syntactics in their relation to - as applied within and by - the functionality (and therefore identity) of language.
And the nature of such an application, (of additional rules and context), matters, for without which, there can be no difference between language and communication in general - at which point language ceases to exist.
For this reason, grammar only truly makes sense to describe the application of syntactics in the functionality of language, not semantics, for which we require another label - (i.e. content).
To perceive matters of semantics as and by (being) matters of syntactics, (or possibly even vice-versa), is the biggest problem such a definition and use of grammar IS causing - (or at least, helping to cause) - currently.
