My talk will involve a few topics that I have developed or considered in my experience of teaching. For BA students, it always seemed to me that teaching the "how" of linguistics and the "why" -- how we do what we do, and why -- was more important than the "what", that is, the details of any given particular framework or theoretical approach. This is not to deny that one needs a framework to demonstrate some hows and whys, but the framework itself is not necessarily the focal point of the pedagogical content.
One strand of my teaching has been to take basic analytical ideas and concepts from linguistics -- ideas from semiology in part -- and apply them to domains that are not purely linguistic. I will illustrate some of these basic ideas with regard to the analysis of the text and images of advertising. One can show students how to understand that there are structural components to an object like an advertisement, which to the unschooled mind would seem to be an essentially holistic entity (though clearly with "bits" in it, like words and images). With regard to advertisements, one can show students that it is possible to give some critical substance to initially uncritical intuitions like "I like it" or "This one looks lively" or "These words seem powerful".
The semiotic approach only goes so far, and does not really allow one to analyse advertisements at the emic level. Getting to the emic level is something that I have taken to be central to teaching linguistics -- showing students or other audiences how to find the underlying components of language, and their surface form(s) and organization(s). We typically also consider this part of the core of the "what" of linguistics -- if we don't get this far, we haven't really presented what linguistics is about. So what are our minimal goals? The goals that we have in teaching linguistics might include:
An appreciation of the kinds of regularities found in languages. (How to ask questions about language and appreciate why they have some intrinsic interest or significance.)
The value of a consistent and incremental approach to hypothesis generation and testing. (Thinking objectively and critically.)
An appreciation of linguistic diversity. (Broadening horizons beyond western European languages.)
Often we can introduce these topics through examples that are either known to the audience, or which they can easily pick up. I will illustrate with some simple examples from English and Japanese. Our examples need to have some resonance with the audience in order for them to understand the "why" of what we do.