One of the most important logical relations is between a generalisation and an example, as signalled by "e.g."; yet this little thinking-tool eludes a great many otherwise literate school leavers. Why?
Maybe it's because "e.g." is so small that it slips below the radar screens of all concerned - of pupils who just skip it in their reading, of teachers who assume that because it's short it's therefore easy to learn. Maybe it's because some English teachers frown on abbreviations of any kind, and the teachers of subjects like geography and science where abbreviations are 10 a penny are far too busy with the subject-matter to bother with general-purpose abbreviations like "e.g.".
But maybe it's because pupils aren't clear about the logical difference between identity and example. That would explain why the full phrase "for example" is almost as rare as "e.g."; and it would explain why pupils (and undergraduates) often use "i.e." when they mean "e.g.".
Whatever the reason, it matters. "The Head, i.e. Mr Jones" makes sense; "The Head, e.g. Mr Jones" does not. Conversely, "Some member of staff, i.e.
Mr Jones" doesn't make sense; but "Some member of staff, e.g. Mr Jones" does. If you write "A, i.e. B", then A and B are the same person or thing; but if you write "A, e.g. B", A is a general category (e.g. member of staff - notice our "e.g.") of which B is an example. This is not a difficult distinction to make once you pay attention to it, but it's one that is often ignored.
We think it may be helpful to break this area of teaching into three steps.
First make sure pupils can distinguish examples from identity using the verb "to be" and contrasts like this: "My friend is a footballer" (example) and "My friend is the best footballer" (identity). In the first case you can always slip in the word "example": "My friend is an example of a footballer", but this isn't possible in the second case: "My friend is an example of the best footballer."
Then make sure they understand the phrases "for example" and "that is", bearing in mind that these can introduce clauses as well as phrases: "We often win at football; for example, we won last week's match", compared with: "We won 10 out of 12 matches: that is, we only lost two matches."
Then move on to the abbreviations "e.g." and "i.e". Point out that the first two sounds of "example" are, very conveniently, e and g. (If you don't believe us, listen to yourself.) It's up to you to talk about the Latin origins and the punctuation. The most important thing is the meaning - the fundamental logical difference between identity and example. If that's not a thinking skill, nothing is.